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# A Comprehensive Survey on Imbalanced Regression: Definitions, Solutions, and Future Directions

Samuel Stocksieker, Denys Pommeret

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Samuel Stocksieker, Denys Pommeret. A Comprehensive Survey on Imbalanced Regression: Definitions, Solutions, and Future Directions. 2025. hal-05213741

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# A COMPREHENSIVE SURVEY ON IMBALANCED REGRESSION: DEFINITIONS, SOLUTIONS, AND FUTURE DIRECTIONS

**Samuel Stocksieker**

Aix Marseille Université
I2M, CNRS, Centrale Marseille
Marseille, France

**Denys Pommeret**

Aix Marseille Université
I2M, CNRS, Centrale Marseille
Marseille, France

## ABSTRACT

Imbalanced regression occurs when the distribution of a numeric target variable contains rare values, biasing models toward majority regions. Unlike imbalanced classification, it poses unique challenges due to continuous targets and unclear boundaries between frequent and rare values. This survey synthesizes recent advances, covering problem definitions, evaluation metrics, and state-of-the-art methods, distinguishing between tabular and deep settings. An imbalance coefficient for regression, optionally incorporating relevance, is proposed. A curated benchmark dataset mapping is provided. Open challenges and research directions are identified to advance theoretical understanding and practical solutions.

**Keywords** Imbalanced Regression, tabular imbalanced regression, deep imbalanced regression

## 1 Introduction

The effectiveness of machine learning algorithms, and statistical modeling more broadly, depends heavily on the quality of the training data. In this context, learning from imbalanced data remains a major challenge in machine learning. Traditionally, this issue has been extensively studied in the context of classification, where one or more classes are underrepresented compared to others. In standard approaches, learning is not adapted to imbalanced class frequencies: all observations are treated with equal importance. Since model parameters are typically optimized by minimizing a global loss function over the training set, learning tends to favor frequent classes, as they contribute more significantly to the loss than rarely observed ones. This phenomenon also affects regression tasks, where the objective is to explain and/or predict a numeric target variable. In practice, many applications involve numerical targets, such as age estimation or economic value prediction, where the variable of interest is often skewed. Imbalanced regression aims to address situations where certain ranges of the target variable are underrepresented in the dataset. Unlike classification, where categories are clearly defined, regression operates over continuous or discrete spaces, making it more challenging to directly apply standard resampling or weighting techniques. As a result, it becomes necessary to develop specific methods that improve model performance in rare regions of the target variable, while still ensuring generalization across the full range of values. In contrast to classification tasks, where numerous methods and solutions have been proposed, the problem of imbalanced regression remains underexplored, even at the level of its formal definition. Although various contributions have addressed the problem with proposed solutions, the concept of imbalanced regression still lacks a formal and universally accepted definition. Only a few works attempt a rigorous formalization, while the majority rely on intuitive or broad descriptions. This survey provides a comprehensive analysis of the concept of imbalanced regression by examining the various definitions associated with it. Since the phenomenon is not binary ("balanced vs. imbalanced"), it is unrealistic to define imbalanced regression strictly in contrast to standard regression. This is why an imbalance coefficient is introduced to provide a formal definition. We also provide a numerical illustration to empirically analyze this phenomenon. This survey further offers a thorough review of existing techniques and recent advances in imbalanced regression, including pre-processing approaches (data-level), in-processing methods (algorithm-level), and dedicated evaluation metrics. Finally, we outline open challenges and suggest future research directions. Our main contributions are summarized as follows:
* We present the first dedicated survey on imbalanced regression, encompassing both tabular imbalanced regression (TIR) and deep imbalanced regression (DIR), which address the same core issue but differ in context and methodology. Since most related works have been published only recently, existing surveys are either outdated, incomplete, or not specific to regression ([1, 2, 3, 4, 5, 6, 7]).

* Given the lack of consensus in the literature, we provide a comprehensive review and critical analysis of the various definitions associated with the problem.

* We propose a formal and generalized definition of imbalanced regression, introducing a measurable imbalance coefficient that can optionally incorporate a relevance function and available in a dedicated public repository<fnref n="1" />.

* We conduct an empirical analysis to investigate the phenomenon and identify some key sensitivity factors.

* We map and analyze all existing works on imbalanced regression to date, covering both TIR and DIR approaches.

* We identify all datasets used in the literature, provide a detailed mapping of their characteristics, and make them publicly available in the dedicated repository.

* Finally, we highlight promising research directions and outline the key challenges for future work.

## Structure of the paper

<table><tr><td>1</td><td>Introduction</td><td>1</td></tr><tr><td>2</td><td>Imbalanced Regression Definition</td><td>2</td></tr><tr><td>2.1</td><td>Background</td><td>2</td></tr><tr><td>2.2</td><td>One Issue but Different Definitions</td><td>4</td></tr><tr><td>2.3</td><td>Revisiting the Definition of Imbalanced Regression</td><td>8</td></tr><tr><td>2.4</td><td>Empirical Analyses</td><td>13</td></tr><tr><td>3</td><td>Imbalanced Regression Solutions</td><td>15</td></tr><tr><td>3.1</td><td>Tabular Imbalanced Regression</td><td>16</td></tr><tr><td>3.2</td><td>Deep Imbalanced Regression</td><td>19</td></tr><tr><td>3.3</td><td>Analyses of Solutions</td><td>21</td></tr><tr><td>3.4</td><td>Datasets Benchmark</td><td>21</td></tr><tr><td>4</td><td>Discussion and Perspectives</td><td>22</td></tr><tr><td>4.1</td><td>Tabular Imbalanced Regression Work</td><td>30</td></tr><tr><td>4.2</td><td>Deep Imbalanced Regression Work</td><td>33</td></tr><tr><td>4.3</td><td>Tabular Imbalanced Regression Datasets</td><td>34</td></tr></table>

The structure of this paper is as follows. In Section 2, we investigate the various definitions of the imbalanced regression problem, tracing its evolution from early formulations to current conceptual frameworks. We begin by outlining the problem setting, reviewing historical definitions, and subsequently proposing an imbalance coefficient and a formal definition, after critically evaluating existing alternatives. This section also includes an empirical analysis of the pathological aspects of IR. Section 3 reviews the main methodological contributions addressing IR, with a clear distinction between approaches applied to Tabular Imbalanced Regression and those related to Deep Imbalanced Regression. We offer a critical perspective on these contributions and analyze the datasets most frequently used in the literature. Finally, Section 4 concludes the paper by summarizing key insights, identifying current limitations, and outlining promising directions for future research.

# 2 Imbalanced Regression Definition

## 2.1 Background

### 2.1.1 Data Format

Data constitutes a fundamental pillar of machine learning, serving as the raw material required to train statistical models and algorithms. Various types of data are used in practice and can be categorized as follows:

* Structured: Data organized according to a predefined schema, typically in tabular form, and often stored in relational databases. This is the most common type of data. Variables may be quantitative, either continuous or discrete, or qualitative, either ordinal or nominal.

* Unstructured: Data without a predefined format, such as text, images, videos, or audio files.

* Semi-structured: Data that does not follow a strict tabular format but still includes some form of organizational markers (e.g., tags or metadata). Graph data and multimodal data can often be considered semi-structured.

In addition, certain types of structured or unstructured data may exhibit specific characteristics that require special consideration:

<footnote n="1">¹https://huggingface.co/datasets/samgohan/Tabular_Imbalanced_Regression</footnote>
* Temporal: Data collected over time, typically used in domains such as finance or meteorology.

* Geospatial: Data linked to geographical coordinates or regions, relevant for applications such as mapping, transportation, or logistics.

## 2.1.2 Purpose of Regression and Notations

Supervised learning is a subfield of machine learning that involves training a model using labeled data, meaning data for which the expected response is known (i.e., one or more variables of interest). The main objective is to build a model capable of learning an association between the features $X$ and the variable(s) of interest $y$. This association is inferred from the examples provided in the training data. This type of modeling aims to define a function $\mathcal{F}$ such that $\mathbb{E}(y|X) = \mathcal{F}(X)$, based on the observed sample $(X, y)$. Other approaches may also focus on quantiles, variance, or other aspects of the target distribution. These models are often learned through an optimization process that aims to find the best model parameters according to a given criterion. This criterion usually corresponds to an error measure, such as classification error in classification tasks or mean squared error in regression. Regression is a specific type of supervised learning that focuses on explaining and/or predicting a numeric variable, in contrast to classification, which deals with a categorical variable.

In the case of regression, we assume that the data are labeled, meaning we have features $X$ and a target variable $y$. We assume that there are $n$ observations and, in the case of structured data, $p$ features. We also assume that $y$ is univariate and of a quantitative type (continuous or discrete). The data are therefore structured as follows:

* $y = (y_i)_{i=1,...,n} \in \mathcal{Y} \subset \mathbb{R}^n$, the target variable. $y_i$ represents the realization of a univariate quantitative random variable $Y$ for observation $i$.

* $X = (x_i)_{i=1,...,n} \in \mathcal{X}$, the feature set composed of $n$ observations.

## 2.1.3 Imbalanced Learning

Despite advances in data availability and machine learning methods, some challenges persist and remain active research topics. One such challenge is learning from imbalanced data, or imbalanced learning, where the objective is to train predictive or explanatory models from datasets with skewed distributions, meaning some values are rarely observed. In supervised learning, imbalanced learning refers to cases where the distribution of the target variable is highly skewed. This issue first appeared in binary classification, where the variable $y$ often contains far more false (0) values than true (1) values, making one class underrepresented. However, rare values can be the most important for the modeling. In many cases, the goal is to predict specific ranges of the target variable that represent critical phenomena. For example, in medical datasets, the class of patients with a rare disease is typically much smaller than that of healthy individuals. Similarly, in industrial or economic contexts, rare but significant events such as insurance claims, customer churn, or fraud may occur infrequently but carry high impact. These events are crucial for risk prevention and management. In such cases, the most relevant data for practitioners are rarely observed in the sample. This mismatch between modeling objectives and the scarcity of relevant observations introduces specific challenges. As shown later, standard learning techniques tend to favor majority-class data at the expense of rare observations. This can lead to biased models and poor predictions of rare events. Addressing this requires dedicated approaches that mitigate such bias, including adapted evaluation metrics and learning algorithms that focus on underrepresented data. Even when a distribution is naturally asymmetric, the lack of representation in certain segments can cause learning bias when using standard methods. Traditional modeling techniques often assume sample representativeness (as in maximum likelihood estimation) but become unstable when parts of the support are sparsely observed. In many real-world settings, some regions of the input space contain little or no data, while others are overrepresented. This imbalance can distort training and must be addressed to ensure consistent and generalizable models. It is also important to note that imbalanced learning is not defined solely by a high imbalance ratio. For example, even a small class may be sufficiently distinct or well-represented to allow standard algorithms to perform well. As noted by [8], this area has been extensively studied, with many applications across domains ([9]). The expansion of machine learning has fostered early research in this field while introducing new challenges. Developing methods that effectively handle imbalanced distributions remains an active and important research direction.

To summarize, learning from imbalanced data presents the following challenges:

* Standard approaches are designed for ideally balanced data, and their performance may degrade when applied to imbalanced datasets.

* Standard performance metrics and optimization criteria, such as accuracy or mean squared error, are also unsuitable for this context, as they naturally introduce a bias in favor of frequent values at the expense of rare ones. These indicators may yield misleadingly good results. For instance, a classifier that assigns all observations to class 0 will appear highly accurate if class 1 is rare.
* Rare values risk being ignored, as they may be treated as noise by standard models. As a result, they are likely to be underestimated or poorly predicted.

* Data imbalance increases modeling complexity (e.g., difficulty in properly separating classes in supervised classification).

* In many cases, rare values are the most important, making standard approaches inadequate since they do not account for non-uniform importance and neglect infrequent values.

* The asymptotic properties of estimators may be affected, degrading generalization in standard learning algorithms. A similar issue arises in survey sampling when a dataset is not representative, requiring bias correction in the estimators.

* The implemented solutions must not have unintended consequences, such as favoring rare values over frequent ones.

The case of imbalanced regression is particularly specific and often more complex than classification, introducing the following additional challenges:

* It is not straightforward to define what constitutes a rare value and to distinguish it from frequent or majority values, unlike in classification, where such categories are predefined.

* As a result, measuring imbalance is complex. In classification, it suffices to compare class frequencies, whereas in regression, imbalance is harder to quantify.

* Since the target variable is quantitative, rarity is a gradual concept. The same applies to user-defined importance, which may increase continuously with the value of y. Thus, defining a strict boundary between "rare" and "frequent" values is simplistic and inherits too directly from classification thinking.

* In resampling, there is not always a clear notion of what constitutes a "balanced" sample, making it difficult to define a target distribution of y.

* When using a cost or benefit function, assigning appropriate penalties to different values of y can be challenging.

* In synthetic data generation, a new value of y must be generated, unlike in classification, where the label remains unchanged.

As stated by [6]: "The scarce representation of the most important cases leads to models that tend to be more focused on the normal examples, neglecting the rare events.". In other words, the learning imbalance is directly explained by the weight imbalance between the observations. Indeed, in supervised learning, the expected risk for a model $f_{\theta}(x)$ and a loss function $L(y, f_{\theta}(x))$ is defined as follows:

$$R(\theta) = \mathbb{E}_{(X,Y)\sim p(x,y)}[L(Y, f_{\theta}(X))] = \int_X \int_Y L(y, f_{\theta}(x)) p(x, y) dy dx.$$ 
$$p(x, y) = p(y) p(x|y) \text{ yields } R(\theta) = \int_Y p(y) \underbrace{\left[ \int_X L(y, f_{\theta}(x)) p(x|y) dx \right]}_{\ell(y, \theta)} dy,$$

where $\ell(y, \theta)$ is the conditional average loss for value y. $p(y)$ can be seen as a weight of $\ell(y, \theta)$ in $R(\theta)$. This means that each y contributes to the total risk proportionally to its marginal probability $p(y)$. So, if $p(y)$ is large (frequent values), the contribution to the risk is heavily weighted; if $p(y)$ is small (rare values), even a large error $\ell(y, \theta)$ has little impact on $R(\theta)$.

## 2.2 One Issue but Different Definitions

### 2.2.1 Origins

The problem of imbalanced regression (IR) originates from the utility-based regression framework. Although not initially defined explicitly as an imbalanced regression problem, early instances of this issue can be found in [10, 11, 12, 13, 14]. These studies address regression by focusing on the prediction of rare and extreme values of a continuous target variable. According to the authors, the main distinction from standard regression tasks lies in the notion of interest: accurately predicting rare low or high values of the target variable. To achieve this goal, rare and extreme values must first be formally defined. The authors propose using box plots, specifically Tukey's Interquartile Range (IQR) method [15]. Rare and extreme values are defined as those exceeding certain threshold values: the upper (resp. lower) adjacent value is the largest observation less than or equal to the third quartile plus 1.5 times the IQR (resp. the smallest observation greater than or equal to the first quartile minus 1.5 times the IQR). Within this context, the authors introduce the concept of Utility-Based Regression [16, 17], which refers to regression tasks with non-uniform interest across the target variable. This approach extends cost-sensitive learning to regression, with a particular focus on rare and extreme values. The first
explicit connection between imbalance and regression can be found in [18], which consolidates earlier work. Based on the concept of a utility function, the authors propose defining two classes using a threshold, thereby transforming the regression task into a binary classification problem. This transformation enables the use of utility-based performance metrics such as precision, recall, and F-measure. As suggested by [19], rare values in regression can also be defined using a relevance function, which is based on a utility function (taking values in [0, 1]), and a threshold to identify rare instances (a threshold of 0.75 is proposed). However, the default utility function follows earlier work, where rare values are identified using the box plot method, i.e., values considered extreme. This methodology, which reframes the problem as a classification task, facilitates the adaptation of several techniques from imbalanced binary classification to imbalanced regression (e.g., [20, 21, 22]). With [6], the concepts of imbalanced learning and utility-based regression are explicitly linked. The authors present metrics and methods for handling regression tasks in imbalanced domains, along with a general definition of the imbalance problem applicable to both classification and regression, based on a relevance function. The authors specify: "*Frequently, these specific sub-ranges of the target variable are poorly represented in the available training sample. In these cases, we face what is usually known as a problem of imbalanced data distributions or imbalanced datasets. In other words, in these domains, the cases that are more important for the user are rare and few exist in the available training set.*" As also noted in [18], this issue is often referred to as a utility-based regression problem, but it is closely related to imbalanced regression (IR) when the most important values are also the rarest in the dataset.

### 2.2.2 Extreme values prediction

Outlier values have long been a significant topic in regression [23, 24]. Even though the concept of regression in imbalanced scenarios had already been explored, it was [8] who first introduced the term imbalanced regression, defining it as "predicting rare and extreme values of a continuous target variable". In [22, 25, 26, 27], the term imbalanced regression is formally defined according to two assertions (referred to here as the Utility-Based Learning (UBL) approach): "Imbalanced regression tasks are a particular class of regression problems that can be characterized by two properties: i) the user has non-uniform preferences across the target variable domain, and ii) the most important ranges are poorly represented." Although the problem concerns rare values, the authors later clarify that the method proposed for estimating the relevance function relies on the assumption that rare and extreme cases are the most relevant to the user. [28] further generalizes this definition to cover both classification and regression tasks. [29] states that "In the context of regression, imbalanced learning means the prediction of rare and extreme values of a continuous target variable" and reuses the relevance function proposed by [18] in their approach. As noted in [30], "The imbalance learning correspondence for regression tasks is the correct prediction of rare extreme values of a continuous target variable." The same definition appears in the book dedicated to the imbalanced learning topic [9], where imbalanced regression is described as the prediction of rare and extreme values of a continuous variable. In [31], the authors further specify that "For regression tasks, we consider that the target variable distribution is imbalanced when extreme values (or outliers) are present. Commonly, but not necessarily, it translates to a skewed distribution." They propose a new taxonomy, stating that "Learning tasks are considered imbalanced regression tasks when, given a particular distribution of continuous values, (i) such distribution shows the presence of outliers, (ii) domain preferences are not uniform, and (iii) predictive focus is on extreme values." According to [32], imbalanced learning primarily focuses on the ability to model and accurately predict rare and extreme events. The authors state that the framework of imbalanced regression is based on two key aspects: i) user preferences vary across specific ranges of target values, meaning that certain errors are more critical than others. ii) estimation error is not a relevant metric for evaluating performance across all possible target values. This view is consistent with the utility-based regression framework [18]. [33] state that the problem of imbalanced regression arises when the target variable $y \in \mathbb{R}$ has a skewed distribution, and the most important values for the prediction task are rare and extreme. All these works use the UBL approach to define rare and extreme values.

### 2.2.3 From extreme values to rare values

[34] states that "Data imbalance is defined as the existence of an over-representation of a given class(es) or numeric value interval(s) over another [...] This means that learning from imbalanced domains is a particular class of predictive tasks where the user assigns more importance to the performance of the model approximation in certain poorly represented ranges of the target variable." However, in practice, the authors assume that the most extreme and rare cases of the target variable domain are the most relevant for the user. The problem of imbalanced regression takes a new turn with [35]. Without explicitly redefining the problem, the authors propose a weighting approach that assigns greater importance to rare values, whether extreme or not. This approach thus generalizes previous definitions where the goal was to focus only on rare and extreme values: "This automatic method, for estimating the relevance function, assumes that extreme values are rare, which is in contrast to our work, where rare values are automatically detected without such assumptions." Although they do not formally define the problem, this perspective is later reiterated by [36], who write: "Cases that are more important to the user are the rare events which are very few in the available training set."
[37] supports the same idea, stating that data imbalance negatively impacts the predictive performance of models for underrepresented observations. [38] addresses the problem by defining imbalanced data as a binary, multi-class, or regression dataset in which one class or value range occurs significantly more often than others. The authors propose adapting the previously introduced relevance function [20] to identify rare values, using a custom-defined function based on a kernel density estimate. [39] provides the first resampling solution for imbalanced regression in a big data context, relying on the relevance function (UBL approach) to distinguish between rare and normal cases: "The relevance function helps in determining the rare (important) and normal (unimportant) cases by mapping the target variable into a scale of relevance between 0 and 1." [5] suggests that the imbalanced regression problem consists in predicting a continuous target variable where certain value ranges occur much more frequently than others. These frequently observed ranges are referred to as frequent ranges, while those that are rarely or sparsely observed are called rare observations or tail distribution observations (again, rarity is associated with extremity). In [40], imbalance is defined as a situation where the frequency of occurrence of target values in certain intervals is significantly lower than in others. The authors also state that, in imbalanced regression tasks, each value of the target variable carries a different level of relevance. As in [38, 35], they propose using a kernel density estimator as a relevance function. [4] provides a survey on imbalanced classification and regression, but defines the problem only as: "The imbalanced learning issue is related to the performance of learning algorithms in the presence of asymmetrical class distribution." [41] defines imbalanced regression as a scenario where "user-relevant data are present in underrepresented sub-domains of the continuous output variable." The authors adopt the formal definition based on the relevance function, as introduced in [22]. [42] states that, in imbalanced regression, "certain parts of the target variable distribution might be underrepresented, making it difficult for a model built using this data to make accurate predictions for unseen samples falling in the underrepresented regions." [43] state that the problem arises when a specific interval of the target variable is underrepresented in the dataset. The authors adopt the relevance function with a threshold to distinguish between two subsets: rare and frequent values. They then reiterate the previously proposed formal definition, identifying two key conditions under which imbalanced regression occurs: i) Accurate prediction of rare values is more crucial for determining the performance of the model. ii) The cardinality of the set of rare values is significantly smaller than that of the frequent values. [3] also uses the UBL approach, separating normal and rare values through the relevance function: "The relevance value determines the examples that are normal and those that are rare, with the rare ones being the least represented in the dataset." However, the relevance function is not unique. Alternatives have been proposed by [35], [38], and [40]. In [2], imbalance refers to situations where some target values occur significantly less often than others, creating asymmetry in the dataset. This makes accurate prediction difficult due to limited training data for rare values. [44] emphasizes the continuous nature of target variables in regression, which lack clear boundaries. The rarity of extreme events makes their accurate prediction a major challenge. [45] and [46] adopt the UBL framework without referencing the term "extreme". They define imbalanced regression as occurring when: i) the target distribution includes common and rare values, ii) domain preferences are non-uniform, and iii) the predictive goal focuses on rare values. Both studies apply the automatic relevance function proposed by [18]. [47] presents a similar view, characterizing imbalanced regression by: i) an asymmetric target distribution, ii) unequal importance across value ranges, and iii) a focus on rare (underrepresented) values. They also employ the UBL approach and the automatic relevance function. [48] defines the problem under two conditions: i) the target distribution in the training set is asymmetric, with low-density regions, and ii) the model should perform well on instances located in these low-density areas. Unlike previous works, the authors adopt a continuous relevance perspective using the DenseWeight method [35]. [49] defines imbalanced regression as a subset of regression problems where the target distribution is non-uniform, with certain value ranges being significantly underrepresented. The authors also rely on the UBL framework and its relevance function. Similarly, [50] describes the issue as the underrepresentation of important intervals within a continuous target variable. [51] defines imbalanced regression as "learning from continuous distributions that include rare values (including extremes) that are precisely relevant to the studied phenomenon". They propose a formal mathematical definition to assess rarity, whether or not it involves extreme values (see Section 2.3.3). [52] and [53] also provide formal mathematical definitions, although they do not explicitly introduce the concept itself (see Section 2.3.3). Finally, [54] states that "in a regression problem, the imbalance problem occurs when data is significantly more available for certain values of the output variable and not so much for some other values." They propose a new approach to identifying rare values without referencing the notion of extremity.

### 2.2.4 Missing labels and uniform distribution

[55] introduces the concept of "Deep Imbalanced Regression (DIR) as learning from such imbalanced data with continuous targets, dealing with potential missing data for certain target values, and generalizing to the entire target range." The term "Deep" refers to the use of deep learning (neural networks), which is essential for handling unstructured data. Although this paper was the first to focus imbalanced regression for unstructured data, the problem remains fundamentally that of imbalanced regression, which had already been studied in the context of tabular data. Unlike previous definitions, the authors explicitly consider unobserved (missing) value ranges in their formulation. [56]
proposes defining the problem as follows: "Imbalanced regression assumes that the training set and test set are drawn from different joint distributions, $p_{train}(x, y)$ and $p_{bal}(x, y)$ respectively, where the training set's label distribution $p_{train}(y)$ is skewed and the balanced test set's label distribution $p_{bal}(y)$ is uniform." This assumption is unrealistic, as real-world distributions are often asymmetric and naturally imbalanced. Consequently, constructing a truly balanced test set is difficult, since including rare values in the test set often excludes them from the training set. This definition also reflects a sampling bias issue rather than imbalance itself, although both may be related (see 2.3.2). Still, comparing the training set distribution to a uniform reference remains a useful idea (see 2.3.3). This idea of comparing to a uniform distribution is also adopted by [57], who state that a key characteristic of imbalanced regression is that the histogram of the target variable exhibits an asymmetric rather than a uniform distribution. [58] expresses the same idea: "In imbalanced regression, the distribution of the labels deviates significantly from a uniform distribution." [59] supports this view, noting that the distribution of the target variable in the training data is generally asymmetric, while the test data are assumed to follow a uniform distribution. [60] does not provide a formal definition but notes that modern real-world datasets often exhibit highly asymmetric, or long-tailed, distributions. In such cases, a small number of classes dominate the dataset, while most are underrepresented. [61] relates imbalanced regression to the broader deep learning challenge of Long-Tailed Learning, introducing the term Long-Tailed Regression. The authors describe the issue not in terms of rare or extreme values, but rather in terms of significant differences in the distribution of target values between the validation and test sets. Similarly, [62] observes that imbalanced datasets lead models to develop a bias toward majority labels and underrepresent minority ones, without referring to rare or extreme values. This point is reiterated by [63], who note that working with asymmetric and imbalanced datasets is particularly challenging, as machine learning models tend to perform well only when sufficient representative training samples are available, again without explicitly referencing rarity. In the survey by [64], the authors link the problem of Deep Imbalanced Regression (DIR) to Long-Tailed Regression: "Long-tailed regression aims to deal with long-tailed learning with continuous label space. In such a task, how to simultaneously resolve long-tailed class imbalance and handle potential missing data for certain labels remains an open question." [65] suggests a slightly more general definition: "The problem caused by the unbalanced distribution of the target value in the regression task is called the unbalanced regression problem. The unbalanced regression problem is shown in the following three aspects: (1) The distribution of the target value of the sample is unbalanced; (2) Samples in some ranges of the target value are missing; (3) Samples in different intervals of the target value are divided into different importance levels." Aside from the first point, which appears relatively self-evident, the authors incorporate into their definition the notion of missing labels, or more precisely, missing label ranges. They approach the problem by categorizing imbalanced distributions into three types: left-skewed, right-skewed, and symmetric. According to [66, 67], data imbalance is the norm rather than the exception in real-world machine learning, especially in regression tasks. Outside of carefully curated research datasets, target variable distributions are generally non-uniform, which biases learning models toward well-represented regions and away from underrepresented areas. Moreover, these rare regions are often the most critical from a predictive standpoint. [68] summarizes this limitation as follows: "Data imbalances impair the generalization and fairness of models." A similar observation is made by [69], who note that imbalanced distributions hinder learning, particularly affecting generalization. This results in over-prediction in high-density regions and substantial bias in low-density areas, making model predictions unreliable. Likewise, [70] defines the objective of Deep Imbalanced Regression (DIR) as follows: "The objective of DIR is to learn a model from this highly skewed training set to generalize well on an unseen test set with the balanced distribution." [71] states that imbalance exists when the probability density function of empirical data is not constant across the domain. More precisely, "Data imbalance refers to the deviation of a variable's empirical probability distribution from its relevance probability distribution." According to [72] and [73], imbalanced regression arises when the frequency of certain target values is extremely low. For the authors, conventional deep learning models tend to favor accurate prediction in high-density regions to minimize overall loss, which leads to strong performance on the majority of samples but considerably higher errors in underrepresented areas.

### 2.2.5 Some extensions

Note that extensions to Imbalanced Regression allow addressing related issues: [74] for Mixed Imbalanced Regression, [75] for imbalance in self-supervised/multi-supervised learning (autoencoders), [76] tackling the feature imbalance problem in regression, [77] introducing the Graph Imbalanced Regression problem, [78] for the Multi-output regression problem in imbalanced data streams, Imbalanced Label Distribution Learning with [79], and Multi-Domain Imbalanced Regression with [80].
## 2.3 Revisiting the Definition of Imbalanced Regression

### 2.3.1 Analysis of concept

Figure 1a shows the number of papers published on imbalanced regression over the years (numbers for 2024 and especially 2025 are not yet definitive). Details of the papers are given in the Appendix. Before proposing a definition of the problem, it is first necessary to offer commentary on the definitions that have been previously presented.

<figure><img src="image_4.png" /><figcaption>Figure 1: Cartography of Imbalanced Regression Papers</figcaption></figure>

**Non-universal and evolving definition** As stated in the survey conducted by [6], there is an absence of a precise definition of the problem. This might explain why, as shown in the map 1b, the concept has evolved over time. Definitions appear to be cumulative: from extreme values ☞ to rare values ☞ to sparsely or unobserved ones (i.e., rare + missing labels), which in turn affect generalization due to a non-representative training set and a non-uniform distribution. Ultimately, imbalanced regression is part of a broader issue: the generalization of regression algorithms. The goal of rebalancing, whether via synthetic data generation [81, 82, 83], weighting, or other techniques, is to improve learning performance regardless of $Y$'s value. This aligns with the motivation in [84], who propose C-mixup algorithm to improve generalization in regression tasks, without explicitly referring to imbalance. Notably, the synthetic data generation method they use is based on interpolation between an observation and one of its nearest neighbors, as SMOTE approach. This also echoes the remark from [61]: "A desire for imbalanced regression enables models produced on an imbalanced training set to be potentially generalized to a balanced validation and testing set to the maximum extent possible." This perspective also relates to works that compare the label distribution to a uniform reference [56, 57, 58], where a uniform distribution is treated as an ideal scenario that guarantees full representativeness across the target space. Finally, Deep Imbalanced Regression is sometimes referred to as Long-Tailed Regression. As highlighted by [64]: "Long-tailed regression aims to deal with long-tailed learning with continuous label space. In such a task, how to simultaneously resolve long-tailed class imbalance and handle potential missing data for certain labels remains an open question." This equivalence is also discussed in [61].

**Rare values are not necessarily more important** It is often assumed that, in imbalanced regression, rare values are more important than frequent ones. However, this is not always true. Data imbalance causes unequal (imbalanced) learning by favoring frequent values/ranges and neglecting rare ones. Reassigning importance to rare values helps rebalance the learning process, giving equal influence to all observations and improving performance across the full range of $Y$. In some cases, all values of $Y$ are equally important, and the goal is simply to avoid neglecting rare ones. This aligns with the idea of comparing the label distribution to a uniform distribution. Giving more weight to rare values during training allows the model to better discriminate observations and identify the factors contributing to rare cases. This can improve generalization across the target space. A similar logic applies in classification: distinguishing between classes is key, and importance is often reassigned to prevent certain classes from being overlooked. However, the classes themselves are not inherently more important to the user; it is the ability to distinguish them that matters. In regression, the same holds true: accurate predictions are expected for all values of $y$, regardless of their frequency. Rare values are not necessarily more relevant. This leads to confusion between imbalanced regression and utility-based regression. In the utility-based learning framework, imbalanced regression is defined by a greater interest in rare values. Specifically, if the user assigns uniform importance across the domain, it is not considered an imbalanced regression problem in
the sense of [26]. Yet, the core issue in imbalanced regression is that learning becomes biased: the rarer a value, the less accurately it is predicted by standard models. Regardless of user-defined importance, the objective remains to improve predictions throughout the full range of y, which naturally includes rare values. Therefore, the definition proposed in [6] appears to describe only a special case of the broader problem. This connects with the observation in [71], who distinguishes between empirical imbalance and domain imbalance. In practice, however, rare values are not always more relevant. For instance, in age prediction [55], the goal is to improve predictive performance across all ages, without elderly or young ages being inherently more important. Still, the UBL approach helps address imbalance by reassigning weight to rare values, leading to more balanced training. However, this raises confusion between weighting and importance. Rare values are indeed overweighted to improve learning stability, but they are not necessarily more relevant to the underlying phenomenon.

**Rare values are not necessarily extreme** In recent definitions, particularly those emerging from Deep Imbalanced Regression, rare values are not necessarily extreme. For example, [56] defines imbalance as arising when the training set is not sufficiently balanced (approximately uniform). Similarly, [55] includes missing label intervals and non-extreme rare values in the problem. This introduces confusion between rare and extreme values: while rare values are often extreme, this is not always the case. This distinction is also emphasized by [35, 65, 76]. [85] highlights this point: "Because this technique makes no assumptions about the location of the rare instances, and in case the rare ones coincide with the extremes, they will also be identified and will receive the appropriate weight. [...] According to the authors, the notion of a rare instance is defined by associating rarity with extreme values in the target distribution. While some low-density areas may be of interest, in many applications, the most important instances are those that combine rarity with extreme events." This is further supported by [35], who notes: "The automatic method for obtaining the utility function assumes that extreme values are rare, which is in contrast to our work, where rare values are automatically detected without such assumptions."

**The Utility-Based Learning approach** This first formalization of imbalanced regression issue originates from the Utility-Based Learning (UBL) framework [18, 6], where a non-uniform utility function $\phi(y) : \mathcal{Y} \to [0, 1]$ is used to express the relevance of target values: 1 indicates maximum importance and 0 the minimum. Standard evaluation metrics generally ignore $\phi(y)$, assuming it is uniform. With a threshold $t_r$, training data is split into:

$$ \mathcal{D}_r := \{(x_i, y_i) : \phi(y_i) > t_r\}, \quad \mathcal{D}_n := \{(x_i, y_i) : \phi(y_i) \le t_r\}, $$

under the assumptions that $\phi(y)$ is non-uniform and $|\mathcal{D}_r| \ll |\mathcal{D}_n|$. While UBL was not designed specifically for imbalanced regression, it naturally applies when rare values are considered most important. Assigning higher relevance to such values helps rebalance learning and improve performance. However, this framework has the drawback of binarizing the problem and ignoring the continuous nature of the target variable. Morevoer, the approach relies on two difficult-to-define parameters: the relevance function and the rarity threshold. The former is subjective and unbounded; the latter is arbitrary but significantly impacts results. This shifts the core difficulty of imbalanced regression toward selecting these parameters. To automate this process, [18] proposed a method based on Tukey's boxplot definition of outliers, where values beyond 1.5 times the interquartile range from Q1 or Q3 receive a relevance of 1, and the median receives 0. A Piecewise Cubic Hermite Interpolation smooths the transition. Although non-parametric, this method emphasizes tails and assumes extreme values are the most relevant. To address limitations of Tukey's rule, such as its assumption of symmetric distributions, [31] introduced an adjusted boxplot method. Yet, this adaptation remains suited only for unimodal distributions and fails with multimodal data or missing intervals, as encountered in deep imbalanced regression [55] (see Figure 2). Users can override the default by specifying custom relevance functions [26]. Multiple authors reiterate that the automatic function presumes rare values are extreme: "The assumption made to achieve this goal regards the most usual setting, where the extreme rare values are the most important to the user" [21]; "To estimate the relevance function, it is assumed that the most extreme and rare cases... are the most relevant" [34]; "These measures assume a utility framework developed specifically for... rare extreme values" [28]. Despite the authors' warning (e.g. "the proposed automatic method is only suitable for the particular sub-class of imbalanced regression where the more relevant cases are the rare extreme values. [...] These applications are a specific type of imbalanced regression where rarity occurs in the extreme values of the domain"), some studies apply the default method without verifying whether rare values are indeed extreme. While the method works well for unimodal distributions, it performs poorly in other settings. Moreover, the smoothed function is linear between inflection points (utility 0 or 1), which may not suit all modeling needs.

**Discretizing the variable is not necessarily relevant** The target variable is not necessarily continuous. Although many definitions assume a continuous variable, it may also be discrete, as in the case of age [55]. More generally, the target variable is quantitative, either continuous or discrete, and may be bounded. In the discrete case, it may be natural to discretize the support of $Y$. However, for continuous variables, discretization can result in information loss. Moreover, choosing the right intervals is a key issue: how should values of the target variable be aggregated? The notion
<figure><img src="image_5.png" /><figcaption>Figure 2: Illustration of UBL relevance automatic function</figcaption></figure>

of a strict boundary between "rare" and "normal" values does not reflect reality. In regression, where $Y$ is numeric and potentially continuous and unbounded, rarity is a gradual, not binary, concept. Creating hard distinctions such as "normal" versus "rare" is overly simplistic and misleading. This binarization introduces artificial class boundaries that do not naturally exist in regression, leading to issues like class overlap [86]. Arbitrarily grouping observations using continuous relevance scores is not necessarily relevant. For instance, using a threshold of 0.8, a value with relevance 0.79 would be considered non-rare, while 0.81 would be treated as rare. Yet, a value at 0.79 would be treated the same as one at 0.3, and differently from one at 0.81, which lacks consistency. [9] raised this issue: "A first idea is to transform the regression problem into an imbalanced classification problem... But it will ignore the numeric difference notion among the output values, achieving a counter-intuitive approach to deal with regression problems." [8] similarly emphasized: "It seems interesting to investigate the possibility of adapting the cost not only to the minority group, but to each individual observation. This would allow for a more flexible prediction of rare events of differing importance". This also illustrates the difficulty in measuring imbalance and adapting performance metrics. Even after discretization (e.g., into two groups), imbalance may persist within each group. This intra-class imbalance also impacts learning, since rarity varies continuously with the target variable.

## 2.3.2 Intrinsic imbalance vs. extrinsic imbalance

As stated by [55]: "Data imbalance is ubiquitous and inherent in the real world." This imbalance in the target variable's distribution may stem from two non-exclusive causes: a natural imbalance of the variable itself, or one induced by external factors. We refer to intrinsic imbalance when the distribution is naturally skewed. This includes asymmetric variables such as claim costs or healthcare expenses, as well as a binary target variable like fraud or churn. Extrinsic imbalance, by contrast, results from external influences, even when the original distribution is balanced or mildly skewed. The most common case is selection bias, where the observed sample does not reflect the true population. This bias can be caused by factors directly or indirectly correlated with the target variable, leading to distortions in its observed distribution. Such structural effects can create data scarcity and give rise to imbalanced regression scenarios. This distinction is consistent with definitions of imbalanced regression based on differences between training and test distributions [61, 68, 69].

## 2.3.3 Imbalance Metrics

**Existing measures** More recently, alternative formal definitions to the UBL approach (see 2.3.1) have been proposed in order to broaden the scope of the problem. [52] introduces a mathematical measure of imbalance in regression based on a utility function derived from a probability measure $\mu$. According to the authors, imbalance should be defined with respect to relevance over the target domain. However, this assumption is not always valid (see 2.3.1). While the theoretical appeal of using a probability-based measure is clear, in practice the imbalance is evaluated by measuring the distance between the observed distribution $F_y$ and a reference distribution $F_\mu$ linked to utility. The authors suggest using the Kolmogorov metric: $\sup_{y \in \mathbb{R}} |F_\mu(y) - F_y(y)|$ or the Wasserstein distance: $\int_{\mathbb{R}} |F_\mu(y) - F_y(y)|dy$. Though this framework allows for quantifying imbalance, it is closer to a utility-based regression setting. It compares the empirical distribution to a relevance-weighted reference, without necessarily confirming the presence of rare values or an actual imbalance in the data.

In a similar vein, [71] proposes to measure imbalance as the disparity between the data distribution and an associated relevance distribution. To adequately quantify data imbalance, they introduce the metric mean imbalanced ratio (mIR), defined as the average deviation (ratio) between the reference distribution ($f_r$) and the observed distribution ($f_y$) across all data points: $\frac{1}{n} \sum_{i=1}^{n} IR(y_i) = \frac{1}{n} \sum_{i=1}^{n} \exp(\text{abs}(\log(\frac{f_y(y_i)}{f_r(y_i)})))$. For the relevance distribution, the authors assume no preference within the domain and therefore suggest a uniform importance, modeling the function as a uniform distribution. They compare the proposed metric to the Wasserstein distance: $\frac{1}{n} \sum_{i=1}^{n} ||f_y(y_i) - f_r(y_i)||$, and the
Kullback-Leibler divergence: $\frac{1}{n} \sum_{i=1}^{n} f_r(y_i) \log \left( \frac{f_r(y_i)}{f_y(y_i)} \right)$. The observed probability density is estimated via a kernel density estimate, while the relevance function is represented by the uniform distribution. The authors empirically suggest that their metric is more robust and more correlated with prediction errors than the two alternatives. However, the proposed metric is not bounded between 0 and 1, and does not allow for direct measurement of imbalance. To address this, they propose an indicator that depends on a threshold $t$: $ISP_t := \frac{1}{n} \sum_{i=1}^{n} \mathbb{1}_{\frac{f_y(y_i)}{f_r(y_i)} > t} \times 100\%$.

These comparisons between observed and reference distributions echo the framework proposed by [51], who define imbalance as occurring under one of two conditions: (i) Case 1: when $\hat{f}_Y$ deviates significantly from a reference distribution; (ii) Case 2: when $\hat{f}_Y$ is significantly too small. Let $f_0$ denote the reference distribution: either user-defined (Case 1) or uniform (Case 2). A regression task is said to be $(\alpha, \beta)$-imbalanced if there exists a subset $\chi \subset \mathcal{Y}$ such that:

$\int_{\chi} f_0(y) dy \ge \beta$ and $\frac{\int_{\chi} \hat{f}_Y(y) dy}{\int_{\chi} f_0(y) dy} < \alpha$. In other words, imbalance arises when the observed distribution significantly deviates from a reference distribution over a non-negligible portion of the support. This view is consistent with earlier formulations that define imbalance in terms of deviation from a reference distribution (often uniform), and aligns with the distinction made by [71] between empirical and domain imbalance.

Finally, [53] propose defining imbalance through the *Complexity-to-Density Ratio (CDR)*. Unlike methods based solely on target value frequency, this approach incorporates both data complexity and density. For a given region $\Omega$, the CDR considers its complexity (via the Frobenius norm of the Hessian), its size (as the maximum Euclidean distance between two points), and the number of data points in the region. Formally: $CDR(\Omega, D) = \frac{g_c(\Omega) \cdot g_s(\Omega)}{|\Omega \cap D|}$ where $g_c(\Omega)$ is the local complexity, $g_s(\Omega)$ the region size, and $|\Omega \cap D|$ the number of data pairs in $D$ that lie within $\Omega$. A high CDR indicates a complex but sparsely sampled region, which may signal imbalance. Conversely, a low CDR reflects a simple, well-represented area.

**Formal definition and Imbalance Coefficient** We propose a formal definition of the Imbalanced Regression problem that unifies and extends previous definitions while addressing the analysis presented in Section 2.3.1. First, as in binary classification, imbalance in regression is a gradual and continuous phenomenon; it is not a binary state of "balanced vs. imbalanced." Therefore, it is more appropriate to define a measure of imbalance rather than to categorize a dataset as either balanced or imbalanced strictly. The problem is sometimes expressed in terms of a non-uniform relevance function, and other times in relation to a uniform (i.e., balanced) reference distribution. As noted by [71], a distinction must be made between domain imbalance (resulting from a non-uniform relevance function) and empirical imbalance (resulting from a non-uniform empirical density function). However, as discussed in Section 2.3.1, there is often confusion between Imbalanced Regression and Utility-Based Regression. The presence of a non-uniform relevance function alone does not define an Imbalanced Regression problem, but rather a Utility-Based Regression one, as formulated in [16, 18]. These two settings coincide when the most important values are also rare. Similar to the case in binary classification, we suggest to define the IR issue as follows: *Imbalanced Regression occurs when a distributional imbalance induces a learning imbalance, rare values are underrepresented and therefore neglected during training, while frequent values dominate, regardless of their actual importance in the underlying phenomenon.* Nevertheless, these rare values may be highly informative. Finally, it is important to emphasize that rare or missing values are not necessarily extreme values, although they often are in practice.

We propose here a generalized, formal Imbalanced Regression metric that incorporates and builds upon previous formulations [51, 52, 71, 6]. Let $\hat{f}_y$ denote the observed probability density function of the target variable $y$, estimated, for example, via kernel density estimation. Let $f_u$ be the reference density, uniform by default, but possibly defined differently (e.g., based on population distribution), over the same domain $[\min(y), \max(y)]$. Additionally, let $\omega(y)$ be a relevance function assigning importance weights to values of $y$, which may be uniform or not. Since imbalance is not a binary phenomenon (i.e., not simply "balanced vs. imbalanced"), it is more appropriate to define a continuous measure of imbalance as a divergence between $\hat{f}_y$ and $f_u$. Let $|x - y|$ the $L^1$ norm. To ensure interpretability, we propose a bounded coefficient in $[0, 1]$ to quantify the divergence: 0 represents perfect balance; 1 reflects maximum imbalance. While many distances (e.g., Wasserstein, KL divergence) can compare distributions, they lack a fixed scale and are typically used for relative comparison only, unsuitable for quantifying the absolute degree of imbalance. In the case where no importance weighting is applied, the ideal distribution is the uniform $f_u$, representing full coverage over the support of $y$. The worst case is a degenerate distribution, concentrated on a single value (i.e., Dirac mass), which prevents any discrimination among observations. If certain values are deemed more relevant, the divergence can be weighted accordingly using $\omega(y)$. We propose focusing specifically on regions where the observed distribution falls below the reference (i.e., underrepresented areas), since these reflect imbalance. Conversely, areas where $\hat{f}_y$ exceeds $f_u$ may indicate beneficial concentration, potentially improving model estimation. To avoid over-penalizing such regions, the divergence should be evaluated asymmetrically, considering only where $\hat{f}_y < f_u$. Thus, imbalance can be measured using a simple coefficient ranging from 0 to 1.
**Definition 2.1.** The imbalance coefficient, denoted by imb_coef, is defined as follows:

$$ imb\_coef(y) (= imb\_coef(f_y, f_u)) := \frac{\int_{\min(y)}^{\max(y)} |f_u(y) - \hat{f}_y(y)| \times \mathbb{1}_{f_y(y) \le f_u(y)} \times \omega(y) dy}{\int_{\min(y)}^{\max(y)} \omega(y) dy} \\ = \frac{\int_{\min(y)}^{\max(y)} \max(0, f_u(y) - \hat{f}_y(y)) \times \omega(y) dy}{\int_{\min(y)}^{\max(y)} \omega(y) dy} \quad (1) $$

It is worth noting that the proposed definition resembles a conditioned and weighted Wasserstein distance between probability densities, or alternatively, a weighted Total Variation distance. As a consequence of the properties of the Total Variation distance, this imbalance coefficient can be interpreted as a statistical distance. Specifically, it satisfies the following properties: (i) non-negativity ($imb\_coef(y) \ge 0$), (ii) identity of indiscernible ($imb\_coef(y) = 0 \iff f_u(y) = f_y(y)$), (iii) symmetry ($imb\_coef(f_y, f_u) = imb\_coef(f_u, f_y)$), and (iv) subadditivity ($imb\_coef(f_y, f_u) \le imb\_coef(f_y, f_z) + imb\_coef(f_z, f_u)$). Importantly, this distance should not be computed using cumulative distribution functions (CDFs), as they aggregate deviations from the minimum and distort the impact of local differences. As a result, identical deviations may lead to different distances depending on their position in the distribution (see the last two distributions in Figure 4 for illustration). Alternatively, the Hellinger distance could be utilized as a metric but the results were deemed unsatisfactory (not discriminating enough and unstable). Moreover, common metrics such as the Wasserstein or Kolmogorov distances are not bounded between 0 and 1, making them useful for comparing distributions but not for directly quantifying imbalance. Figures 3 (for continuous distributions) and 4 (for discrete ones) illustrate the proposed imbalance coefficient in the unweighted case (i.e., $\omega(y) = 1, \forall y \in \mathcal{Y}$ and $f_u$ is uniform). The results show that:

i) The coefficient is invariant under symmetric transformations of the distribution.

ii) Distributions close to uniform yield values near 0%, while highly concentrated ones (e.g., Dirac masses) yield values near 100%.

<figure><img src="image_6.png" /><figcaption>Figure 3: Imbalanced coefficient for a continuous distribution, without weighting</figcaption></figure>

When a relevance function $\omega(y)$ is introduced, the measure is weighted to reflect the user's preference. Figure 5 shows an example where only the non-shaded region is considered (i.e., $\omega(y) = 1$). This relevance function can take various weighting forms, such as Gaussian or asymmetric distributions. This coefficient is stable under scaling, since the densities are normalized over $[0, 1]$. It also offers several advantages:

i) It defines an imbalance coefficient bounded between 0 and 1 (similar to a correlation coefficient), enabling interpretation and cross-dataset comparison;

ii) It remains consistent with the framework of [6], by incorporating a non-uniform relevance function that emphasizes rare values;
<figure><img src="image_7.png" /><figcaption>Figure 4: Imbalanced coefficient for a discrete distribution, without weighting</figcaption></figure>

iii) It aligns with recent approaches [52, 71, 51] by comparing the observed distribution to a reference one.

This imbalance coefficient has been applied to a benchmark of over 80 datasets (see Section 4.3).

<figure><img src="image_8.png" /><figcaption>Figure 5: Imbalanced coefficient for a continuous distribution, with weighting</figcaption></figure>

## 2.4 Empirical Analyses

### 2.4.1 The Pathology of Imbalanced Regression

One of the key challenges in imbalanced regression lies in identifying rare values, as rarity is a gradual and continuous notion. Consequently, measuring the degree of imbalance is equally complex. As in binary classification, there is no definitive and universal threshold for the imbalance ratio, beyond which a dataset becomes imbalanced. [8] observes that most studies explore imbalance ratios between 25% and 1%, with ratios below 1% generally considered extreme imbalance. Yet, this lack of formalism is unsurprising, as imbalance effects depend on more than the imbalance ratio alone. Indeed, imbalance-related challenges stem not only from label distribution but also from factors such as
data complexity and representativeness. [8] emphasizes this point: "One of the most interesting directions in binary imbalanced classification is the notion that imbalance ratio is not the sole source of learning difficulties. Even if the disproportion is high, but both classes are well represented and come from non-overlapping distributions, we may obtain good classification rates using canonical classifiers. Degradation of performance may also be caused by the presence of difficult examples, especially within the minority class." [87] studied artificial datasets varying in complexity, sample size, and imbalance level, and reported that: i) Linearly separable data are unaffected by imbalance, regardless of size; ii) As concept complexity increases, sensitivity to imbalance rises; iii) Sample size has little impact on imbalance sensitivity. [86] analyze how data characteristics affect the success of preprocessing in imbalanced regression. Their work, based on the UBL approach (which binarizes the problem), shows that assessing overlap and small disjuncts is more difficult in regression due to the continuity of the target variable. Nevertheless, they empirically observe: i) Increased rarity in extreme values leads to stronger bias; ii) Smaller datasets suffer more from imbalance; iii) High variance complicates learning; iv) Sparse regions in the feature space reduce model performance. In general, they find that standard models minimize global error but often fail on rare values, thus limiting generalization. [34] conducted an empirical study on ensemble methods (bagging and boosting) using 20 real-world imbalanced datasets. They show that models with strong average performance are not necessarily reliable for rare cases. Moreover, they find that increasing dataset size reduces the benefit of ensemble strategies and that the proportion of rare values does not consistently influence improvements. Similarly, [3] analyzed IR strategies on tabular datasets and concluded that the best preprocessing technique depends on the evaluation metric, learning algorithm, and dataset properties. No single method consistently outperforms the others. [71] evaluated multiple algorithms across various datasets and demonstrated a correlation between model error and sample rarity, although the strength of this relationship is dataset-dependent. They confirm a tendency for regression models to favor frequent values, leading to higher errors on rare ones. Finally, [88] investigated different weighting methods and underlined several dataset-specific considerations that impact predictive performance.

## 2.4.2 Experimental Protocol

Imbalanced regression is inherently influenced by multiple factors, including the level of imbalance, sample size, and the complexity of the regression task. This section aims to illustrate and analyze the phenomenon through a series of simulations by varying these characteristics. We assess the sensitivity of predictive performance to the following factors<fnref n="2" />:

* Sample size — 5 ordered levels: [200, 500, 1000, 2000, 5000]

* Regression complexity — 5 unordered levels: [1 (low complexity), 2, 3, 4, 5 (high complexity)]

* Imbalance level — 5 ordered levels: [0.5 (low imbalance) imbalance), 0, -0.5, -1, -1.5 (high imbalance)]

To mitigate random variation, each configuration is evaluated across 5 independent runs using different random seeds. To ensure model-agnostic conclusions, we apply 10 models from the H2O AutoML library [89], covering a range of algorithms such as Distributed Random Forest, Extremely Randomized Trees, Regularized Generalized Linear Models, Gradient Boosting Machines, Extreme Gradient Boosting, and Multi-layer Feedforward Neural Networks. For each configuration, a dataset of size $n = 10,000$ is generated depending solely on the complexity level. A balanced test set of 1,000 observations (approximately uniform) is drawn. From the remaining 9,000 instances, we sample two training sets:

* A balanced training set (baseline), uniformly drawing, serving as an ideal reference.

* An imbalanced training set, varying according to both sample size and imbalance level. A level of 0.5 indicates balance, while -1.5 represents strong imbalance.

Each dataset includes 5 Gaussian features and 5 non-linear transformations of them. The target variable $Y \sim N(\mu, \sigma)$ is constructed using five selected features. At complexity level 1, these are the original Gaussian variables (yielding a simple regression task). At level 5, only the non-linear features are used, making the task highly complex. Intermediate levels (2-4) use a mix of both.

## 2.4.3 Results

The results shown in Figures 6b and 6a confirm that predictive performance degrades as the level of imbalance increases (with 0.5 indicating a balanced setting and -1.5 indicating strong imbalance). This deterioration occurs across all levels of regression complexity, though the extent of degradation varies depending on the complexity of the underlying

<footnote n="2">²Full implementation details and code are available at: https://github.com/sstocksieker/IR_Survey.</footnote>
relationship. Notably, the effect of imbalance is more pronounced with smaller training sample sizes, although the relationship between size and performance is not strictly proportional. Figures 6d and 6c further demonstrate that prediction error is positively correlated with rarity: the rarer the target value, the higher the prediction error. Interestingly, when the training set is highly concentrated, the model may perform better on frequent values compared to a balanced training set, though this benefit does not extend to rare values, where performance declines. As shown in Figure 6c, prediction quality improves with increased data availability. This finding aligns with well-established observations regarding the impact of sample size on model accuracy [90].

<figure><img src="image_9.png" /><figcaption>(a) Test prediction RMSE depending on the imbalance level for different training sizes</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(c) Test prediction RMSE depending on rarity for different imbalance levels (for complexity = 1)</figcaption></figure>

<caption>(d) Test prediction RMSE depending on decile rarity for different training sizes (for complexity = 1)</caption>

<caption>Figure 6: Analyses of test prediction RMSE</caption>

Remarks: A Wilcoxon test comparing the results of the imbalanced sample with those of the baseline (balanced) showed that the difference is significant as soon as the sample is not balanced (imbalance level different from 0.5), regardless of the sample size. This empirical analysis was also conducted on a real dataset, leading to the same conclusions: the results deteriorate with the level of imbalance and the sample size. Additionally, an in-depth analysis was conducted on different models, revealing that imbalance affects all types of models (*Gradient Boosting (GBM)*, *Random Forest (RF)*, *Generalized Linear Model (GLM)*, *Multi-Layer Perceptron (MLP)*, *Extreme Random Tree (XRT)*). The strongest variations were observed in RF, XRT, and deep learning models, while the least impact was found in GLMs.

# 3 Imbalanced Regression Solutions

Solutions for *Imbalanced Learning* are themselves imbalanced. In contrast to imbalanced classification, which is less complex and benefits from a wide array of available methods, imbalanced regression remains relatively underexplored,
but offers an increasing number of solutions, as shown in Figure 7. Methodological approaches to Imbalanced Learning are traditionally grouped into three main categories [6]:

* **Pre-processing solutions**

These techniques rebalance the dataset before training, allowing the use of standard algorithms afterward, a notable advantage in terms of practicality as a universal solution. Approaches include under-sampling, over-sampling, and active learning. Under-sampling can be guided by data cleaning strategies [91, 92, 93], but this presents a potentially significant disadvantage: it risks discarding informative samples, and thus increasing estimator variance, by reducing data availability, especially in small or severely imbalanced datasets. Over-sampling often involves synthetic data generation. Basic replication of minority samples can lead to overfitting, whereas synthetic generation techniques (e.g., [94, 95, 30, 96]) mitigate this by enriching the feature space while preserving diversity, enhancing generalization. Such approaches dominate the field [97]. Active learning methods aim to identify and prioritize the most informative instances for training [98, 99]. Weighting the data space using cost information, such as in cost-sensitive learning, can also rebalance sample distributions [100, 6].

* **In-processing solutions**

These methods modify the model's internal optimization, such as loss functions or cost matrices, to penalize errors more heavily on underrepresented or critical values. This aligns the learning process with evaluation goals and improves interpretability [101, 102].

* **Post-processing solutions**

Here, predictions are adjusted after training a standard model on the imbalanced data. In classification, this includes threshold tuning [103] and cost-sensitive adjustments [18, 104]. However, since neither the data nor the model is altered during training, post-hoc corrections often struggle to eliminate underlying bias toward majority regions.

* **Hybrid and complementary solutions**

Some methods combine pre-processing and in-processing strategies, for example, integrating resampling with algorithmic adjustments [100]. Additionally, efforts have been made to design specific performance metrics tailored to imbalanced regression [7, 105, 106, 6].

<figure><img src="image_11.png" /></figure>

Figure 7: This figure shows the cumulative evolution of the related works. The problem of *Imbalanced Learning* was initially studied in the context of binary classification on structured data (e.g., [6, 97]). Over time, it has been extended to other contexts, such as regression, multi-class classification, and clustering ([8]). Recently, with the increasing research interest in unstructured data, this issue has gained even more importance. Regarding regression, the first adaptations for images and *Natural Language Processing* are relatively recent ([55] in 2021) and still limited in number. These techniques, which often rely on *deep learning*, fall within a specific framework, *Deep Imbalanced Regression (DIR)*, which is distinct from the more traditional approach centered on tabular data, referred to as *Tabular Imbalanced Regression (TIR)*. The papers analyzed are mapped in the Appendix.

## 3.1 Tabular Imbalanced Regression

### 3.1.1 Pre-Processing Solutions

The first dedicated pre-processing solution for imbalanced regression was introduced by [19] with *SmoteR*, an adaptation of the well-known SMOTE algorithm [94]. Using a relevance function (*UBL approach*), the authors reformulate the problem into a binary classification setting, separating rare and normal values. This enables the application of SMOTE to generate synthetic data, with the key distinction that new values of *y* are also generated, unlike in classification. Continuing within the *UBL* framework, [20] extended this work by adapting under-sampling techniques and combining them with *SmoteR*. This binarization of the target variable, using a relevance function and threshold (see 2.3.1), enables the reuse of many strategies from imbalanced classification. [21] introduced the first R package specifically designed for imbalanced regression, implementing various techniques such as random under-sampling, over-sampling, Gaussian perturbation, SMOTE for regression, and importance-based resampling. Building on this, [22] proposed the
<figure><img src="image_12.png" /><figcaption>Figure 8: Analyse of Imbalanced Regression Papers. Figure 8a presents the different types of papers on Imbalanced Regression, while Figure 8b illustrates the various types of proposed solutions — pre-processing methods are predominantly designed for TIR, whereas in-processing methods are more commonly dedicated to DIR.</figcaption></figure>

SMOGN algorithm, which combines under-sampling with two over-sampling methods. The algorithm addresses certain limitations inherent in synthetic sampling. It applies *SmoteR* to generate new observations when the selected sample and its *k*-nearest neighbor are sufficiently close, while Gaussian noise is added when they are farther apart. [25] introduced an adaptive under- and over-sampling method that incorporates neighborhood information to guide the resampling process. The key idea behind neighborhood-biased resampling is to examine the distribution of nearest neighbors to determine which normal cases should be more likely removed and which rare cases should be favored when generating synthetic samples. All previously mentioned approaches rely on a relevance function and a threshold to separate normal from rare values, effectively turning the problem into a binary classification task. To move beyond this binarization, [26] proposed the WERCS method, which avoids discretizing the target variable. The core principle of WERCS is to adjust under- and over-sampling probabilities based on the continuous values of the relevance function. All observations are eligible for resampling: the more relevant an instance, the higher its probability of being selected; the more frequent, the higher its chance of removal. This strategy maintains the continuous nature of the target variable while addressing imbalance. [107] introduced weighted under- and over-sampling strategies for spatio-temporal forecasting of extreme values. The weights are determined by the temporal recency of observations and the relevance of their spatial neighbors, reflecting their potential importance in the learning process. Rather than proposing new methods, [108] developed the Python package *resreg*, which adapts several existing approaches for imbalanced regression. The paper also presents a biased loss function that adjusts error weights based on the frequency of target values, assigning greater importance to errors on rare values. Unlike standard MSE, this method reduces the dominance of frequent values, enhancing the model's performance on underrepresented regions. [37] proposed a hybrid sampling technique that combines two strategies: adding synthetic points near the manifold boundary (based on their nearest neighbor or the average of five neighbors) and performing random sampling in densely populated regions. [39] adapted the SMOGN method to address both imbalanced regression and the computational challenges posed by large-scale datasets. Specifically, they employed Scalable KMeans++ to form coherent clusters that preserve spatial relationships among rare cases. Traditional SMOTE-based methods rely on nearest-neighbor computations, making them suitable for medium-sized datasets but less effective for Big Data applications. In the same vein, [109] proposed two extensions of SMOGN. [85] extended the G-SMOTE algorithm, originally developed for classification [29], to regression tasks. Unlike the original version, this approach generates synthetic samples within a geometric region surrounding a selected instance, rather than interpolating along the line segment between neighbors. [110] introduced a Python package incorporating a variety of oversampling methods, including SMOTE, Gaussian Noise, ADASYN, and natural oversampling. The package also includes under-sampling and data cleaning techniques such as Condensed Nearest Neighbour, Edited Nearest Neighbour, Tomek Links, and natural under-sampling. [43] propose two novel oversampling methods for imbalanced regression: KNNOR-Reg (for small datasets) and KNNOR-DeepReg (for large datasets). Both extend the KNNOR algorithm originally developed for imbalanced classification [50]. The central idea is to use *k*-nearest neighbor models and neural networks to rebalance training data, offering a more effective alternative to traditional approaches such as SmoteR. An accompanying software package is also provided [111]. [45] adapt the SNOCC algorithm, an extension of SMOTE that generates synthetic points within a convex hull, to regression tasks. They also introduce ACOS, a method that produces new samples through affine combinations of original observations. [48] propose the Weighting SMOTE for Regression (WSmoteR) algorithm, which avoids partitioning values into rare and normal categories. Instead, sampling weights
are determined via the *DenseWeight* function [35], enabling the method to handle rare values while preserving the continuity of the target variable’s distribution. [49] focus on improving under-sampling strategies through the *Selective Under-Sampling (SUS)* algorithm, which selects the most representative instances from the dataset. They also introduce a tailored version for iterative learning algorithms (e.g., neural networks). Unlike random under-sampling, SUS aims to retain crucial observations and avoid discarding key data points that carry significant distributional information. [54] propose the iterative algorithm *Uncertainty Quantification-Driven Imbalanced Regression (UQDIR)*, which applies weighted resampling based on predictive *uncertainty quantification*. This technique assesses prediction uncertainty arising from data scarcity and establishes a connection between high uncertainty and data imbalance. UQDIR constructs a subset of the training set containing observations for which the model’s uncertainty estimates are unreliable and assigns resampling weights according to observed prediction errors. [53] introduce the *Error Distribution Smoothing (EDS)* method, which dynamically adjusts data distribution by reducing redundancies in overrepresented regions and enhancing sampling in underrepresented ones. This is guided by the *Complexity-to-Density Ratio (CDR)*. EDS improves regression model robustness and accuracy while reducing both maximum error and training time. [112] present *SMOGAN*, a two-stage oversampling framework that extends SMOTE by integrating a distribution-aware GAN to refine synthetic samples. This enhances alignment with the true feature-target distribution in imbalanced regression. [113] introduce *DistResampleR-Lite*, a scalable and flexible framework for distributed resampling in large-scale regression tasks. It combines efficient K-Means clustering with approximate nearest neighbor search to generalize and accelerate existing resampling methods. [51] show that various generators (e.g., SMOTE variants, Gaussian perturbations) can be expressed under a unified *Smoothed Bootstrap* framework. They propose new generators using non-standard kernels (e.g., discrete, asymmetric) to better respect feature constraints, along with SMOTE extensions in the data space. Additionally, they introduce a method for generating *y* conditionally on the synthetic *x*, preserving the original dependency structure.

### 3.1.2 In-Processing Solutions

[11] propose a novel splitting criterion for regression trees tailored to data mining tasks where the primary objective is to predict rare and extreme values of a continuous target variable and to understand the conditions under which these values arise. This method partitions the domain of *y* using boxplot statistics, enabling the computation of precision, recall, and ultimately the F-measure, which serves as the basis for the tree’s split criterion. In a similar vein, [12, 18] present the *utility-based Rules (ubaRules)* approach, a rule-based regression system designed to forecast rare and extreme values of a continuous target. It also relies on the F-measure and introduces a "base tree," derived from the CART algorithm but modified with a splitting criterion biased toward rare and extreme values. These extreme values are identified via boxplot analysis. [13] introduces a new performance metric that weights observations, giving greater importance to extreme values over frequent ones. Similarly, [18] proposes an automatic method for estimating a relevance function to weight extreme values more heavily (see Section 2.3.1). Following the UBL framework, [114] propose a method that incorporates utility-based metrics directly into the loss function of learning algorithms, with the aim of optimizing predictions for rare and extreme target values. [115] and [116] adapt the *SMOTEBoost* [117] and *RUSBoost* [118] algorithms to the context of imbalanced regression. These methods combine *SmoteR* or random under-sampling with boosting techniques to enhance the prediction of rare values. At each boosting iteration, synthetic data are generated or removed before training the weak learner. Similarly, [27] introduced the *REsampled BAGGING (REBAGG)* algorithm, an ensemble method based on bagging that incorporates data preprocessing strategies using *SmoteR*. All of the previously discussed solutions follow the UBL approach and primarily target the prediction of extreme values. Extending this perspective, [35] propose the *DenseWeight* method, which assigns weights to observations inversely proportional to their estimated frequency via kernel density estimation. This weighting increases the influence of rare observations in the learning process. The function is normalized and modulated by a hyperparameter. Integrated into a neural network’s loss function, it defines a cost-sensitive learning strategy. Along similar lines, [36] introduce a cost-sensitive neural network that minimizes a biased loss function, while [33] employ the *SERA* metric [31] as the objective function for gradient boosting, enabling adaptive weighting to improve rare value predictions. [38] built their utility function as the inverse of the observed density and define rare vs. normal values via a threshold. Rare observations are synthetically generated using a conditional variational autoencoder, which is then integrated into a boosting framework, similar to prior approaches [115, 33]. Finally, [41] empirically examine the performance of pre-processing methods, referred to as "passive" techniques, in the context of imbalanced regression. They also introduce two novel evolutionary algorithms based on fuzzy rules, offering active strategies for handling imbalance during learning. [42] aim to enhance the prediction of rare values by extending a federated ensemble algorithm, "Federated Ensemble Regression Using Classification", which integrates regression and classification. The method identifies critical subregions via classifiers and then applies tailored regressors to these zones, improving rare value accuracy while reducing overall error. [44] incorporated the *Balanced MSE* [56] into a boosting framework. They extend it through a Bayesian version using Gaussian mixture models to enhance learning, performance, and robustness. [46] adapted Support Vector Regression (SVR) by integrating adaptive weight functions to better account for imbalance. [65] proposed *DIRVAE (Deep Imbalanced Regression Variational Autoencoder)*, which generates missing and minority
samples. The VAE is optimized with an adversarial component inspired by GANs to improve learning quality. [47] introduced the *Sernet* approach for feature selection in regression. Leveraging the *SER* metric [31], it highlights features contributing significantly to rare cases, reducing the dominance of common values in the selection process and improving rare-value predictions. In [119], the authors introduced the *Deep Smoothed Bootstrap*, a method for generating synthetic observations from a latent space learned via a Variational Autoencoder. This approach captures complex nonlinear correlations that are difficult to model in the original feature space and facilitates the handling of mixed-type data. [72] proposed *IRGAN* (*Imbalanced Regression Generative Adversarial Network*), a GAN-based framework. It integrates a classical regression model trained on a rebalanced sample generated by the GAN. To handle imbalance during training, a correction module, comprising an agent and a correction network, guides sample generation. A composite loss function is designed to jointly optimize generation quality and model discrimination. In a comparative analysis, [120] underscore the importance of loss function design in predictive neural networks and introduce the *Scaling-Weighted MSE*. Unlike static weighting, this loss function assigns dynamic weights based on the target value *y*. The total MSE is computed as a sum of sub-MSEs over quantile-defined intervals of *y*, enabling more flexible handling of imbalanced regression. [121] presented *MATI*, a mixture-of-experts framework incorporating test-time self-supervised aggregation. It addresses tabular imbalanced regression by dynamically adapting to varying target distributions during inference.

### 3.1.3 Post-processing Solutions

Post-processing methods for imbalanced regression remain relatively underexplored. While some studies do not directly target imbalanced regression, they offer promising avenues for adaptation through the use of custom cost functions in regression settings (e.g., [122], [123], [104], and more recently, [124], [125]).

### 3.1.4 Imbalanced Regression Metrics

[16] introduced the concept of utility-based regression, a framework for evaluating models in the presence of non-uniform costs and benefits across the target domain. A key application involves predicting extreme values of continuous variables, where a relevance function assigns a score between 0 and 1 to each *y* value, typically estimated via boxplot statistics. Building on this concept, [17] proposed new performance metrics to improve the evaluation and comparison of models. [14] and [18] generalized precision and recall for regression tasks by binarizing the target domain, splitting "normal" from "rare" values, using the relevance function. Later, [31] introduced the Squared Error-Relevance Area (SERA) metric, which extends the Mean Squared Error (MSE) by weighting errors according to the relevance of target values. Unlike traditional metrics (e.g., MSE, RMSE), SERA prioritizes prediction accuracy for critical regions of the output space, making it more suitable for imbalanced regression tasks. [32] examined the robustness of machine learning algorithms under uncertainty in domain preferences. Extending SERA, they proposed evaluating models under slight perturbations of the relevance function, identifying models that maintain consistent performance despite changes in relevance assumptions. [40] proposed the Adapted Squared Error Relevance (ASER) metric, which generalizes SERA by introducing both a revised relevance function and an observation weighting scheme. Based on the DenseWeight method [35], ASER assigns more importance to errors on rare, though not necessarily extreme, values, enhancing its alignment with empirical rarity. Finally, [46] introduced localized MAE and RMSE metrics designed to focus specifically on rare values, as defined by the UBL approach using a relevance function and threshold.

## 3.2 Deep Imbalanced Regression

The issue of Imbalanced Learning has recently and naturally extended to unstructured data domains, particularly in image analysis and Natural Language Processing (NLP) tasks [126]. In these contexts, it is often referred to as Deep Long-Tailed Learning [64]. As with structured data, initial efforts focused on binary classification [127, 128], but more recent research has begun to address imbalance in multi-class classification [129] and, increasingly, in regression tasks. However, as in structured settings, regression under imbalance remains a relatively unexplored area with few dedicated solutions to date [64]. The first known link between imbalanced (or long-tailed) learning and regression appears in [130], where the authors tackle information cascade prediction under a long-tailed distribution. Their approach decouples representation learning from the regression step, using a correction sub-network to mitigate bias and improve prediction accuracy.

### 3.2.1 Pre-processing

[61] adapt the concept of similarity and dissimilarity between augmented and original samples from classification to regression. They explore a novel self-supervised learning approach where an agent guides the noise introduced during synthetic data generation to enhance learning. [63] propose a logistic transformation as a pre-processing step to reshape the target distribution before training a neural network, thereby mitigating imbalance. [131] adapt the
Variational Autoencoder (VAE) for imbalanced regression. Unlike the classical VAE, which treats observations as independent and identically distributed, their method incorporates similarity between observations. Each input is encoded into a probabilistic representation, and per-class statistics are computed and smoothed using a kernel-based method. The final representation is refined via whitening-recoloring [55]. The authors also introduce a method to estimate uncertainty errors. With the IRDA approach, [132] extend the concept of implicit data augmentation, commonly used in classification, to regression. They design a new regression loss function tailored to real-world data with unbalanced targets and non-uniform feature distributions. [133] adapt a synthetic data generation method based on CART to address imbalanced regression. Similarly, [134] propose PRIME, a proxy-based method that constructs a balanced and structured feature space, enabling the transfer of class imbalance techniques from classification to regression. Finally, [135] introduce QuanRel, a regularization technique that mitigates the under-representation of rare samples by correcting distorted feature proximities, without relying on label-space continuity.

### 3.2.2 In-processing

The concept of Deep Imbalanced Regression was formalized by [55], who introduced the imbalance problem in unstructured data domains such as computer vision and natural language processing (NLP). They proposed two main preprocessing strategies: (i) smoothing the target distribution (Label Distribution Smoothing, LDS) and the feature distributions (Features Distribution Smoothing, FDS), and (ii) redefining the loss function by weighting it inversely to the LDS. The authors used a Gaussian kernel density estimator for smoothing, discretizing the support of $Y$, computing the mean and covariance within each bin, and applying a whitening-recoloring procedure [136] to transform the data accordingly. They also introduced an adaptation of the Focal-R method from classification [137], which dynamically adjusts weights in the loss function. Notably, the use of kernel density estimators in conjunction with neural networks to handle rare values has precedents, such as in [138] and more recently with DenseWeight [35]. Building on similar ideas, [60] also proposed an arbitrary discretization of $Y$ using uniform intervals, followed by kernel-based smoothing of the target support. Their approach incorporates a cost-sensitive loss function, weighting each bin inversely to its frequency. Like [55], they calculate mean and covariance within bins and apply smoothing, but their contribution differs in the construction of the loss function, which is based on the class-balanced Huber (CBH) loss. Additionally, they introduce CORrelation ALignment (CORAL) to align the latent feature representations with the smoothed targets. Further, [139] addressed the imbalance issue by reframing regression as a classification problem. Emphasizing the importance of bin selection, they proposed a novel partitioning criterion to discretize the target space effectively. [62] propose a regularization technique called RankSim (ranking similarity), which aims to capture both local and global relationships in the data space, an extension of [55], which only considers local relationships via kernel-based methods. The core idea is to ensure that the sorted list of neighbors in the feature space aligns with the sorted list in the target space. In practice, this involves constructing representations such that the neighborhood ranking in the input space mirrors that in the label space. To achieve this, the authors introduce a regularizer based on similarity matrices between the two spaces. As ranking operations are inherently non-differentiable, they approximate them using a family of continuous piecewise-affine interpolation functions. [56] seek to formalize the imbalance problem further, arguing that the commonly used Mean Squared Error (MSE) is unsuitable for imbalanced regression tasks. To address this, they propose a Balanced MSE formulation and offer several implementation variants, showing its superiority over traditional cost-sensitive error weighting strategies. Their framework applies to both univariate and multivariate target variables. For image-based pain recognition, [140] introduce a simple resampling approach along with two weighted metrics, Weighted MSE and Weighted MAE, where averaging is performed based on pain levels. Similarly, [141] propose a quantile-weighted loss function tailored to target distribution imbalance. [142] introduce the Bilateral-Branch Network (BILBN), a dual-branch architecture combining feature extraction and regression. It incorporates a cumulative learning mechanism and a novel loss function, Balanced MSE SPL, to improve visual regression performance under imbalanced label distributions. Following a related path, [143] propose a hierarchical classification-based approach for regression. Their method partitions the continuous target space into discrete hierarchical classes and combines multiple classifiers, each focusing on balancing prediction across different observation subsets. They further integrate hierarchical adjustment and distillation techniques to ensure that the ensemble performs robustly across the full label spectrum. [57] propose a stochastic density-based masking technique to assign greater importance to rarely observed data, combined with feature regularization. Their approach consists of two stages: an encoder first transforms input features, followed by a regressor trained with a weighted loss function. Additionally, two randomly perturbed versions of the input are generated and passed through the encoder. [66] address the imbalance problem using a mixture of experts model combined with uncertainty voting. Multiple specialized experts are trained, and their predictions are aggregated based on uncertainty estimates, improving generalization across underrepresented regions. In a similar effort, [67] introduce Uncertainty VOTing Ensemble (UVOTE), a deep ensemble framework in which $M$ regressors jointly predict both target values and their associated uncertainties. Predictions are then aggregated using uncertainty-aware weights rather than simple averaging, leveraging probabilistic deep learning techniques. [144] propose Label Density-Weighted loss with Ranking Similarity regularization (LDW-RS), which captures local label relationships and
mitigates representational bias. This improves accuracy and generalization, particularly in brain age prediction tasks. Without proposing a direct solution, [145] analyze when and why adding a classification loss improves regression. They show that this auxiliary loss acts as a regularizer, especially in imbalanced scenarios, by mitigating the impact of underrepresented values. [146] introduce Rank-N-Contrast (RNC), a contrastive learning method that builds continuous representations for regression by comparing sample rankings in the target space. [58] adapt a contrastive regularization method from imbalanced classification. Their Contrastive Regularizer (ConR) models both local and global similarities in y, penalizing incorrect proximities and promoting correct ones. They observe that minority samples often blend into majority feature representations, resulting in biased predictions. Like [62], ConR regularizes the latent space to enforce local consistency while preserving global structure. Uniquely, the method operates iteratively and leverages pairwise similarity constraints. As an alternative to classical gradient-based methods, [59] propose context learning to avoid overfitting under-represented regions. Unlike weighted learning, this approach does not require training models from scratch for each dataset. Instead, the pre-trained model adapts to new tasks using contextual examples. IM-Context enables self-conditioning from a sequence of contextual prompts (input-label pairs) to generate predictions without parameter updates. [68] address the problem of limited labeled data by introducing a semi-supervised learning framework for imbalanced regression. Their approach integrates a target deviation function to quantify prediction deviation, a deviation matching strategy to align predicted and true deviations, and an adaptive pseudo-label selection method that dynamically adjusts pseudo-labels to avoid exacerbating data imbalance. This improves generalization, particularly in underrepresented regions. [69, 73] introduce a new loss function, Dist Loss, designed for imbalanced regression. It adjusts the weight given to different values (e.g., age groups) and is computed via a distance metric (MAE or MSE) between expected labels and sorted predictions, enabling better generalization for rare target values. [70] propose a hybrid method combining classification and regression. From a Bayesian standpoint, they decompose the objective into classification and regression tasks. By aggregating labels into ordinal groups, they define an ordinal group contrastive learning loss and employ a multi-expert regressor to maintain data continuity across groups. Finally, [147] introduce the Extreme Loss function, which assigns greater weight to predictions on lower and upper extremes of the target distribution.

## 3.3 Analyses of Solutions

The earliest approaches were grounded in the Utility-Based Learning (UBL) framework. While this methodology effectively addresses the problem by assigning varying importance levels to target values, its main limitation lies in defining an appropriate relevance function. Moreover, most proposed algorithms reformulate the problem as a binary classification task and adapt techniques originally developed for imbalanced classification (cf. 2.3.1). As the definition of Imbalanced Regression has evolved (cf. 2.3.1), it is now more appropriate to develop solutions that directly improve the prediction of rare values, whether extreme or not. Partitioning the target variable may be intuitive in cases involving discrete variables, such as age ([55, 62]). However, for continuous variables, discretization is often arbitrary, potentially unjustified, and may lead to information loss and modeling bias. It also introduces additional complexity and hyperparameters, such as the number of bins and grouping method. Modifying data using the covariance matrix, as in [55, 131], has limitations. Specifically, it fails to capture nonlinear dependencies or higher-order relationships beyond pairwise correlations. Altering data based on this matrix may therefore introduce bias or discard valuable information. Weighting observations inversely to their estimated density using kernel density estimators ([60, 55]) is a promising strategy. However, it is essential to control the assigned weights: highly isolated observations may disproportionately influence the model and degrade its performance on more representative cases. Furthermore, the smoothing window used in density estimation should be determined adaptively based on the data, rather than arbitrarily selected, to ensure robustness. Preprocessing methods also require refinement. In particular: (i) Neighborhood-based methods are often inconsistent, as they generate synthetic data near rare values, which, by definition, lack close neighbors, thus introducing potential bias. (ii) Perturbation-based techniques often disregard existing correlations between features. The generation of target values y should be conditioned on the feature space X, as emphasized by [51]. Additionally, many synthetic data generators fail to accommodate mixed-type features, limiting their applicability in real-world scenarios.

## 3.4 Datasets Benchmark

The most frequently used datasets in Tabular Imbalanced Regression (TIR) and Deep Imbalanced Regression (DIR) are shown in Figures 9a and 9b, respectively. The datasets used in DIR are relatively well-known, having been proposed as benchmarks by [55]. In contrast, the landscape of TIR is more diverse: we identified a total of 236 unique datasets across published studies. To support the scientific community, we compiled a public repository of the 81 most prominent TIR datasets. This collection has been standardized (with the target variable placed in the first column) and fully analyzed. The complete dataset table is presented in the Appendix, and the repository is accessible via the Hugging
Face repository<fnref n="3" />. More specifically, for each dataset, the following information is included: the number of observations (*nobs*), the number of variables (*p_var*), the number of numerical variables (*p_num*) and categorical variables (*p_cat*), the type of the target variable (*Type*), the skewness of the target (*Skew*), the imbalance coefficient (*Imb. Coef.**) as defined in 1, the mean Imbalanced Ratio (*mIR*) proposed by [71], the proportion of missing data (*Miss.*), and the number of times the dataset has been used in published works (*Used*). This repository may serve as a benchmark resource, addressing the concern raised by [6]:

> "Creating a repository of benchmark data sets for this problem. In fact, although several open-access data set repositories exist, no collection of problems with imbalanced domains is currently available for the research community. This is an important issue whose resolution could provide a common baseline for comparison of different solutions in a fair and unified way."

<figure><img src="image_13.png" /><figcaption>Figure 9: Dataset benchmark of Imbalanced Regression: number of uses per dataset</figcaption></figure>

# 4 Discussion and Perspectives

**Conclusions** While imbalance learning has been widely studied in classification, its impact on regression remains much less explored, both in theory and in practice. In this survey, we provided a detailed and in-depth review of the imbalanced regression problem. We focused on the different notions involved and the variety of existing solutions. By carefully reviewing the literature, we pointed out the lack of a clear and commonly accepted definition of imbalance in regression, as also noted by [6]. To address this, we proposed a new general formulation, based on an imbalance coefficient that is scale-invariant, easy to understand, and useful for guiding rebalancing strategies. Our analysis also contributed to bridging the gap between tabular and deep imbalanced regression, two subfields that have addressed the same underlying problem but have so far evolved largely in parallel. In addition, we provided mappings of the main research contributions and datasets used across the literature, offering a structured reference base for future work.

**Limitations** This paper offers initial insights into defining the imbalanced regression problem, emphasizing two key observations: i) a rare value is not necessarily located at the extremes of the distribution, this is particularly evident in multimodal distributions; ii) the notion of rarity is relative and must be defined with respect to a specific reference. This reference may depend on factors such as the importance of rare values for the phenomenon under study, the amount of available data, or the complexity of the data. Indeed, empirical analyses reveal that imbalance alone does not fully explain performance degradation in predictive models. Results also depend on other factors, such as the complexity of the regression task, the size of the dataset, and the presence of noise in the data (see [9, 87, 6, 86, 3]). Many existing techniques aim to increase the influence of rare values, often through weighting schemes or the generation of synthetic observations. However, such approaches carry the risk of giving excessive importance to extremely rare values at the expense of frequent values, which may negatively impact learning.

**Perspectives** In addition to the development of pre-processing, in-processing, and post-processing methods, as well as evaluation metrics, we have identified several promising directions for future research on imbalanced regression.

<footnote n="3">³https://huggingface.co/datasets/samgohan/Tabular_Imbalanced_Regression</footnote>
* Stabilizing weighting functions based on empirical density. To prevent overly emphasizing certain rare values, which could harm model performance, weighting functions should adapt more effectively et dynamically to the data. Additionally, it may be more appropriate to give greater weight to rare values that contribute meaningfully to the predictive task. Current approaches typically base weighting on how rare an observation is, but ideally, weights should also reflect the predictive relevance of those values. For example, two equally rare values might differ significantly: one may be noisy and far from the conditional expectation $E(Y|X)$, while the other is close to $E(Y|X)$ and thus more informative. Finally, the density of the target variable $y$ is often estimated using a Gaussian kernel, which may not be suitable for asymmetric, heavy-tailed, or bounded distributions. In such cases, more appropriate kernels should be considered [51].

* Addressing false rare values. As noted by [18, 6], predicting a rare value with a frequent one should be penalized just as much as the reverse, to avoid a form of reversed overfitting. However, many existing methods only assign high weights to observed rare values, neglecting the cost of misclassifying frequent values as rare. Furthermore, adding weighting schemes may increase the likelihood of predicting rare values, as shown by [88].

* Develop performance metrics that assess model accuracy across both rare and frequent values. For example, a weighted mean squared error may appear lower simply because it improves predictions on rare values, while degrading performance on frequent ones. It is therefore essential to monitor errors across the entire observed range of the target variable, taking care not to obtain an error that is too volatile. Similarly, the train-test split can be paradoxical in practice, as certain values should be included in the training set to enable learning, but also in the test set to allow for the assessment of predictive performance. However, because these values are rare, such a split can be both challenging and particularly impactful.

* Distinguish meaningful rare values from noise. Assigning greater weight to rare values is intuitive and often improves learning and prediction. However, this assumes that all rare values are informative. In practice, rare values may be either relevant (naturally occurring but infrequent) or outliers (errors or anomalies). As suggested by [8], it is important to detect outliers and either correct or exclude them from analysis. Additionally, some extreme values of the target variable $y$ may be unexplainable by the features $X$. These values should be isolated and modeled separately, for example, using extreme value theory, which focuses on the asymptotic behavior of extremes under specific conditions ([148, 149]).

* Improve and optimize synthetic data generators—a paradoxical task, since generating synthetic data requires learning meaningful relationships that the generated data are meant to enhance. The key challenge lies in accurately capturing dependencies between variables to produce realistic samples without biases that distort these dependencies and harm model performance. Future research should focus on training generators that emphasize rare values while leveraging patterns from frequent ones, selecting generator types and parameters suited to the data's characteristics, and ensuring computational efficiency, especially for high-dimensional or large-scale datasets. Before integration into training, synthetic samples should be evaluated for realism, consistency, absence of bias, and diversity (see [150]).

* Address mixed-type data in generators. Handling mixed-type data (i.e., datasets containing both categorical and numerical variables) remains a significant challenge for synthetic data generation. Accurately capturing and reproducing correlations across different variable types is essential for generating high-quality synthetic samples. One promising direction is the use of latent representations, which map mixed-type data into continuous latent spaces where dependencies can be more effectively modeled and preserved [1, 119].

* Assign greater credibility to observed rare values than to synthetic ones. Most synthetic oversampling methods rebalance datasets by generating artificial observations. However, a common limitation is that synthetic and real observations are typically treated with equal importance during training. Given the potential limitations and approximation errors in data generation processes, it is advisable to assign higher weight or credibility to real observations. This perspective aligns with practices in multiple imputation for missing data, where imputed values are treated with more uncertainty than observed ones [151].

* Conduct a theoretical analysis of the imbalanced regression phenomenon, as emphasized by [6]: "Why and when will a particular technique developed for the problem of imbalanced domains fail or succeed? The reasons behind this unstable behavior are not understood, and we believe that only with more efforts regarding the theoretical foundations of imbalanced domains we will be able to answer this question. The lack of a theoretical understanding of the problem is holding back the evolution of the solutions." It is also important to examine the theoretical properties of synthetic data generators (e.g., [51]), which, despite widespread use and empirical validation, lack strong theoretical grounding and often show dataset-dependent performance.
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# Appendix

## 4.1 Tabular Imbalanced Regression Work
<table><thead><tr><th>Reference</th><th>Paper</th><th>Year</th><th>Contribution Type</th><th>Method Type</th><th>Code</th><th>Data</th></tr></thead><tbody><tr><td>[11]</td><td>Predicting Outliers</td><td>2003</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[12]</td><td>Rule-Based Prediction of Rare Extreme Values</td><td>2006</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[13]</td><td>Predicting Rare Extreme Values</td><td>2006</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✗</td></tr><tr><td>[16]</td><td>Utility-Based Regression</td><td>2007</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✗</td></tr><tr><td>[17]</td><td>Utility-based Performance Measures for Regression</td><td>2008</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✗</td></tr><tr><td>[14]</td><td>Precision and Recall for Regression</td><td>2009</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✗</td></tr><tr><td>[18]</td><td>Utility-based Regression</td><td>2011</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✗</td></tr><tr><td>[104]</td><td>An extended tuning method for cost-sensitive regression and forecasting</td><td>2011</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[19]</td><td>SMOTE for Regression</td><td>2013</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[152]</td><td>Imbalanced learning: foundations, algorithms, and applications</td><td>2013</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[20]</td><td>Resampling strategies for regression</td><td>2014</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[8]</td><td>Learning from imbalanced data: open challenges and future directions</td><td>2016</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[21]</td><td>UBL: an R Package for Utility-Based Learning</td><td>2016</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✗</td></tr><tr><td>[6]</td><td>A Survey of Predictive Modeling on Imbalanced Domains</td><td>2016</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[116]</td><td>Learning from imbalanced data for predicting the number of software defects</td><td>2017</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[114]</td><td>Learning Through Utility Optimization in Regression Tasks</td><td>2017</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[34]</td><td>Evaluation of Ensemble Methods in Imbalanced Regression Tasks</td><td>2017</td><td>Analyses</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[22]</td><td>SMOGN: a Pre-processing Approach for Imbalanced Regression</td><td>2017</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[25]</td><td>Exploring Resampling with Neighborhood Bias on Imbalanced Regression Problems</td><td>2017</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[115]</td><td>SMOTEBoost for Regression</td><td>2018</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[26]</td><td>Pre-processing approaches for imbalanced distributions in regression</td><td>2018</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[27]</td><td>REBAGG: REsampled BAGGING for Imbalanced Regression</td><td>2018</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[30]</td><td>SMOTE for Learning from Imbalanced Data</td><td>2018</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[28]</td><td>Utility-based Predictive Analytics</td><td>2018</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[9]</td><td>Learning from Imbalanced Data Sets</td><td>2018</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[86]</td><td>A Study on the Impact of Data Characteristics</td><td>2019</td><td>Analyses</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[107]</td><td>Biased Resampling Strategies</td><td>2019</td><td>Extension</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[31]</td><td>Imbalanced regression and extreme value prediction</td><td>2020</td><td>Methods</td><td>Metrics</td><td>✓</td><td>✓</td></tr><tr><td>[108]</td><td>Improving enzyme optimum temperature prediction</td><td>2020</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>Specific</td></tr><tr><td>[35]</td><td>Density-based weighting for imbalanced regression</td><td>2021</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✗</td></tr><tr><td>[36]</td><td>A novel cost-sensitive algorithm and new evaluation strategies</td><td>2021</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✗</td></tr><tr><td>[37]</td><td>Sampling To Improve Predictions For Underrepresented Observations In Imbalanced Data</td><td>2021</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr></tbody></table>
<table><thead><tr><th>Reference</th><th>Paper</th><th>Year</th><th>Contribution Type</th><th>Method Type</th><th>Code</th><th>Data</th></tr></thead><tbody><tr><td>[153]</td><td>Chebyshev approaches for imbalanced data streams regression models</td><td>2021</td><td>Extension</td><td>Specific Case</td><td>✓</td><td>✓</td></tr><tr><td>[39]</td><td>DistSMOGN: Distributed SMOGN for Imbalanced Regression Problems</td><td>2022</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[85]</td><td>Geometric SMOTE for regression</td><td>2022</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✓</td></tr><tr><td>[33]</td><td>Model Optimization in Imbalanced Regression</td><td>2022</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[38]</td><td>A boosting resampling method based on CVAE</td><td>2022</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[32]</td><td>Robustness Evaluation of Regression Tasks</td><td>2022</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✗</td></tr><tr><td>[5]</td><td>A Survey of Learning with Imbalanced Data</td><td>2023</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[40]</td><td>ASER: Adapted squared error relevance</td><td>2023</td><td>Methods</td><td>Metrics</td><td>✗</td><td>✓</td></tr><tr><td>[154]</td><td>Imbalanced Mixed Linear Regression</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>Specific</td><td>Specific</td></tr><tr><td>[77]</td><td>Semi-Supervised Graph Imbalanced Regression</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>Specific</td><td>Specific</td></tr><tr><td>[4]</td><td>A broad review on class imbalance learning techniques</td><td>2023</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[1]</td><td>A Review of Machine Learning Techniques in Imbalanced Data</td><td>2023</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[41]</td><td>Enhancing soft computing techniques</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✓</td></tr><tr><td>[42]</td><td>Imbalanced regression using regressor-classifier ensembles</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[78]</td><td>Multi-output Regression for Imbalanced Data Stream</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>✓</td><td>✗</td></tr><tr><td>[65]</td><td>Unbalanced regression sample generation algorithm</td><td>2023</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[88]</td><td>Adapting a deep convolutional RNN model</td><td>2023</td><td>Analyses</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[155]</td><td>Spatial-SMOTE for handling imbalance in spatial regression tasks</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>n/a</td><td>n/a</td></tr><tr><td>[110]</td><td>ImbalancedLearningRegression - Python Package</td><td>2023</td><td>Package</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[76]</td><td>Data Augmentation for Imbalanced Regression</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>✗</td><td>✗</td></tr><tr><td>[52]</td><td>Imbalance in Regression Datasets</td><td>2024</td><td>Analyses</td><td>NA</td><td>✗</td><td>✓</td></tr><tr><td>[43]</td><td>Oversampling Techniques for Imbalanced Data in Regression</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✓</td></tr><tr><td>[3]</td><td>Resampling strategies for imbalanced regression</td><td>2024</td><td>Analyses</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[2]</td><td>A survey on imbalanced learning</td><td>2024</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[72]</td><td>Research on Imbalanced Data Regression Based on Confrontation</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[44]</td><td>A novel gradient boosting approach for imbalanced regression</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[45]</td><td>Affine combination-based oversampling for imbalanced regression</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✓</td></tr><tr><td>[46]</td><td>Rare event prediction with adaptive weighted SVR</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[47]</td><td>Sparse feature selection and rare value prediction</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr></tbody></table>
<table><thead><tr><th>Reference</th><th>Paper</th><th>Year</th><th>Contribution Type</th><th>Method Type</th><th>Code</th><th>Data</th></tr></thead><tbody><tr><td>[48]</td><td>WSMOTER: a novel approach for imbalanced regression</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[51]</td><td>Generalized Oversampling for Learning from Imbalanced datasets</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[119]</td><td>Data Augmentation with Variational Autoencoder for Imbalanced Dataset</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[75]</td><td>Boarding for ISS: Imbalanced Self-Supervised</td><td>2024</td><td>Extension</td><td>Specific Case</td><td>✗</td><td>✗</td></tr><tr><td>[49]</td><td>A Selective Under-Sampling (SUS) Method</td><td>2025</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✓</td></tr><tr><td>[53]</td><td>Error Distribution Smoothing</td><td>2025</td><td>Analyses</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[111]</td><td>KNNOR-Reg: a python package for oversampling</td><td>2025</td><td>Package</td><td>NA</td><td>✓</td><td>✗</td></tr><tr><td>[54]</td><td>Uncertainty quantification driven ML</td><td>2025</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✓</td></tr><tr><td>[71]</td><td>Quantification of Data Imbalance</td><td>2025</td><td>Analyses</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[120]</td><td>An Investigation of Imbalanced Regression Loss Functions</td><td>2025</td><td>Analyses</td><td>NA</td><td>✗</td><td>✗</td></tr></tbody></table>

## 4.2 Deep Imbalanced Regression Work

<table><thead><tr><th>Reference</th><th>Paper</th><th>Year</th><th>Contribution Type</th><th>Method Type</th><th>Code</th><th>Data</th></tr></thead><tbody><tr><td>[55]</td><td>Delving into Deep Imbalanced Regression</td><td>2021</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[130]</td><td>Decoupling Representation and Regressor for Long-Tailed Information Cascade Prediction</td><td>2021</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[139]</td><td>Uniformity in heterogeneity: Diving deep into count interval partition for crowd counting</td><td>2021</td><td>Methods</td><td>Specific Case</td><td>✗</td><td>✗</td></tr><tr><td>[56]</td><td>Balanced MSE for Imbalanced Visual Regression</td><td>2022</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[60]</td><td>Deep imbalanced regression using cost-sensitive learning and deep feature transfer for bearing remaining useful life estimation</td><td>2022</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[61]</td><td>Lifting imbalanced regression with self-supervised learning</td><td>2022</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[62]</td><td>RankSim: Ranking Similarity Regularization for Deep Imbalanced Regression</td><td>2022</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[140]</td><td>Imbalanced regression for intensity series of pain expression from videos by regularizing spatiotemporal face nets</td><td>2022</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[84]</td><td>C-mixup: Improving generalization in regression</td><td>2022</td><td>NA</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[142]</td><td>Bilateral-Branch Network for Imbalanced Visual Regression</td><td>2022</td><td>Methods</td><td>In-processing</td><td>n/a</td><td>n/a</td></tr><tr><td>[5]</td><td>A Survey of Learning with Imbalanced Data, Representation Learning and SEP Forecasting</td><td>2023</td><td>Survey</td><td>NA</td><td>✗</td><td>✗</td></tr><tr><td>[63]</td><td>Dealing with imbalanced regression problem using scalable ANN</td><td>2023</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[143]</td><td>Deep Imbalanced Regression via Hierarchical Classification Adjustment</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr></tbody></table>
<table><thead><tr><th>Reference</th><th>Paper</th><th>Year</th><th>Contribution Type</th><th>Method Type</th><th>Code</th><th>Data</th></tr></thead><tbody><tr><td>[64]</td><td>Deep Long-Tailed Learning: A Survey</td><td>2023</td><td>Survey</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[57]</td><td>Toward a Balanced Feature Space for the Deep Imbalanced Regression</td><td>2023</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[79]</td><td>Imbalanced Label Distribution Learning</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>✓</td><td>✓</td></tr><tr><td>[66]</td><td>Mixture of Experts with Uncertainty Voting for Imbalanced Deep Regression Problems</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[80]</td><td>Multi domain imbalanced regression</td><td>2023</td><td>Extension</td><td>Specific Case</td><td>✗</td><td>✗</td></tr><tr><td>[144]</td><td>LDW-RS Loss for Imbalanced Deep Fetal Brain Age Regression</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[141]</td><td>A scalable thin-film defect quantify model under imbalanced regression</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✓</td></tr><tr><td>[145]</td><td>Astep towards understanding why classification helps regression</td><td>2023</td><td>Analyses</td><td>NA</td><td>✓</td><td>✓</td></tr><tr><td>[146]</td><td>Rank-N-Contrast: Learning Continuous Representations for Regression</td><td>2023</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[58]</td><td>CONR: CONTRASTIVE REGULARIZER FOR DEEP IMBALANCED REGRESSION</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[59]</td><td>IM-Context: In-Context Learning for Imbalanced Regression Tasks</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✓</td><td>?</td></tr><tr><td>[132]</td><td>IRDA: Implicit data augmentation for deep imbalanced regression</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✗</td><td>✗</td></tr><tr><td>[131]</td><td>Variational Imbalanced Regression: Fair Uncertainty Quantification</td><td>2024</td><td>Methods</td><td>Pre-processing</td><td>✓</td><td>✓</td></tr><tr><td>[68]</td><td>Boosting semi-supervised learning under imbalanced regression</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[69]</td><td>Deep Imbalanced Regression to Estimate Vascular Age from PPG Data</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[73]</td><td>DIST LOSS: Enhancing Regression in Few-shot Region</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[70]</td><td>Leveraging Group Classification with Descending Soft Labeling</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✗</td></tr><tr><td>[67]</td><td>Uncertainty Voting Ensemble for Imbalanced Deep Regression</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✓</td><td>✓</td></tr><tr><td>[147]</td><td>Predicting Crop Yield Low Through Binned Deep Imbalanced Regression</td><td>2024</td><td>Methods</td><td>In-processing</td><td>✗</td><td>✓</td></tr></tbody></table>

## 4.3 Tabular Imbalanced Regression Datasets

The table below shows the characteristics of the Tabular Imbalanced Regression datasets available in the HuggingFace public repository<fnref n="4" />. For each dataset, the following information is provided: the number of observations (nobs), the number of variables (p_var), the number of numerical variables (p_num) and categorical variables (p_cat), the type of the target variable (Type), the skewness of the target variable (Skew), the imbalance coefficient (Imb. Coef.) as previously defined in 1, the mean Imbalanced Ratio (mIR) proposed by [71], the proportion of missing data (Miss.), and the number of times the dataset has been used in published papers (Used).

<table><caption>Table 3: TIR Datasets Characteristics</caption><thead><tr><th>Dataset</th><th>nobs</th><th>p_var</th><th>p_num</th><th>p_cat</th><th>Type</th><th>Skew</th><th>Imb. Coef.</th><th>mIR</th><th>Miss.</th><th>Used</th></tr></thead><tbody><tr><td>abalone</td><td>4177</td><td>11</td><td>11</td><td>0</td><td>int</td><td>1.11</td><td>54.23</td><td>345.73</td><td>0.0</td><td>32</td></tr><tr><td>boston</td><td>506</td><td>14</td><td>14</td><td>0</td><td>float</td><td>1.1</td><td>36.0</td><td>218.31</td><td>0.0</td><td>30</td></tr><tr><td>accel</td><td>1732</td><td>23</td><td>23</td><td>0</td><td>float</td><td>0.77</td><td>51.58</td><td>292.14</td><td>0.0</td><td>23</td></tr></tbody></table>

<footnote n="4">⁴https://huggingface.co/datasets/samgohan/Tabular_Imbalanced_Regression</footnote>
Running Title for Header

<table><thead><tr><th>Dataset</th><th>nobs</th><th>p_var</th><th>p_num</th><th>p_cat</th><th>Type</th><th>Skew</th><th>Imb. Coef.</th><th>mIR</th><th>Miss.</th><th>Used</th></tr></thead><tbody><tr><td>availPwr</td><td>1802</td><td>16</td><td>9</td><td>7</td><td>int</td><td>1.9</td><td>55.97</td><td>348.26</td><td>0.0</td><td>23</td></tr><tr><td>cpusm</td><td>8192</td><td>13</td><td>13</td><td>0</td><td>int</td><td>-3.42</td><td>63.69</td><td>358.7</td><td>0.0</td><td>23</td></tr><tr><td>a7</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>3.72</td><td>70.01</td><td>456.38</td><td>0.0</td><td>22</td></tr><tr><td>bank8fm</td><td>4499</td><td>9</td><td>9</td><td>0</td><td>float</td><td>1.08</td><td>44.18</td><td>252.74</td><td>0.0</td><td>22</td></tr><tr><td>a1</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>1.46</td><td>46.56</td><td>242.44</td><td>0.0</td><td>20</td></tr><tr><td>airfoil</td><td>1503</td><td>6</td><td>6</td><td>0</td><td>float</td><td>-0.42</td><td>31.86</td><td>189.28</td><td>0.0</td><td>18</td></tr><tr><td>fuelCons</td><td>1764</td><td>38</td><td>26</td><td>12</td><td>float</td><td>1.14</td><td>52.08</td><td>303.6</td><td>0.0</td><td>18</td></tr><tr><td>maxTorque</td><td>1802</td><td>33</td><td>20</td><td>13</td><td>int</td><td>1.63</td><td>55.67</td><td>331.58</td><td>0.0</td><td>18</td></tr><tr><td>a2</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>2.41</td><td>61.29</td><td>365.26</td><td>0.0</td><td>16</td></tr><tr><td>a3</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>2.47</td><td>62.7</td><td>391.33</td><td>0.0</td><td>16</td></tr><tr><td>a4</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>5.96</td><td>77.89</td><td>624.82</td><td>0.0</td><td>15</td></tr><tr><td>a6</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>3.14</td><td>67.32</td><td>453.93</td><td>0.0</td><td>15</td></tr><tr><td>heat</td><td>7400</td><td>12</td><td>12</td><td>0</td><td>float</td><td>1.63</td><td>56.2</td><td>365.29</td><td>0.0</td><td>14</td></tr><tr><td>a5</td><td>198</td><td>12</td><td>9</td><td>3</td><td>float</td><td>2.33</td><td>59.89</td><td>335.47</td><td>0.0</td><td>13</td></tr><tr><td>machineCpu</td><td>209</td><td>7</td><td>7</td><td>0</td><td>int</td><td>3.86</td><td>68.46</td><td>487.1</td><td>0.0</td><td>13</td></tr><tr><td>mortgage</td><td>1049</td><td>16</td><td>16</td><td>0</td><td>float</td><td>1.03</td><td>33.32</td><td>198.8</td><td>0.0</td><td>13</td></tr><tr><td>servo</td><td>167</td><td>5</td><td>3</td><td>2</td><td>float</td><td>1.77</td><td>54.11</td><td>305.16</td><td>0.0</td><td>12</td></tr><tr><td>treasury</td><td>1049</td><td>16</td><td>16</td><td>0</td><td>float</td><td>1.33</td><td>43.97</td><td>242.9</td><td>0.0</td><td>11</td></tr><tr><td>deltaAilerons</td><td>7129</td><td>6</td><td>6</td><td>0</td><td>float</td><td>-0.15</td><td>43.91</td><td>258.89</td><td>0.0</td><td>10</td></tr><tr><td>forestFires</td><td>517</td><td>13</td><td>13</td><td>0</td><td>float</td><td>12.81</td><td>90.15</td><td>1824.05</td><td>0.0</td><td>10</td></tr><tr><td>fremotor1prem0304a_sev</td><td>51949</td><td>31</td><td>17</td><td>14</td><td>int</td><td>170.33</td><td>98.64</td><td>57674.8</td><td>4.34</td><td>10</td></tr><tr><td>dataset_Facebook</td><td>500</td><td>19</td><td>18</td><td>1</td><td>int</td><td>9.68</td><td>84.84</td><td>1234.7</td><td>0.06</td><td>9</td></tr><tr><td>debutanizer</td><td>2394</td><td>8</td><td>8</td><td>0</td><td>float</td><td>1.71</td><td>48.21</td><td>291.81</td><td>0.0</td><td>9</td></tr><tr><td>strikes</td><td>625</td><td>7</td><td>7</td><td>0</td><td>int</td><td>6.4</td><td>78.86</td><td>837.8</td><td>0.0</td><td>9</td></tr><tr><td>student-mat</td><td>395</td><td>33</td><td>16</td><td>17</td><td>int</td><td>0.24</td><td>24.1</td><td>157.34</td><td>0.0</td><td>9</td></tr><tr><td>ailerons</td><td>13750</td><td>41</td><td>41</td><td>0</td><td>float</td><td>-1.35</td><td>57.42</td><td>363.56</td><td>0.0</td><td>8</td></tr><tr><td>wine_quality</td><td>6497</td><td>12</td><td>12</td><td>0</td><td>float</td><td>0.19</td><td>60.26</td><td>515.63</td><td>0.0</td><td>8</td></tr><tr><td>autoPrice</td><td>205</td><td>26</td><td>16</td><td>10</td><td>int</td><td>1.79</td><td>48.82</td><td>266.97</td><td>0.0</td><td>7</td></tr><tr><td>elevators</td><td>16599</td><td>19</td><td>19</td><td>0</td><td>int</td><td>0.15</td><td>44.14</td><td>248.2</td><td>0.0</td><td>7</td></tr><tr><td>baseball</td><td>337</td><td>17</td><td>17</td><td>0</td><td>int</td><td>1.16</td><td>42.7</td><td>244.45</td><td>0.0</td><td>6</td></tr><tr><td>californiaHousing</td><td>20640</td><td>9</td><td>9</td><td>0</td><td>int</td><td>0.98</td><td>31.16</td><td></td><td>0.0</td><td>6</td></tr><tr><td>triazines</td><td>186</td><td>61</td><td>61</td><td>0</td><td>float</td><td>-1.34</td><td>37.29</td><td>217.24</td><td>0.0</td><td>6</td></tr><tr><td>analcatdata_apnea3</td><td>450</td><td>12</td><td>12</td><td>0</td><td>float</td><td>5.0</td><td>82.68</td><td>859.26</td><td>0.0</td><td>5</td></tr><tr><td>cpuAct</td><td>8192</td><td>22</td><td>22</td><td>0</td><td>int</td><td>-3.42</td><td>63.69</td><td>358.7</td><td>0.0</td><td>5</td></tr><tr><td>diabetes</td><td>43</td><td>3</td><td>3</td><td>0</td><td>float</td><td>-0.23</td><td>29.83</td><td>196.25</td><td>0.0</td><td>5</td></tr><tr><td>house8H</td><td>22784</td><td>9</td><td>8</td><td>1</td><td>int</td><td>3.75</td><td>69.98</td><td></td><td>0.0</td><td>5</td></tr><tr><td>kinematics8fh</td><td>8192</td><td>9</td><td>9</td><td>0</td><td>float</td><td>-0.4</td><td>45.58</td><td>256.79</td><td>0.0</td><td>5</td></tr><tr><td>laser</td><td>993</td><td>5</td><td>5</td><td>0</td><td>int</td><td>1.19</td><td>42.06</td><td>245.05</td><td>0.0</td><td>5</td></tr><tr><td>musicorigin</td><td>1059</td><td>118</td><td>118</td><td>0</td><td>float</td><td>3.21</td><td>66.67</td><td>486.74</td><td>0.0</td><td>5</td></tr><tr><td>pollen</td><td>3848</td><td>5</td><td>5</td><td>0</td><td>float</td><td>-0.13</td><td>42.93</td><td>245.29</td><td>0.0</td><td>5</td></tr><tr><td>space_ga</td><td>3107</td><td>7</td><td>7</td><td>0</td><td>float</td><td>-1.02</td><td>71.07</td><td>496.47</td><td>0.0</td><td>5</td></tr><tr><td>wages</td><td>534</td><td>11</td><td>4</td><td>7</td><td>float</td><td>1.69</td><td>56.78</td><td>329.52</td><td>0.0</td><td>5</td></tr><tr><td>ele-1</td><td>495</td><td>3</td><td>3</td><td>0</td><td>float</td><td>1.51</td><td>49.24</td><td>275.72</td><td>0.0</td><td>4</td></tr><tr><td>ele-2</td><td>1056</td><td>5</td><td>5</td><td>0</td><td>float</td><td>1.44</td><td>44.31</td><td>261.91</td><td>0.0</td><td>4</td></tr><tr><td>quake</td><td>2178</td><td>4</td><td>4</td><td>0</td><td>float</td><td>1.3</td><td>50.91</td><td>286.97</td><td>0.0</td><td>4</td></tr><tr><td>sulfur</td><td>10081</td><td>6</td><td>6</td><td>0</td><td>float</td><td>2.5</td><td>73.58</td><td>738.32</td><td>0.0</td><td>4</td></tr><tr><td>NO2Emissions</td><td>500</td><td>8</td><td>8</td><td>0</td><td>float</td><td>-0.55</td><td>44.96</td><td>266.89</td><td>0.0</td><td>3</td></tr><tr><td>wankara</td><td>1609</td><td>10</td><td>10</td><td>0</td><td>float</td><td>0.02</td><td>17.64</td><td>135.47</td><td>0.0</td><td>3</td></tr><tr><td>energy</td><td>19735</td><td>28</td><td>28</td><td>0</td><td>int</td><td>3.39</td><td>74.6</td><td>990.58</td><td>0.0</td><td>2</td></tr><tr><td>superconductivity</td><td>21263</td><td>82</td><td>82</td><td>0</td><td>float</td><td>0.86</td><td>46.97</td><td>301.53</td><td>0.0</td><td>2</td></tr><tr><td>AmesHousing</td><td>2930</td><td>82</td><td>39</td><td>43</td><td>int</td><td>1.74</td><td>58.78</td><td></td><td>6.55</td><td>1</td></tr><tr><td>AutoBi</td><td>1340</td><td>8</td><td>8</td><td>0</td><td>float</td><td>25.69</td><td>94.24</td><td>4290.81</td><td>2.85</td><td>1</td></tr><tr><td>avocado</td><td>18249</td><td>13</td><td>10</td><td>3</td><td>float</td><td>0.58</td><td>45.34</td><td>250.35</td><td>0.0</td><td>1</td></tr><tr><td>cocomo_numeric</td><td>60</td><td>57</td><td>57</td><td>0</td><td>float</td><td>2.61</td><td>60.26</td><td>321.34</td><td>0.0</td><td>1</td></tr><tr><td>College</td><td>777</td><td>19</td><td>17</td><td>2</td><td>int</td><td>-0.11</td><td>37.58</td><td>213.18</td><td>0.0</td><td>1</td></tr><tr><td>communitiesCrime</td><td>1994</td><td>127</td><td>127</td><td>0</td><td>float</td><td>1.52</td><td>42.98</td><td>246.4</td><td>0.0</td><td>1</td></tr><tr><td>concreteStrength</td><td>1030</td><td>9</td><td>9</td><td>0</td><td>float</td><td>0.42</td><td>25.74</td><td>166.68</td><td>0.0</td><td>1</td></tr><tr><td>delta_ailerons</td><td>7129</td><td>6</td><td>6</td><td>0</td><td>float</td><td>0.29</td><td>68.04</td><td>580.68</td><td>0.0</td><td>1</td></tr><tr><td>delta_elv</td><td>9517</td><td>7</td><td>7</td><td>0</td><td>float</td><td>0.16</td><td>38.24</td><td>215.0</td><td>0.0</td><td>1</td></tr><tr><td>electrical</td><td>10000</td><td>14</td><td>13</td><td>1</td><td>float</td><td>-0.0</td><td>3.66</td><td>105.7</td><td>0.0</td><td>1</td></tr><tr><td>hour</td><td>17379</td><td>17</td><td>16</td><td>1</td><td>int</td><td>1.28</td><td>47.0</td><td>273.61</td><td>0.0</td><td>1</td></tr><tr><td>house</td><td>22784</td><td>17</td><td>17</td><td>0</td><td>float</td><td>3.75</td><td>69.98</td><td></td><td>0.0</td><td>1</td></tr><tr><td>housing</td><td>1460</td><td>81</td><td>38</td><td>43</td><td>int</td><td>1.88</td><td>58.35</td><td></td><td>6.62</td><td>1</td></tr><tr><td>Housing_2</td><td>545</td><td>13</td><td>6</td><td>7</td><td>int</td><td>1.21</td><td>43.52</td><td></td><td>0.0</td><td>1</td></tr></tbody></table>
<table><thead><tr><th>Dataset</th><th>n_ob</th><th>p_var</th><th>p_num</th><th>p_cat</th><th>Type</th><th>Skew</th><th>Imb. Coef.</th><th>mIR</th><th>Miss.</th><th>Used</th></tr></thead><tbody><tr><td>insurance</td><td>1338</td><td>7</td><td>4</td><td>3</td><td>float</td><td>1.51</td><td>49.56</td><td>276.45</td><td>0.0</td><td>1</td></tr><tr><td>kdd_coil_1</td><td>316</td><td>19</td><td>19</td><td>0</td><td>float</td><td>1.45</td><td>45.75</td><td>243.23</td><td>0.0</td><td>1</td></tr><tr><td>lungcancer_shedden</td><td>442</td><td>25</td><td>25</td><td>0</td><td>float</td><td>0.94</td><td>40.87</td><td>216.06</td><td>0.0</td><td>1</td></tr><tr><td>meta</td><td>528</td><td>66</td><td>66</td><td>0</td><td>float</td><td>14.65</td><td>92.53</td><td>1880.28</td><td>0.0</td><td>1</td></tr><tr><td>pdgfr</td><td>79</td><td>321</td><td>321</td><td>0</td><td>float</td><td>-0.64</td><td>25.99</td><td>171.82</td><td>0.0</td><td>1</td></tr><tr><td>pendigits</td><td>10992</td><td>17</td><td>17</td><td>0</td><td>int</td><td>0.03</td><td>10.25</td><td>110.63</td><td>0.0</td><td>1</td></tr><tr><td>PricingGame</td><td>100021</td><td>20</td><td>14</td><td>6</td><td>float</td><td>7.4</td><td>89.52</td><td>8627.91</td><td>0.0</td><td>1</td></tr><tr><td>puma32h</td><td>8192</td><td>33</td><td>33</td><td>0</td><td>float</td><td>-0.02</td><td>4.6</td><td>107.38</td><td>0.0</td><td>1</td></tr><tr><td>qsar_aquatic_toxicity</td><td>546</td><td>9</td><td>9</td><td>0</td><td>float</td><td>0.32</td><td>38.27</td><td>223.42</td><td>0.0</td><td>1</td></tr><tr><td>red_wine</td><td>1599</td><td>12</td><td>12</td><td>0</td><td>int</td><td>0.22</td><td>52.19</td><td>392.51</td><td>0.0</td><td>1</td></tr><tr><td>sensory</td><td>576</td><td>12</td><td>12</td><td>0</td><td>float</td><td>-0.04</td><td>37.04</td><td>219.66</td><td>0.0</td><td>1</td></tr><tr><td>SynchronousMachine</td><td>557</td><td>5</td><td>5</td><td>0</td><td>float</td><td>0.0</td><td>8.22</td><td>113.58</td><td>0.0</td><td>1</td></tr><tr><td>telematics_syn-032021</td><td>100000</td><td>51</td><td>43</td><td>8</td><td>float</td><td>22.7</td><td>96.34</td><td>28783.35</td><td>0.0</td><td>1</td></tr><tr><td>yacht_hydrodynamics</td><td>308</td><td>7</td><td>7</td><td>0</td><td>float</td><td>1.75</td><td>52.68</td><td>289.73</td><td>0.0</td><td>1</td></tr></tbody></table>