PRIME: Deep Imbalanced Regression with Proxies
Authors: Jongin Lim
Sucheol Lee
Daeho Um
Sung-Un Park
Jinwoo Shin
Venue: ICML 2025 poster (2025)
Keywords: Imbalanced Regression
Representation Learning
Proxy
Primary area: deep_learning->other_representation_learning
TL;DR: This paper introduces PRIME, a novel proxy-based representation learning scheme for imbalanced regression.

Abstract: Data imbalance remains a fundamental challenge in real-world machine learning. However, most existing work has focused on classification, leaving imbalanced regression underexplored despite its importance in many applications. To address this gap, we propose PRIME, a framework that leverages learnable proxies to construct a balanced and well-ordered feature space for imbalanced regression. At its core, PRIME arranges proxies to be uniformly distributed in the feature space while preserving the ordinal structure of regression targets, and then aligns each sample feature to its corresponding proxy. By using proxies as reference points, PRIME induces the desired structure of learned representations, promoting better generalization, especially in underrepresented target regions. Moreover, since proxy-based alignment resembles classification, PRIME enables the seamless application of class imbalance techniques to regression, facilitating more balanced feature learning. Extensive experiments demonstrate the effectiveness and broad applicability of PRIME, achieving state-of-the-art performance on four real-world regression benchmark datasets across diverse target domains.

PRIME:
Deep Imbalanced Regression with Proxies
Jongin Lim Sucheol Lee'
Daeho Um
Sung-Un Park
Jinwoo Shin
Abstract
Proxy loss (Cyow)) loss (Gag))
Feature Space (E")
Data imbalance remains fundamental challenge in real-world machine learning. However, most ex- isting work has focused on classification, leaving imbalanced regression underexplored despite its importance in many applications. To address this gap, we propose PRIME, a framework that lever- ages learnable proxies construct balanced and well-ordered feature space for imbalanced regres- sion. At its core, PRIME arranges proxies to be uniformly distributed in the feature space while preserving the ordinal structure of regression tar- gets, and then aligns each sample feature to its corresponding proxy. By using proxies as refer- ence points, PRIME induces the desired struc- ture of Icarned representations, promoting better generalization, especially in underrepresented tar- get regions. Moreover, since proxy-based align- ment resembles classification, PRIME enables the seamless application class imbalance tech- niques regression, facilitating more balanced feature learning. Extensive experiments demon- strate the effectiveness and broad applicability of PRIME, achieving state-of-the-ard performance on four real-wer world regression benchmark datasets across diverse target domains.
X:
1
21
61
y:
Sample
(Minority)
Proxies
Figure 1. An overview of PRIME. Given sample, PRIME lever- ages synthetic reference points, termed proxies, to facilitate feature Icarning. These proxies provide global guidance for effective posi- tioning in the feature space, even for minority samples, enabling model f to learn balanced and well-ordered representations.
primarily focused on classification setups, leaving deep im- balanced regression (DIR) underexplored (Yang et al., 2021), despite its significance in various applications.
Unlike classification, regression deals with continuous tar- gets, making it challenging to apply the notion of class imbalance directly. Early works DIR adapted techniques from imbalanced classification, such as re-weighting (Yang et al., 2021; Steininger et al., 2021) or logit adjustment (Ren et al., 2022), with minor modifications to handle continuous targets. Although intuitive, these methods mainly focus on adjusting loss functions for the final predictions without con- sidering the underlying feature representations, As result, the learned representations 2023) and fail to reflect the ordinal relationships of target values (Gong et al., 2022), limiting their effectiveness in real-world applications (Zhang et al., 2023a).
1. Introduction
Data imbalance is prominent, yet standitanding challenge in most real-world machine learning scenarios (Buda et al., 2018), where certain target values are significantly underrep- resented. This imbalance hinders deep models from effec- tively generalizing minority groups with limited training samples, driving extensive research efforts address this challenge (Liu et al., 2019b; Tang et al., 2020; Menon al., 2021; Zhang et al., 2023b). However, most studies have
often fragmented (Zha et al.,
tackle these issues, recent studies (Gong et al., 2022: Keramati et al., 2024) have explored representation learn- ing approaches for DIR. Specifically, better reflect the continuous nature of regression targets, these methods im- pose additional feature regularization terms that encourage samples closer in target space to be positioned closer in fea- ture space. While demonstrating promising results, previous representation learning methods suffer from inherent limi- tations, as they rely solely on sample relationships within
'AI Center, Samsung Electronics *Korea Advanced Institute of Science and Technology (KAIST). Correspondence to: Jongin Lim <jonny.lim samsung.com
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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PRIME; Deep Imbalanced Regression with Proxies
individual batches. Due data imbalance, batches predom- inantly contain samples with majority targets, causing the learned representations to be biased toward the majority while overlooking or misreppesenting samples with minority targets. Furthermore, representations of minority samples often collapse into those of the majority, which hampers generalization for minority targets. In short, existing repre- sentation learning methods remain insufficient for mitigating data imbalance in regression tasks.
of class imbalance techniques regression setups, bridging imbalanced regression and classification. (iii) We theoreti- cally demonstrate that PRIME provides bound on the gen- eralization eπror under balanced test criteria. (iv) Extensive experiments demonstrate the effectiveness and broad appli- cability of PRIME, achieving up to 9.0%, 2.0%, 4.5%, and 3.7% lower regression error on minority targets compared to sate-of-the-aae methods on Age D--DIR IMDB-WIKI- -IKI-I,R,, NYUD2-DIR, and STS-B- respectively.
In this paper, we propose Proxy-based Representation learn- ing for IMbalanced rEgression (PRIME), a novel represen- tation learning scheme for DIR that effectively addresses the aforementioned limitations. Figure 1 provides an overview of PRIME. Proxies (Movshovitz-Attias et al., 2017) are learnable, synthetic features that serve as representatives of the global feature distribution. The key idea of PRIME is to use proxies as explicit anchors for the desired feature ceaributtionbbllancee (i.e., preserving minority features) and well-ordered (i.e., reflecting the ordinality of target values) and to aligm sample features with these proxies. To this end, we propose two novel loss functions: proxy loss (Epeoxy) and and alignment loss (Catign). Specifically, prosy struc- tures the proxies in the feature space to reflect the ordinal relationships of the targets while maintaining sufficient sep- aration to enhance their representative power. Meanwhile, Lalign promotes feature alignment with the corresponding proxy based on target similarity. Unlike prior representation learning methods (Gong et al., 2022; Keramati et al., 2024), PRIME leverages rich sample-prox, relationships to pro- vide holistic supervision for effective feature positioning. By using proxies as reference points, PRIME steers features toward the intended structure for both majority and minority targets, resulting in more generalizable representations.
2. Related Work
Imbalanced regression. Early studies (Yang et al., 2021; Steininger et al., 2021) estimate effective label density using kernel density estimation and re- weight samples accordingly. Balanced MSE (Ren et al., 2022) modifies MSE in a man- ner similar to logit adjustment, while VIR (Wang & Wang, 2023) introduces probabilistic re-weighting to capture pre- diction uncertainty. However, these methods only focus on the final predictions, which are complementary to our work. RankSim (Gong et al., 2022) and ConR (Keramati et al., 2024) regularize feature representations for imbalanced re- gression, but are limited to intra-batch relationships, which hinders effective learning of minority features. HCA (Xiong & Yao, 2024) formulates regression as hierarchical classifi- cation, incurring higher computational cost and quantization errors. Recently, IM-Context (Nejjar et al., 2024) employs in-context learning with large-scale models such as GPT to handle data imbalance in regression tasks.
Representation learning for regression. Several stud- ies have explored representations tailored for regression. Rank-N-Contrast (Zha et al., 2023) ranks samples and con- trasts them based on their relative rankings. Ordinal En- tropy (Zhang et al., 2023a) promotes higher-entropy feature space. In addition, contrastive learning approaches (Dufu- mier et al., 2021a;b; Wang et al., 2022; Schneider et al., 2023; Barbano et al., 2023) have been actively studicd. How- ever, these methods overlook the imbalanced target distri- bution. In contrast, PRIME uses proxies to directly address data imbalance and promote balanced representations.
Furthermore, aligning each feature with its corresponding proxy can be viewed as a classification task, where each proxy serves as a class prototype. This perspective enables PRIME to leverage advances in imbalanced classification to promote balanced feature learning. Indeed, by integrating class imbalance techniques, PRIME further enhances its effectiveness in DIR, bridging the gap between imbalanced regression and classification. To demonstrate its general applicability, we incorporate three widely used methods in imbalanced classification into PRIME: Proxy-wise Re- Weighting (PRW) (Huang et al., 2016), Class-Balanced (CB) loss (Cui et al., 2019), and Siabbll-istrbbutio--nwee (LDAM) loss (Cao et al., 2019), all of which consistently improve performance on minority targets.
Proxy learning. Proxies (or prototypes) have been widely studied in deep metric learning (Movshovitz-Atiin et al., 2017: Kim et al., 2020; Teh et al., 2020; Lim et al., 2022) and few-shot learning (Snell et al., 2017: Gao al., 2019; Pan et al., 2019), where each proxy serves as class repre- sentative. Similarly, learnable class centers (Cui et al., 2021; Wang et al., 2021) have been proposed for imbalanced clas- sification, but they do not extend naturally to regression, where handling target-wise proxies is inherently complex. While several studies (Mettes et al., 2019; Dufumier et al., 2021a;b) have explored proxies for continuous values, these methods rely on fixed proxies rather than learning adaptive ones, which distinguishes our approach.
Margin
In summary, our contributions are as follows: (i) We pro- pose PRIME, a simple yet effective method for learning balanced and well-ordered representations. To the best of our knowledge, PRIME is the first to introduce proxies for imbalanced regression. (ii) PRIME enables the application
2

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PRIME: Deep Imbalanced Regression with Proxies
3. Proposed Method
Ji=1 as the (C + 1) quaantiles of the range [Wminn Umea For multi-dimensional target, we can employ K-means clustering to define {y²)== as the
gets from S and define {y?) C
3.1. Problem Definition
We consider a regression problem that predicts the target Y E Y based on the input x E X. where the underlying data distribution D is imbalanced. Specifically, we consider the imbalanced training dataset & = {x) y:) drawn ti.d. from D, where the target distribution p(y) significantly deviates from uniformity. Given S, we aim to train neural network model h : X' + y composed of a feature encoder f + 2 and a predictor
cluster centers. Once [ are determined, the corre-
C
sponding feature points {zş]] Ji-1 are randomly initialized
and jointly learned as part of the model parameters.
Now, we formalize our proxy loss Cproxy, which ensures that {z]) Fi=1 well-ordered according to {y?") ) i==1 Motivated by stochastic neighbor embedding (Hinton & Roweis, 2002), we define two probability distributions, P and Q, which represent pairwise similarities among {y?) and {z])==1 C
C
2 ++ y. where 2 represents the feature space. We denote z = [x) E Rf as the feature of x and y g(z) E RTT as the prediction of y. Typically, the encoder f and the predictor g are learned by minimizing regression loss (e.g.. L1 loss) to ensure the prediction y aligns with the target y. However, the imbalanced target distribution in S causes the predictions to be biased towards the majority targets. Specifically, the features of minority targets often collapse into those of the majority, leading to higher test errors for minority targets (Yang et al., 2021).
respectively. We then optimize {z,"}== by aligning these two distributions. Specifically, we define the probability distribution P E RCxC to represent pairwise similarities within [y with its (i,,))thh element defined as:
Púj = ΣXEI E Eedeettt
(I)
To address this problem, we aim to construct well-ordered feature representations, ensuring that samples closer in y are mapped closer in 2. Formally, we define the features { as well-ordered if the following condition holds for all i.j. k E []: if y,)) S de (y)..))), then dz(2;, m3) S d 21)), where d<(:..) and (:):,)) denote distance metrics defined over y and Z, respectively. By en- couraging, / encode well-ordered features, we can prevent the features of minority targets from collapsing into those of the majority, enhancing the minority performance.
where T; > 0 is the temperature hyperparameter, and set Pi = 0. For nearby targets, Pıj is relatively high, while for distant targets. Ptj is small. Similarly, we define the probabil- ity distribution Q E IRC to represent pairwise similarities within {2,)
i== with its (1, element defined as:
C
9i5 = Σ (ydd
(2)
As before, Ty > is the temperature hyperparameter, and we set qu = 0. Then, we minimize the Kullback-Leibler divergence between P and Q:
To this end, we propose PRIME, a simple and effective rep- resentation learning scheme for imbalanced regression that introduces synthetic reference points, referred as prox- ies (Movshovitz-Attiae et al., 2017: Kim et al., 2020). At the core of PRIME, we design proxies represent a balanced (i.e., uniform target distribution) and well-ordered feature distribution, serving as anchors for representation learning ($3.2). Then, we align features with proxies in accordance with target similarity, providing global guidelines to struc- ture the desired feature space ($3.3). Lastly, we demonstrate that PRIME enables the application of class imbalance tech- niques to imbalanced regression tasks ($3.4).
DR 11 = Σ
Pij
log
Psi
Pif
$
C si=1 are positioned to reflect sim- ilarity orders of {y 1 imm1 However, since 2 typically has higher dimensions than V, trivial solutions (e.g. appending zeros to {y. ) may arise. To prevent trivial solutions and promote diversity in {x,). we introduce regularization term that encourages features to spread apart. Specifically, we increase the cosine distance between z! and zi propor- tionally to de(y., vy)) Hence, fuprxy is defined as:
By minimizing (3), [2))
3.2. Proxy for Imbalanced Regression
We first introduce proxies, defined as synthetic data points in the product space 2 x y. Concretely, we define C' proxies as P = ((2,,,")))))) ) where z E Z denotes a feature point and y E y' its corresponding target. Our goal is to design P to represent balanced and well-ordered feature distribution. To achieve this, we distribute {y?) uniformly across the target values. Specifically, for a scalar target, we compute the minimum (ymin) and maximum (Fmax) values of the tar-
Eproxy -' ifj
Pis log qs
Pij
wiy(1 (1 - cos 82 22 (4)
where way = cyd (yF. vr) with a > 0. In Lyrayy. the first term ensures that proxies are well-ordered, while the second term promotes feature space uniformity (Wang & Isola, 2020), encouraging expressive representations that fully utilize the entire feature space.
3

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PRIME: Deep Imbalanced Regression with Proxies
3.3. Proxy-based Representation Learning
often struggle to align properly with their proxies, leading to suboptimal feature representations. Notably, we tackle this issue by leveraging class imbalance techniques.
We leverage the proxy set P = {<x">>?)) yD as explicit anchors to provide informative associations during rep- resentation learning. Concretely, given a training sample yx E S, its feature z is associated with {2 These feature associations are represented by the association vector A E RR, where the j-th element defined as:
Attentive readers may notice that PRIME naturally aligns with classification, where each proxy acts as a class center, and Lalign in (7) functions as a classífication loss. Hence, any loss-based class imbalance techniques can be seam- lessly integrated into our framework. Here, we showcase the application of three widely used techniques, Proxy-wise Re- Weighting (PRW) (Huang et al., 2016), Class-Balanced (CB) loss (Cui et al., 2019), and Margin (LDAM) loss (Cao et al., 2019), into PRIME.
C 7xd)(2x))) 2k=1 e (2))())))))
Aj-
(5)
Here, A quantifies the association between and zij, repre- senting the likelihood that z would select zJ, as its neighbor based on feature similarity. We aim to ensure that such as- sociations are stronger for proxies closer in Y' and weaker for those farther away. To this end, we define T E RC to represent the target associations between y and {y? where the j-th element is defined as:
PRIME + PRW. Re-weighting (Huang et al., 2016; Wang et al., 2017), which assigns adaptive weights to different classes inversely proportional to their frequency, is the most fundamental approach addressing class imbalance. PRW adapts this to the proxy setting. Specifically, for each batch, we define the scaling variable 8, for the j-th proxy as C Σn Tyly=y,- where N₂, denotes the batch size. 8j = No Intuitively, 8j represents the proxy frequency, i.e., the num- ber of samples in the batch associated with the j-th proxy. Consequently, the alignment loss with PRW is defined as:
C
C (Tdd(
(6)
Σ (-dde(x))
To align the feature associations A with the target associa- tions T. we formalize our alignment loss Latign. Specifically, Lalign is defined as the cross-entropy between A and T:
Calign-PRW = =-
Σ
1 T, log Aj. 83
C Calign = - - T, log A,
where 5) = max( (sj, Smin). with mmin > 0 as a hyperparame- truncate excessively small 8y for stable training.
j=1
In essence, Lalign aligns the sample feature with proxies by pulling z closer to proxies with similar targets while pushing away from proxies with dissimilar targets. Since (y?) balance the target distribution and {z]) are well-ordered with maximal representative power, the proxies serve as global guidelines for structuring the desired feature space, enabling the encoder learn more generalizable representations for imbalanced regression.
PRIME- + CB. CB loss(Cui et al., 2019) is another seminal work on class imbalance that introduces reiieigtting based on the inverse effective number of samples. The aligmment loss with CB is given as follows:
C 1-8 Σ
Lalign-CB
T, log AJ,
(10)
1- 3ms
Finally, the overall loss function LPRIME is defined as:
where 3 E [0, denotes the effective number parameter and ny represents the total number of samples belonging to the j-th proxy. We compute n; by assigning each training sample to the proxy with the closest target. Following (Cui et al., 2019), we set B = 0.99 for all experiments.
CPRIME y: h, P) = Lrgg + Aprnyy + Xa Calign: (8)
where Creg is the task-specific regression loss, and Xp > 0 and An > 0 are trade-off hyperparameters for Lpexyy and Calign. respectively. Note that the model parameters of h and C i==
the proxy features { are jointly optimized by mini- mizing LPRIME. Furthermore, our PRIME is orthogonal to other imbalanced regression methods and can be seamlessly integrated with existing approaches by simply adding Lyroxy and Calign to the respective regression loss Lieg.
PRIME + LDAM. Margin-based loss functions have also been extensively studied for class imbalance. As the feature association in (5) corresponds to the classification logit, margin-based losses can also be applied without algorithmic changes. LDAM loss (Cao et al., 2019) is one of the most popular margin-based losses, encouraging larger margins for minority classes The alignment loss formulated with I.DAM is defined as follows:
3.4. I Leveraging Class Imbalance Techniques
Although proxies represent a balanced feature distribution, the alignment process in (7) still faces challenges due to sam- ple imbalance. Minority samples, occurring less frequently,
- = Σ T, log et:-A; A, + Eezs eta' (11)
C
Lalign-LDAM
j=1
4

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PRIME: Deep Imbalanced Regression with Proxies
where Jj -T,d 2f), and A = MM/n //4 with M as hyperparameter, denotes the margin for the j-th proxy.
Theorem 4.1. For any positive d < 1, with probability at
least 26, the following generalization bound holds for all h E H and f E F:
Remark. The use of class imbalance techniques ensures that minority samples receive sufficient alignment focus, ultimately leading to more balanced feature learning. Impor- tantly, PRIME is generalizable and facilitates the use of a wide range of class imbalance techniques, which lays the foundation for future research exploring additional methods. Further discussion is provided in Appendix C.4.
Rhul(h S CD [ss(h) + (H, + An
(16)
where (H, 5) and Ds(F. 8)) represent the empirical Rademacher complexities of and F with some additional terms, respectively.
4. Theoretical Analysis
Proof. Please refer to Appendix A.2.
In imbalanced regression, the ultimate goal is to learn a model h = go that minimizes the expected regression error (or risk) under balanced test criteria, denoted as Reat (h). In this section, we prove that optimizing our loss function LRRMME in (8) bounds the balanced risk Reai (h), supporting the effectiveness of our PRIME.
Theorem 4.1 confirms that optimizing LPRIME provides a bound on the generalization error under a balanced testing distribution, Further analysis can be found in Appendix A.
5. Experiments
The balanced risk associated with LPRIME is defined as:
5.1. Experimental Setup
Datasets. We conduct experiments on four real-world im- balanced regression benchmarks introduced by (Yang et al., 2021): (i) AgeDB-DIR is a facial age estimation dataset derived from AgeDB (Moschoglou et al., 2017). (ii) IMDB- WIKI-DIR is an age estimation dataset constructed from IMDB-WIKI (Rothe et al., 2018). (iii) NYUD2-DIR is de- rived from the NYU Depth Dataset V2 (Silberman et al., 2012) for depth prediction from RGB indoor scenes. (iv) STS-B-DIR is natural language dataset based on STS- B (Cer et al., 2017: Wang, 2018), providing continuous similarity scores between pairs of sentences. Detailed de- scriptions of these datasets are provided in Appendix B.1.
Rea (h) Ebal [CPRIME(X, yx y; P)],
(12)
where [:] represents the expectation over the balanced distribution. Note that, as LPRIEE accounts for both the re- gression error and the feature alignment error, it is straight- forward to show that (h) < (h). Unfortunately, since the balanced distribution is unknown, we can only minimize the empirical risk based on the imbalanced train- ing set S. The empirical risk R. (h) is defined as:
N
Rs(11)
Σ
Yx;, (13)
=
Evaluation metries. For each dataset, adopt metrics from (Gong et al., 2022; Keramati et al., 2024). For AgeDB- DIR and IMDB-W WIKI-DIR, we use Mean Absolute Error (MAE) and Geometric Mean (GM). For NYUD2-DIR, we adopt Root Mean Squared Error (RMSE) and Threshold Accuracy (61). For STS-B-DIR, we employ Mean Squared Error (MSE) and Pearson correlation. For all datasets, we report results for four subsets: All, Many, Median, and Few. All refers to the entire test set. Based the number of training samples per label, Many includes labels with over 100 samples, Median covers those with 20 to 100 samples, and Few consists of labels with fewer than 20 samples.
Let 52 + (l,..., C} be a random variable representing the index of proxy. Note that & is a hypothetical random variable with the probability distribution defined as:
p(E) / ((ll))p(r)dy
(14)
where ((Ely) represents our probabilistic model for p(Ely), and the target association T, in (6) offers a natural way to
detine q(E = jly). We then formalize the skewness of the underlying distribution D, as follows:
Baselines. We compare our method against state-of-the-art approaches for DIR, including re-weighting (SQInv and Inv) (Yang et al., 2021), Label Distribution Smoothing (LDS) (Yang et al., 2021), Feature Distribution Smooth- ing (FDS) (Yang et al., 2021), Balanced MSE (Ren et al., 2022), RankSim (Gong et al., 2022), VIR (Wang & Wang,
Phat (y) ED max sup
Phul (5 = (] ) P(E= }
max p(y) 3
(15)
where P)a and (h)(() denote the balanced distributions (i.e., uniform distributions) over and ç. respectively. The term CD 2 1 quantifies the imbalance in D. taking larger values as the imbalance becomes more severe, and equals when D perfectly balanced.
2023), ConR (Keramati et al., 2024), HCA (Xiong & Yao,
2024), and IM-Context (Nejjar et al., 2024). For all methods,
we use the official implementations when available.
5

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PRIME: Deep Imbalanced Regression with Proxies
Table Comparison with state-of-the-art methods on AgeDB-DIR. indicates that the results are quoted from the original paper, as the code is not publicly available. The best results are marked in bold, while the second best are underlined.
MAE (L)
GM (L)
Method
All
Many
Median
Few
All
Many
Median
Few
SQInv (MAE)
7.42:1006
6.78
8.55
10.7
4.77=20.8
4.37
5.73
7.39
LDS (Ying al., 2021)
1:008
6,93
8.43
10.40:052
4.80
4.44
5,50:1026
6.98:20.8
FDS (Yang al.. 2021)
7.45
1004
8.52:10.17
10:21::0:2
4.75
4.30
5.57
6.69=0.51
LDS + FDS (Yang al., 2021)
7.40##000
6.82:20m6
8.26+
10.45=0445
4.70=
4.29+
5.58
6.97=060
Balanced MSE (Ren et at., 2023)
7.60
7.00=
8.08
11.96:0300
4.83
4.4
5.34
8.42-2008
RankSim (Gong et al., 2022)
7.10
6,48
8.19
10.32:t0
4.53
4.10
5.46.10.6
6.95
VIR (Wing& & Wang. 2022)
7.39 0:008
6.73
8.42
10.86:10.88
4.66
4.22
5,51
7.51 00224
ConR (Keramati al., 2024)
+.00
6,74:10.4
8.34
10.26
a.73
1.34
4.59
6,80
HCA (Xiogg& & Yan, 2014)
7.45
6.86
8.22
10.90
PRIME
7.09
6,38
8.39
10.13:036
4.39
3.91
5.58
6.57=0.49
PRIME PRW
7.06:20009
6.67-209
7.27
9.
4.39
4.14::0m
4.69.1000
6.39
PRIME + CB
7.12+00.9
6.61 +0.09
8.07++0.11
9.29
4.47
4.16+to.s
5,23++007
5.81 -0.46
PRIME LDAM
7.24++0.6
6,85
+.84
9.29+0.44
4.47
4.26++0.12
5.60=054 4.89
Table 2. Comparison with state-of-the-art methods IMDB-WIKI-DIR, i indicates that the results are quoted from the original paper, as the code is not publicly available. The best results are marked in bold, while the second best are underlined.
MAE (
GM (L)
Method
All
Many
Median
Fow
All
Many
Median
Few
SQInv (MAE)
7.57
6.98
12.23
23.2110013
4.23
3.99
6.94
15.25
LDS (Ying et al.. 2021)
7.75
7.15
12.70
22.77:1043
4.39
4.13
7.43
14.14::0.7
FDS (Yang et al., 3021)
6,98
12.50
23.05=00.18
4.25
3.99
7.41
14.89
LDS FDS (Yang at. 2011)
7.75
7.16#t00
12.47=0.18
22.80=0..0
4.39=
4.15+
7.17+024
14.47=00.3
Balanced MSE (Ren 2023)
7.95
7.39
12.27
23.35
4.57
4.34-10.12
7.03
15.04=1.75
RankSim (Gong et al., 2022)
6.85
12.06
22.77:10.9
4.14
3.91 1:000
6.80
13.47
VIR (Wing & Wang, 2023)
+.50
6,90
1..49
23.34
4.16
3.90
4.35
15.93
ConR (Keramati al., 2024)
7.45 +.005
6.87
12.07++0.2
22.78
4.15
3.92+-0.04
6.774031
14.61
HCA! 1 (Xiong & Yoo, 2024)
7.54
6.91
12.69
22.96
PRIME
7.362000
6,73
12.48
23.01
2.98
3.73
7.17
14.38
PRIME PRW
7.37
6.74
12.04+0.28
22.3440023
4.00+0aa
3.76+-0.7
6.67
13.45
PRIME + CB
7.48 4-0.01
6,90+
12.05 +0.15
22.71
4.15
3.91 +-0.2
6.74440.6
13.91 +0.0
PRIME + LDAM
7.49:t0.04
6.91 +000
+2.23
22.32 +026
4.17
3.94+
6.94
13.44
Implementation details. For all experiments, we adopt the benchmark settings of (Yang et al., 2021). To ensure fair
5.2. Main Results
Age estimation. Tables 1 and show the overall results on AgeDB-DIR and IMDB-WIKI-DIE respectively. For fair comparisons, LDS, FDS, RankSim, ConR, and our methods all use the square root inverse (SQInv) re-weighted MAE loss as the regression loss, following the convention of (Yang et al., 2021). Notably, PRIME itself already achieves state- of-the-art performance on both datasets, highlighting the effectivvnness of the proposed proxy-basee approach. Fur- thermore, PRW, CB, and LDAM consistently improve per- formance in the Median and Few categories.
comparisons, we use the same backbones and training set- tings as prior work (e.g., RankSim (Gong et al., 2022) and
ConR (Keramati et al., 2024)), tuning only the hyperparam- eters of PRIME. For AgeDB-DIR and IMDB-WIIH WIKI-DIR, we use ResNet50 (He et al., 2016) as the backbone, while for NYUD2-DIR, we adopt the ResNet50-based encoder- decoder architecture (Hu al., 2019). For STS-B-DIR, we employ BiLSTM+ + Ve (Pennington et al., 2014) word embeddings as the feature extractor. Our proxy features C {=])== are randomly initialized using He initialization (He et al., 2015) and leamned jointly with the model parameters. All results are reported as mean and standard deviation over five independent runs. The complete implementation details are provided in Appendix B.2.
To further validate the effectiveness of PRIME, we addition- ally compare it against IM-Context (Nejjar et al., 2024), a recent method that leverages large-scale models (e.g., GPT2 (Garg et al., 2022) and PFN (Müller et al., 2022)) for
6

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PRIME: Deep Imbalanced Regression with Proxies
Table Comparison with state-of-the-art methods on NYUD2-DIR. t indicates that the results are quoted from the original paper, as the code is not publicly available. The best results are marked in bold, while the second best are underlined.
RMSE (L)
81 (t)
Method
All
Many
Median
Few
All
Many
Median
Few
Inv (RMSE)
1.314:10.022
0.000
1:0050
0.804
1.801:007
0.687
0.666110.033
0.740.10025
0.688:20.017
LDS
1.386:10:008
0.690.10.038
0.887
1.952:1007
0. 16682.0007
0.701 :00000
0.730
0.612:00.000
FDS
1.343.10019
0.727 1:0004
0..03
1.865 1866:100077
0.004
0.686.10.026
0.749
0.660
LDS FDS
+.335
0.691
+:0051
0.883
a.
0.686
0.699
0.743
0.666=0036
Balanced MSE
0.819
0.881=0002
1.761 #00077
0.672+00014
0.595
0.808
0.698
ConR
0.326
10.0
0.885
1.784
10.07
0.604
0.812
0.690
HCA!
1,475
0.689
PRIME
1.0000
0.782.10.022
0,881 0.001
1.752
1..000
0.624
0,810
=.704
PRIME + PRW
1.272
0.837
0.920=0.020
1.682:0001
0.68910000
0.607
0.8 1.8141002
0.724=0.m
PRIME+ + CB
0.823
0.900=20:34
1.734
0.685
0.605
0.8 1.819
0.712=00077
PRIME + LDAM
1.302
0,807 1:0000
0,871
1.758
0.682
0.613
0.822
0.698-20017
Table 4. Comparison with state-of-the-art methods on STS-B-DIR. The best results are in bold, while the second best are underlined.
MSE (L)
Pearson correlation (1)
Method
All
Many
Median
Few
All
Many
Median
Few
Inv (MSE)
1.298
1.300
10.09
1.319
0.628
0.603.10011
0.596.10015
0.663:20016
LDS
0,990110038
0,931 1:0050
1.270.10.048
0,954
0.742110003
0.703
0,701 10018
0.766
FDS
1.262.10.01
1.254:10.14
1.274-20.217
1.316:10064
0.606.10.015
0.592:10.027
0.61210004
0.665
LDS + FDS
0.974
0.929
1.161 =0.000
0.983
00.07
0. 0.709
0.709
0.755
RankSim
0.980
0.928
1.208
0.985
0.745
0.707
0.702
0.756=2009
PRIME
0.970=10004
0.8942.0112
1.325
0.930
0.750
0.712
0.710+
0.773=0011
PRIME + PRW
0.967=
0.885
1,351 20.061
0.925
0.753
0.715
1
0.775 2000
PRIME+ + CB
00
0.906220010
1.035
0.922+00m
0.748 20:001
0.708=
0.711 1:0004
0.777=000m
PRIME + LDAM
0.975+00016
0.893 +-0.00
1.366+00088
0.919 #0003
0.751 +-0.00
0.712++0003
0.709
0.778 =0.015
in-context learning in regression. Following IM-Context, we adopt the pre-trained CLIP image encoder (ViT-B/32) (Rad- ford et al., 2021) as the backbone, and fine-tune it jointly with a two-layer MLP regression head using our PRIME loss. To ensure robustness, we report the average perfor- mance of PRIME over five independent runs. As shown in Table 5, PRIME substantially outperforms both PFN- localized and GPT2-localized across all evaluation metrics. These results confirm that PRIME remains effective even on top of strong pre-traine pre-trained backbonn model, highlighting its compatibility with powerful feature extractors.
performance, achieving -het---rtt results across the All, Median, and Few categories.
Text similarity estimation. Table 4 reports the performance on STS-B-DIK Since STS-B-DII ---DIIRR exhibits a highly discrete target distribution (Yang et al., 2021), we smooth using LDS and employ inverse (INV) re-weighted MSE loss as the regression loss, following RankSim. Overall, PRIME and its variants achieve tfate-of-the-an results, demonstrating their effectiveness across diverse target domains.
5.3. Analysis
Depth estimation. Table 3 presents the depth estimation re- sults on NYUD2-DIR, more challenging setting where the high-dimensional target space exhibits non-linear relation- ships. Following ConR, measure target similarity based on the difference between the average depth values and use Balanced MSE as the regression loss. PRIME outperforms Balanced MSE and ConR, demonstrating its effectiveness even for complex targets. Notably, PRIME significantly improves performance in the Few category, underscoring its ability to mitigate data imbalance. Furthermore, incor- porating PRW, CB, and LDAM further enhances minority
PRIME facilitates effective feature learning. We investi- gate the effect of proxies on feature learning. Figure 2 illus- trates feature space similarities between the learned proxies and the features of the test samples in AgeDB-DIR. For clarity, data points are sorted by their target values, with the expectation that matrix values gradually decrease from the diagonal to the periphery. As shown in Figure 2(a), thanks to Cpraxy. the proxies are well-ordered in the feature space according to their target values. Figure 2(b) confirms that features are generally well aligned with their corresponding
7

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PRIME: Deep Imbalanced Regression with Proxies
Table Comparison with IM-Context on AgeDB-DIR and IMDE- IM-Context results are taken from the original paper. Both PRIME and the two IM-Context variants (PFN- localizdd and GPT2 oPT2-localized) use the CLIP image encoder (VIT-B/32) as their feature extractor. Under same backbone, PRIME achieves consistently superior performance.
MAE (L)
GM ())
Method
All
Many
Median
Few
All
Many
Median
Few
Results for AgeDB-DIR:
PFN- -Pc-local (Nejaar al., 2024)
6.58
5.61
8.49
10.49
4.29
3,58
6.30
8.19
(Neijar et al. 2024)
6.05
5.67
6.71
7.83
3.79
3.59
4.17
4.90
PRIME
5.47:10.0
5,46:1008
5.48
5.57.
3.48
3.45
3.64
3.35.:0.27
Results for IMDB- -III--RI
PFN -localized (Nejaar et al., 2024)
8,96
8.71
10.79
16.33
5.26
5.17
6,00
9.42
(Neijar al. 2024)
7.76
7.35
11.15
17.71
4.29
4.13
5,96
11.00
PRIME
6.42
5.98
9.92#0.32
16.28
3.49
3.33
5.17
9.41=2011
Web PRIME
PRIME
Table 6. Spearman correlation between feature and label sim- ilarities on AgeDB-DIR. A higher correlation indicates better ali aligmment between learned fcatures and targets, implying more well-ordered representations.
(a) Praxy-Prax
(b) Feature
(c) Feature Feature
Method
All
Few
Figure 2. Feature space similarities on AgeDB-DIR. (a) Simi- larity matrix among proxies. (b) Similarity matrix between proxies and the means of their associated features. (c) Similarity matrices among features, with (right) and without (left) PRIME.
RankSim (Gong al., 2002)
0.804
0.587 1000
ConR (Kermanti al., 2024) 0. 0.790
0.61410044
PRIME
0, t.042
0.828
Table 7. Comparison with representation learning methods for general regression. See Appendix C.I for the complete results.
proxies'. The plot the left of Figure 2(c) shows that, with- out PRIME, the features are poorly ordered, and the model for mi-
Method
MAE (L)
GM (1)
fails to learn effective representations--aatteee nority targets (i.e., those at both ends of the matrix diagonal). As shown in the right plot of Figure 2(c), incorporating prox- ies allows PRIME to guide the features towards the intended structure for both majority and minority targets, resulting in more balanced and well-ordered representations.
HPN (Metes et al., 2019)
7.38
4.66
Ordinal Entropy (Zhing al., 20134)
7.33
4.68
Rank-N- Rank-N-Contrast ---ntraat (Zhaet al. 2023)
7.27
4.69.004
PRIME
7.09::0.8
2.39
PRIME ensures well-ordered representations in the Few category. To assess how well PRIME captures the ordinal- ity of target values, we evaluate the Spearman correlation between feature and label similarity matrices on the AgeDB- DIR test set. higher correlation suggests that the learned features more faithfully reflect the ordinal structure of the label space, which is an essential property for effective re- gression. As shown in Table 6, PRIME achieves consistently strong correlations across All samples and, notably, main- tains a high correlation in the Few category. In contrast, RankSim and ConR exhibit marked degradation in this un- derrepresented regime. These results underscore the strength of our proxy-based formulation, which offers holistic guid- ance for feature positioning and enables minority samples to align with the overall label structure.
Comparison with recent representation learning meth- ods for general regression. To further demonstrate the effectiveness of PRIME, we compare it with three recent techniques proposed for general regression: HPN (Mettes et al., 2019), Ordinal Entropy (Zhang al., 2023a), and Rank-N-Contrast (Zha et al., 2023). As shown in Table 7, PRIME achieves clear margins over the compared baselines. In particular, compared to HPN, which uses fixed proto- types on a hypersphere, PRIME achieves significantly better performance, verifying the effectiveness of our proxy de- sign tailored for DIR. Notably, PRIME outperforms Ordinal Entropy and Rank-N-Contrast two leading representation learning methods for general ability to learn robust and reliable representations under imbalanced target distributions.
its
See Appendix C.I for a discussion on the twisted pattern in the top left of Figure 2(b).
Effectiveness of our proxy formulation. To validate the effectiveness of our proxy formulation, we compare PRIME
8

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PRIME: Deep Imbalanced Regression with Proxies
12
(a) ConR
(b) PRIME
(c) PRIME +PRW
(d) PRIME + CB
(e) PRIME + +DAM
Figure 3. Feature visualization with I-SNE on AgeDB-DIR. By leveraging proxies as global reference points, PRIME clearly demon-
strates well-ordered features with fewer minority feature collapses, effectively capturing the continuity of target values.
ment over random initialization. Finally, from M3 to M4 (PRIME), performance further improves, as regression deals with continuous targets, making distance proportional as- signment as in (6), more effective than one-hot encoding.
Table Comparison with proxy-based alternatives on DB- DIR. See Appendix C.I for the complete results.
Method
MAE (1)
GM (1)
ProxyNCA MMosstuiiteAAiia al., 2017)
7.33
4.64
Feature visualization. Figure 3 presents t-SNE (Van der Maaten & Hinton, 2008) visualizations of the learned rep- resentations from the AgeDB-DIR test set. As shown in Figure 3(a), ConR is biased toward learning discriminative representations only for majority targets (red), failing to capture the continuity of target values. Moreover, minority features (blue and green) collapse into the majority (red), leading to poor performance for minority targets. In Fig- ure 3(b), PRIME produces well-ordered features with fewer minority feature collapses, effectively capturing the continu- ity of target values. Figure ((b) shows that incorporating class imbalance techniques further promotes balanced fea- ture learning, leading more structured representations.
Non-learnable (centroid)
7.10+t0s
4.53
PRIME
7.09
4.39
Table 9. Ablation study on AgeDB-DIR. See Appendix C.I for the complete results.
Init. y?
Eyenny
Align
MAE (L)
GM (4)
MI
Random
One-Hot
7.34:1008
4.66
M2
Random
One-Hot
7.24:100
4.
M3
Unif.
/
One-Hot
7.23
4.55.1012
M4
Unif.
Eq. (6)
7.09
4.39
Computational efficiency (Appendix C.2). We confirm that PRIME offers training efficiency comparable to other imbalanced regression methods.
with two proxy-based alternatives: ProxyNCA (Movshovitz- Attias et al., 2017) and a non-learnable variant of PRIME. For ProxyNCA, we adapt the original method to the regres- sion setup by assigning proxies so that associated targets are uniformly distributed, as PRIME. For the non-learnable variant, proxy features are updated the centroids of sam- ple features assigned to each proxy, rather than learned. As shown in Table 8, PRIME consistently outperforms both ProxyNCA and the non-learaalle variant, attributed to its formulation that optimizes learnable proxies to preserve the ordinal structure of the target space. This leads to more stable and effective feature representations, particularly in data-sparse regions.
Hyperparameter sensitivity (Appendix C.3). We analyze the impact of PRIME's s hyperparameters (C, Xp. Xa Ty. Tts and a). Overall, PRIME demonstrates reliable and robust performance across wide range of hyperparameter choices.
6. Conclusion
We introduce PRIME, a novel representation learning frame- work for imbalanced regression that leverages proxies to learn balanced and well-ordered feature representations. By using proxies global reference points, PRIME facilitates effective feature learning for both majority and minority tar- gets. Theoretical analysis and extensive experiments on four benchmark datasets spanning diverse target domains demon- strate its effectiveness.. Furthermore, PRIME seamlessly integrates with any loss-based class imbalance technique. We believe our work provides a flexible and unified frame- work for incorporating various class imbalance techniques into regression problems, introducing new paradigm for addressing imbalanced regression.
Ablation study. As shown in Table 9, we ablate three key C design choices: (i) whether randomly initialize Jyp
or assign them uniformly in the target space, (ii) whether to include Epraxy, and (iii) whether to perform feature align- ment as in (6) or align features to their nearest proxy using one-hot strategy. Comparing the ablation models, MI to M2 shows a significant performance gain, demonstrating the effectiveness of Eproxy. From M2 to M3, assigning proxies uniformly in the target space provides a slight improve-

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PRIME; Deep Imbalanced Regression with Proxies
Impact Statement
Dufumier, B., Gori, P., Vietor, J., Grigis, A., Wessa, M., Brambilla, P., Favre, P., Polosan, M., Mcdonald, C., Piguet, C. M., et al. Contrastive learning with continuous proxy meta-data for 3d mri classification. In Medical Image Computing and Computer Assisted Intervention- MICCAI 2021: 24th International Conference, Stras- bourg, France, September 27- 27-October 1, 2021, Proceed- ings, Part 24, pp. 58-68. Springer, 2021b.
This paper presents work whose goal is to advance the field of imbalanced regression. Imbalanced regression can have socictal implications. particularly in applications where ac- curate predictions across the entire target range are critical. For instance, in social sciences, models trained on imbal- anced data may disproportionately favor well-represented groups while yielding less reliable predictions for underrep- resented populations. Such biases can exacerbate existing inequalities, leading to unfair decision-making Our work can mitigate these issues and contribute more equitable predictive modeling.
Gao, T., Han, X., Liu, Z., and Sun, M. Hybrid attention- based prototypical networks for noisy few-shot relation classification. In Proceedings of the AAAI conference on artificial intelligence, volume 33, pp. 6407-6414, 2019.
Garg, S., Tsipras, D., Liang, P. S., and Valiant, G. What can transformers learn in-context? a case study of sim- ple function classes. Advances in Neural Information Processing Systems, 35:30583-3033 2022.
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PRIME; Deep Imbalanced Regression with Proxies
Appendix
The Appendix includes additional descriptions, experimental results, and analyses omitted from the main manuscript due to space constraints. Section A. we present a detailed theoretical analysis. Section B, we provide further details on the experimental setup. In Section C, we report additional experimental results and analyses.
A. Detailed Theoretical Analysis
In this section, we provide theoretical justifications for the proposed method. In $A.1, we provide a complete description of the definitions and notations used this analysis. In $A.2. we present the proof of Theorem 4.1 from the main manuscript. In $A.3, we present an extended theoretical analysis of Theorem 4.1 under non-optimal proxy settings. In $A.4, we provide further theoretical evidence for the claim that the use of class imbalance techniques promotes balanced feature learning.
A.1. Definitions and Notations
We first rigorously clarify the underlying probabilistic distributions used throughout the paper. Specifically, while x and y are random variables with given probability density function p(x. y). the corresponding proxy index is a hypothetical random variable for which we need define a probability distribution. Therefore, we define our joint probability density function follows:
v.) p((x))))=ooxx))
(17)
where ((Ely) our probabilistic modeling function of p((ly). For instance, in PRIME, we take
dE jly) = TT 1k=1" (
for j C..., C.
(18)
Next, the balanced distributions for and are defined as follows:
Peal (x. y) : Paaa Poat))))))))))))))) (y),
(19)
Pual y. == pE)
(20)
Here, (y) and (E) correspond the uniform distributions over the spaces y and {1,.... C}. respectively.
We assume that the proxies are optimally positioned i.e., Spoxy = 0. This assumption is justified, the proxies can be pre-optimized using (4) prior to model training. Hence, LpRIME in (8) simplifies to Lreg + A Calainn Then, our balanced risk defined as the weighted sum of the balanced regression risk and the balanced alignment risk:
Red (h) = - f(x)) Poaa tha / (-log po (E)x)) Poal (x. y, (, E)xxdyde,
(21)
balanced regression risk (.e.,RRa(h))
balanced alignment risk
where po(E is our feature association with proxy, which we take
E TTddy(ax))
1o j(xx A₁
for j I,...,C
(22)
- L (x)d)(
(h) is always greater than the balanced regression risk in our PRIME model. Note that the balanced risk with respect to (h)
Roal (h) because the balanced alignment risk is always positive.
We later relax assumption and extend analysis to non-optimal proxy settings; see Section A.3.
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PRIME; Deep Imbalanced Regression with Proxies
A.2. Proof of Theorem 4.1
Theorem A.1 (Full description of Theorem 4.1). For any positive å & with probability at least 28, the following generalization bound holds for all h E H and f E F:
C
Raa(h) 1 ED
Aa
q(E jly,) log logpo(E = =j(=]]]] =)(x))
7
n
Rs(h)
log 3
log
+ cp,.. Rs( + 3.M...y)
+ha 2pl + 3.
2n
2n
(7,,8)
4bs(F,6)
ply) maxj p(==1) 8r ML and μ.t. are Lipschitz continuity of y Eigly, for forall all y y for any fixed y' E y and x + أ-= - q( = j'y') log po (E = j|x) for all X for any fixed y' E V, respectively, Mc.. and Mr are constants satisfying Lreg(y (y, < M all y, E and ES= 9(5 = jly) log = j|x) < fo all yx E X x V, respectively, and Rgg denotes the Rademacher complexity.
where CD max {sup, purly)
pailE=0)
Proof.
/ Lo o y)pa + da / (- log logpe(E(x)) Peal (x. (x. y. dxxdyd
(h)
/ Co f(xx, v) (x(x))//)) dxdy + Xa / (- log (=logpo(E)x)) p(x, y|E Ptaal (E)
Pball))
ply) )
sup
Crog (g xo(x)))))))
max Ph =j) - Xn (()
PuE j)
sup Poal Poully)
Cooglg
ply)
max Phbl = (5)) Xr2 f- loggo -log_ooo
Ddxxddd
sup Poal (y) / Crog(o (g
ply)
max (b =
X/
-q((ly) log -o log dxxddd
P(E- j) sup Phol (y)
Crog ()xx,))((x,)))
p(y)
+ max Phat (5 = =]) 1)) P
Xa --E
( dxxdy..
where the second-to-lad equality follows from the definition, p(x, y) = applying Theorem 11.3 in (Mohri, 2018) the regression risk and alignment risk separately, the following inequality holds
Hence, by
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PRIME: Deep Imbalanced Regression with Proxies
with probability at least 26.
Reall (1) S sup )
1
Σ
n
Leg (g (x) + 2uc, Rs(H)++++++))))))))))))))))))R 3M
log &
ply)
7 i=1
2n
max PhailE = -)
a
log 224 2n
Ao
( = llys)logpo(E - j|xx) + 2ur Rs(F + +3M11
p(g = 1)
Then, the rest of the proof follows directly from the definition of CD.
Remark. Theorem 4.1 covers various algorithms, such PRIME, PRIME PRW, PRIME+CB, and PRIME+LDAM, by modeling y(ll)) and po(E)x) appropriately.
A.3. Extension Non-optimal Proxy Settings
We now extend the theoretical analysis to settings with non-optimal proxies, where the learned proxy features deviate from their optimal positions due to approximation errors.
Let (2)) j=,...... denote the optimal proxy features that minimize Eproxy. and define the corresponding feature association
" as (E DE= 3yd for all j = I...., C. Then, we define the learned proxy features as zJ := 2 + + for all
(7 j C, where Ej represents the estimation error, and pe (E]x) Eis 11 denotes the corresponding feature
association with respect to the learned proxies.
To analyze the non-optimal case, we revisit the balanced alignment risk term in (21), originally derived under the assumption of optimally positioned proxies, and rewrite - log Po (E]x)) using the following identity:
- log (E(x)) = - log pa (E(x)) + (logPe(E)x) - log (e(x)))
Based on this formulation, the first term, - log (f)xx) follows the same derivation as in the proof of Theorem 4.1. The second term, (o x) - log (C) x). quantifies the discrepancy arising from the deviation between the learned and optimal proxies. This discrepancy term can be bounded using the following inequality:
tydy(e.
(x,)(x
log po(p)))))) loggo((())) =1:: log
log
2k=1e 7-dd 2k (yd,(
k== Tyd)
=T/ (z)(z,zg) z²² - (z, 2 + +(E))
+ log
dy (2. (2.2
2k=1
--dd((()))
STi (z z - dr(2, +EE) log max
e-
k
= (d 2 - dz 25 + +(s) + + T/ (dy 2h + + - -dy(z, z())
<2n max (2, + tx) (2,
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PRIME; Deep Imbalanced Regression with Proxies
Consequently, obtain the following upper bound the desired balanced risk:
Rebll (h) = L0 o y (x, y)dxdy + Xa S (- (-log (o(())) Pba(( y: E)xxdydg
sup P )
Co f(x),,))((x ())pppxxx)eee dxxdy
y p(y)
+
max Phatls =1)
Xe
--
- ((El)) log (e(E)x)p(x, y dxxdy
P(E =
sup Pbaly)
/
Cr ()))) y) dxxdy
p(y)
max Phatl = j) plE 5)
Xaa f /E((el>)
(((l)) (- log (logpo(E)x)) log p(x, ddxdy
sup P)ult)) ply)
/
Crosl f(x), (elpp((x))xxle y)xxy
Aa ( - /lll ydxody
+ max Phull = 5)
plg =
/ 2 max (d, 2h + cx) d,(2, p().
If y is norm, we can apply the triangle inequality simplify the last term of the inequality:
(1) S sup ( ) / Crog x)x), ( y)dxdy
p(y)
+ max (E = =1) Ao (f-
Σ
+ 2r, maxd, + ck. 2b)
p(E = j)
Remark. Importantly, as training progresses and the proxies become accurate (i.e., Eg becomes smaller), the residual term decreases accordingly, resulting in a tighter bound. Empirically, we also observe that PRIME performs robustly even when the proxies are randomly initialized.
A.4. Further Theoretical Insight
Another perspective offered by Theorem 1 is that (h) is bounded by constant multiple of Cp. A higher value of Cp leads to a larger deviation between Rh (h) and (R(),, Intuitively, incorporating data skewness into an effective balancing of the loss function facilitates more direct estimation of the balanced risk. Specifically, PRIME focuses aligning features with proxies, we direct our analysis to the risk associated with Latign-
Theorem A.2. For any loss function L(x. y, E), we have
[(X,Y, W. /
where the reweighted loss, L,, defined as
Pbal(E)
C, =
L. J (gEly)p(y)dd
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PRIME; Deep Imbalanced Regression with Proxies
Proof.
/ (( J ((El))((y)dd p(x, v E)xxdyde / y(x, Poall)) p(x, plx(y)())()))xxd P(E)
PoalE)
(x.xx. Eddddddd
/ y(x,y,))p(x, y Poal dxdydg
/ C(x. y, P) y, & dxddyd..
Remark. If L = -Te log Ag and ((Ely) TT. L reduces to our alignment loss Lalign-
Theorem A.2 confirms that employing C, allows the balanced alignment risk to minimized directly. Note that the weighting term (E)p(() is related to the proxy frequency. Since PRW, CB, and LDAM perform re-weighting, balancing. and margin control based on the proxy frequency, they empirically approximate C, Specifically, for PRW, using g(ll) Tş and applying batch-wise Monte Carlo,
derive 8j follows:
Pbal (5 =j) rl5 = 5) J = jly)ply)dy
Peals j)
1
(23)
D No 1= of jly = yi) 8j
A similar deriviation is possible for CB, LDAM by appropriately modeling d(Ely) and po (5]x). Finally, we conclude that incorporating class imbalance techniques approximately induces the balanced alignment risk, leading to balanced feature learning.
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PRIME: Deep Imbalanced Regression with Proxies
B. Detailed Experimental Setup
This section presents additional details our experimental setup. In $B.1, we first provide a detailed explanation of the datasets used in our experiments. In $B.2, we provide the implementation details of PRIME.
B.1. Dataset Details
In this work, we conduct experiments on four real-world imbalanced regression benchmarks introduced by (Yang et al., 2021): AgeDB-DIR, IMDB-WIKI-DEE WIKI-DIR, NYUD2-DIR, STS-B-DIR. For fair and meaningful comparison with existing methods, we evaluate the proposed method using the same experimental setup, following the previous state-of-the -ortt--rrtt methods for each dataset (Yang et al., 2021; Gong al., 2022; Keramati al., 2024). Table 10 provides the overall statistics of the four datasets. Please refer to (Yang al., 2021) for more details.
Table 10. Overall dataset statistics.
Dataset AgeDB-DIR
Target type
Target range
Bin size
Max bin
Min bin
# *Training
# Val.
# Test
Age
0. 101]
353
1
12,208
2,140
2,140
INDB-WIKI-DIR
Age
00, 186
7,149
1
191,509
11,022
11,022
NYUD2-DIR
Depth
[0.7, 10)
0.1
1.46 x 10
1.13 x 10
50,688
654
STS-B-DIR
Text similarity
[0,5]
0.1
428
1
5,249
1,000
1,000
B.2. Implementation Details
For fair comparisons, follow the benchmark settings of (Yang et al., 2021) for all baselines and method. Specifically, the same backbones and training details in existing methods and tune only the hyperparameters of PRIME. HIDB-WIKI-DIR, NYUD2-DIR, and
Tables 11, 12, 13, and 14 summarize the implementation details for AgeDB-DIR, STS-B-DIR, respectively. Overall, PRIME is easy to implement and can be integrated into existing regression methods by simply adding Cpruyy and Lalign to the regression loss Lug. We will release the code after publication.
The number of proxies C' is empirically determined for each dataset. Proxy embeddings {z,);- 1+1=11 initialized with He initialization (He et al., 2015) and trained jointly with the model. The Proxy Ir refers to the multiplication factor applied to the learning rate of the proxy. The hyperparameters Ap. A₂ Ty, and are set empirically. Especially, we use high values following (Movshovitz-Attie et al., 2017; Kim et al., 2020; Teh et al., 2020; Lim et al., 2022).
PRIME.
Class imbalance techniques. The implementations of class imbalance techniques follow their original codes, with hyperpa- rameters set as in the respective papers. In PRW, the truncation threshold 8min for excessively small 8, values is set as a scaled multiple of the median value Smed- In CB, 3 0.99 is used for all experiments, while in LDAM, the max margin value defines the upper limit of the enforced margin. DRW, short for Deferred Re- weighting (Cao et al., 2019), is optionally applied to all three methods, meaning that re- re-weighting is applied only after the specified DRW epoch.
Training details. For AgeDB-DIR and IMDB-WIKI-DIR, we use ResNet50 (He et al., 2016) as the backbone and the square root inverse (SQInv) re- reighte MAE loss as the regression loss fug. For NYUD2-DIR, we adopt a ResNet50- based encoder-decoder architecture (Hu et al., 2019) and Balanced MSE (Ren al., 2022) as freg. For STS-B-DIR, we employ BiLSTM with GloVe (Pennington et al., 2014) word embeddings as the feature extractor and use LDS + inverse (Inv) re-weighted MSE loss freg- The training hyperparameters, including epoch, batch size, learning rate, weight decay, optimizer, and scheduler, are primarily chosen based on the previous state-of-the-a art methods (Gong et al., 2022; Ren et al., 2022; Keramati et al., 2024) for each dataset.
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PRIME; Deep Imbalanced Regression with Proxies
Table 11. Implementation details for experiments on AgeDE-DIR.
Module
Name
PRIME
PRW
CB
+ LDAM
PRIME
# Proxy
20
20
20
Proxy Ir
1
Xp
5
10
5
10
Aa
25
50
25
50
Tf
5
7:
2
5
0.005
0.0005
0.001
0.001
PRW
Smin
0.05 x 8med
DRW
X
CB
0.99 x
DRW
LDAM
Max margin
0.5
DRW
40
Training
Backbone
ResNet50 SQInv (MAE)
ResNet50 SQInv (MAE)
ResNet50 SQInv (MAE)
ResNet50
Ceeg
SQInv (MAE)
Epoch
80
Batch size
64
Learning rate
2.5 10
2.5 x 10
2.5 x 10
2.5 10
Weight decay
1.0 10
x 10
1.0 x 10m4
1.0 10
Optimizer
Adam
Adam
Adam
Adam
Scheduler
StepLR (60/0.1)
StepLR (60/0.1)
StepLR (60/0.1)
StepLR (4010.5)
Table 12. Implementation details for experiments on IMDB- -III-IR...
Module
Name
PRIME
PRW
CB
+ L.DAM
PRIME
Proxy Proxy lr
40
5
1
Ap An
5
5
5
25
25
25
25
Tf
T:
5
0.001
0.001
0.001
0.001
PRW
mmin
1.0 x 8wed
DRW
60
CB
0.99
DRW
x
LDAM
Max margin
0.5
DRW
X
Training
Backbone
ResNet50 SQInv (MAE)
ResNet50 SQInv (MAE)
ResNet50 SQInv (MAE)
ResNer50
Cres
SQInv (MAB)
Epoch
80
80
80
80
Batch size
64
Learning rate
2.5 10
2.5 x 10
2.5 x 10
2.5 10
Weight decay
1.0 10
10
1.0 10
1.0 10-
Optimizer
Adam
Adam
Adam
Adam
Scheduler
StepLR (60/0.1)
StepLR (60/0.1) 1)
StepLR (60/0.1)
StepLR (60/0.5)
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PRIME; Deep Imbalanced Regression with Proxies
Table 13. Implementation details for experiments on NYUD2-DIR.
Module
Name
PRIME
PRW
+
+ L.AMM
PRIME
# Proxy
10
10
10
10
Proxy Ir
1
Xp
0.1
0.1
0.1
0.1
An
0.5
0.5
0.5
0.5
Ty
10
10
10
Th
2
a
0.0001
0.0005
0.0005
0.0005
PRW
Omin DRW
0.05
9mod
X
3
0.99
DRW
X
LDAM
Max margin
0.5
DRW
Training
Backbone
ResNet50 E-D Balanced MSE
ResNet50 E-D
ResNet50 E-D
ResNet50 E-D
Lreg
Balanced MSE
Balanced MSE
Balanced MSE
Epoch
20
20
20
20
Batch size
64
64
64
Learning rate
1.0 x 10-4
1.0 x 10
1.0 x 10-4
1.0 10-4
Weight decay
1.0 10
1.0 10
1.0 x 10
1.0 10
Optimizer
Adam
Adam
Adam
Adam
Scheduler
StepLR (5/0.1)
StepLR (5/0.1)
StepLR (5/0.1)
StepLR (5/0.1)
Table 14. Implementation details for experiments STS-B-DIR.
Module
Name
PRIME
PRW
CB
+ LDAM
PRIME
# Proxy
26
26
26
26
Proxy ir
1
1
1
Ap
x
x 10
2
10
10
Xa
5 x 10
1 X 10
1
10
5
10
5
Ty
5
5
5
5
0.001
0.01
0.01
PRW
8min
3.0 Smed
DRW
X
0.99
DRW
X
LDAM
Max margin
0.5
DRW
X
Training
Backbone
BiLSTM + GloVe
BiLSTM + GloVe
BiLSTM GloVe
BiLSTM + GloVe
Lrg
LDS + Inv (MSE)
LDS + Inv (MSE)
LDS Inv (MSE)
LDS + Inv (MSE)
Epoch
300
300
300
300
Batch size
16
16
16
16
Learning rate
2.5 x
2.5 x 10
2.5 x 10
2.5 x 10
Optimizer
Adam
Adam
Adam
Adam
Patience
100
100
100
100
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PRIME; Deep Imbalanced Regression with Proxies
C. Further Analyses
In this section, we present additional experimental results and analyses. $C.1, we present additional details and complete results for the experiments discussed in the manuscript. In SC.2, we evaluate the computational efficiency of PRIME. In $C.3, we conduct sensitivity analysis on the hyperparameters of PRIME. Lastly, in $C.4, we discuss the differences between PRIME and Regression-as- -sClaasifiiaiiiinnnn approaches, which reformulate regression classification problem.
C.1. Additional Results
C.1.1. PRIME FACILITATES EFFECTIVE FEATURE LEARNING
The twisted line in Figure 2(b) appears due suboptimal alignment between features and their corresponding proxies in the Few category. Although the proxies represent balanced feature distribution, the alignment process in (7) still faces challenges under sample imbalance. Minority samples, which occur infreeuently, often fail to align properly with their proxies, resulting in distorted feature -atuue--pooyy alignment. The use of class imbalance techniques (e.g., PRW, CB, and LDAM) provides better alignment focus on minority samples, mitigating this issue. To empirically validate their effect, we conduct an additional analysis on the AgeDB-DIE dataset, measuring the Spearman correlation between the proxy-feature similarity matrix (as visualized in Figure 2(b)) and the label similarity matrix. higher correlation indicates better alignment and reduced distortion the learned feature space. Table 15 reports the Spearman correlation values when PRIME is combined with various class imbalance techniques. Results are averaged over five runs. Incorporating class imbalance techniques significantly improves the correlation, confirming their effectiveness in facilitating better alignment, particularly for samples in the Few category.
Table 15. Spearman correlation between proxy-feature and label similarity matrices AgeDB-DIR, A higher correlation indicates better alignment between learned features and the corresponding proxies.
Method
P (t)
PRIME
0.722+0.00
PRIME + PRW
0.802+0001
PRIME + CB
0.800
PRIME + LDAM
0.837
C.1.2. COMPARISON WITH RECENT REPRESENTATION LEARNING METHODS FOR GENERAL REGRESSION
In Table 7 of the manuscript, only the results for the entire test set (i.e., All) reported. In Table 16 below, we present the complete results. HPN shows slightly better performance than PRIME in Few. However, since HPN uses fixed prototypes on hypersphere, it cannot effectively represent the entire dataset, leading to suboptimal performance in Many and Median. Notably, PRIME outperforms state-of-the-art representation learning methods designed for general regression, such as Rank-N- Rank-N-Contrast NN-Cottrsst and Ordinal Entropy, demonstrating its ability to learn effective representations that are robust to data imbalance. Furthermore, PRIME exhibits the flexibility to incorporate various class imbalance techniques for balanced feature learning in regression problems. Applying these techniques effectively enhances the performance of minority targets.
Table 16. Comparison with representation learning methods for general regression on AgeDB-DIR. The best results are marked bold, and the second best are underlined.
MAE (L)
GM (L)
Method
All
Many
Median
Few
All
Many
Median
Few
SQInv (MAE)
7.42+000
6.78-2012
8.55 +0.1
10.71 +0.31
4.77=
4.37+a0.4
5.73+a29
7.39
HPN (Menes
7.38
6.78
8.44
10.10
4.66=009
4.30+
5,4644.16
6.41 +0.39
Ordinal Entropy (Zhing 2023g)
7.33
6.77
8.24
10.16
2.68
4.321000
5,3940.19
6.32
TRank-N-Contir (Zba 2023)
7.27:1005
6.52-10.3
8.62.1015
10.6620.4
4.69
4.23
5,73
7.12
+ PRIME
7.09
6.38 10.1
8.39
13.33
4.39
3.91
5.58:10.22
6.57
PRIME PRW
7.06=2009
6.67
7.27 20:25
9.91+1.16
4.39
4.14+:002
4,6944220
6.39
PRIME CB
7.12
6.60
8.07 20:11
9.29
4.47=nas
4.1622008
5.23
5.81
PRIME LDAM
0.24+006
6.85
2.84
9.29
4.47
4.261:012
4.89
5.60=0.54
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PRIME; Deep Imbalanced Regression with Proxies
C.1.3. EFFECTIVENESS OF OUR PROXY FORMULATION
Table 8 in the manuscript reports only the results for the entire test set (i.e, All.. In Table 17 below, we present the complete results. For ProxyNCA, we adapt the original method to the regression setting. Similar to PRIME, proxy assignment is designed ensure that the associated targets which explicitly optimizes proxy features to be well-ordered in the feature space via Lppaxy, ProxyNCA relies solely on feature-proxy alignment. As shown in our results, PRIME significantly outperforms ProxyNCA, demonstrating the advantage of our Die-spcc proxy formulation. For the non-learnable variant of PRIME, proxy features are computed as the centroids of sample features assigned to each proxy. To enable proper backpropagation of the proxy and alignment losses, these proxy features are updated within each mini-batch based on the current sample-to-pooxt assignments. While the centroid-based method achieves slightly better performance than the learnable proxy in the Median category, it suffers from notable performance degradation in the other regions. In particular, Few category, indicating that the centroid- bassedd-based proxies struggle under severe data sparsity. This performance gap stems from their inherent limitations: centroid quality depends on the number of assigned samples and becomes unstable when only a few are available. In contrast, learnable proxies are global parameters updated via backpropagation, offering greater stability and robustness under sparse conditions.
uniformly distributed in the target space. However, unlike PRIME,
observe significant performance drop in the
Table 17. Comparison with proxy-based alternatives on AgeDB-DIR, The best results are marked bold, and the second best are underlined.
MAE (L)
GM (L)
Method
All
Many
Median
Few
All
Many
Median
Few
ProxyNCA (Mooshoviz-Atiiss et al. 2017)
7.33
6.52
8.69
11.14
4.66
4.12
5.80
7.60+a.s
Non-learnable (centroid)
7.21 +0.09
6.57
8.20
4.67 10.89
4.24
5,42
7.64
PRIME
7.09
6.38
8.39
10.13
4.39
3.91
5.58+022
6.57
C. ABLATION STUDY
Table 9 in the manuscript reports only the results for the entire test set All). In Table 18 below, present the complete results. Comparing the ablation models, the transition from M1 to M2 leads to a significant performance improvement across All, Many, and Few, highlighting the effectiveness of Cpoxy. From M2 to M3, assigning proxies uniformly in the target space leads to a notable performance gain in Few compared to random initialization, demonstrating the effectiveness of ensuring that proxies represent the target space a balanced manner. Finally, the transition from M3 to M4 (PRIME) further enhances performance, as regression involves continuous targets, making distance- propootoooooo assignment, as described in (6), more effective than one-hot encoding.
Table 18. Performance comparison of ablation models AgeDB-DIR, The best results are marked in bold.
MAE (1)
GM (L)
Method
All
Many
Median
Few
All
Many
Median
Few
MI
7.34
6.49
8.8420.9
11 31.24:103
4.6620m
4.1 4.112000
5.961004
7.882048
M2
7.24+.00
6.47-a11
8, 8.40=a18
11.324047
4,61
4.09_0.12
5.71
7.962060
M3
7.23
6.45
8.5220.2
10.964051
4.55
4.01-0.11
5.74
7.762036
M4 (PRIME)
7.09
6.38
8.39
10.13
4.39
3.91=0.10
5.58
6.57+049
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PRIME; Deep Imbalanced Regression with Proxies
C.2. Computational Efficiency
To analyze the computational efficiency of PRIME, we compute the average wall-clock training time (in seconds) using four NVIDIA Tesla V100 GPUs. Table 19 presents comparisons with existing representation learning methods AgeDB-DIR, For fair comparisons, we apply the same training details (e.g., epochs, batch size, optimizer, etc.) to all methods. The training time of PRIME is considerably lower than that of FDS and ranking-based methods (RankSim and Rank-N-Contrast) while remaining comparable to the time complexity of ProxyNCA, Ordinal Entropy, and ConR. Although incorporating class imbalance techniques introduces a slight computational overhead, it remains comparable to other well-established methods. Overall, these results demonstrate that PRIME is an effective representation learning framework that does not compromise efficiency.
Table 19. Average wall-clock training time (in seconds) on AgeDB-DIR.
Method
Training time (sec) (1)
A
SQInv (MAR)
1818.0 + 58.7
ProxyNCA (Mossovin-Anias 2017)
1934.8 + 77.4
(+ 116.8)
HPN (Mettes at.l.,
1833.8 + 13.2
15.8)
FDS (Yang et al., 2021)
3380.0 + 21.5
(+ 1562.0)
RankSim (Giong et al., 2022)
2254.4 1 20.9
(+44))4
Ordinal Entropy
20258)
2067.6 1 79.9
(+ 249.6)
Rank-N-Contrast
2023)
2122.6 1 33.7
(+ 304.6)
ConR (Keramati et al., 2024)
1952.6 23.0
(+ 134.6)
+ PRIME
1936.6 + 45.4
(+ 118.6)
+ PRIME + PRW
2094.6 + 20.6
(+ 276.6)
PRIME CB
1990.2 + 41.4
(+ 172.2)
PRIME IDAM
1987.6 18.7
169.6)
C.3. Sensitivity Analysis
We analyze the impact of PRIME's hyperparameters using the AgeDB-DIR dataset. Specifically, we examine the effects of the number of proxies (C), the trade-off hyperparameters for Fproxy and Lalign in (8) (A, and X²), the temperature hyperparameters (Ty and Tı), and the coefficient for the regularization term in (4) (ax). We evaluate their influence by varying the values follows: C' (10, 20, 30, 40), Ap E {0.5, 2.5, 5.0, 10.0), >a E (5, 10, 25, 50), Tf (0.5, 1.0, 5.0). {0.5, 1.0, 2.0, 5.0). and a {0, 0.0001, 0.0005, 0.001, 0.005). Tables 20, 21, 22, 24, 23, and 25 summarize the results. Overall, PRIME demonstrates reliable and robust performance across different hyperparameter choices. In particular, PRIME consistently outperforms the w/o PRIME baseline in almost all cases (SQInv (MAE) serves as the baseline), further demonstrating its effectiveness. As mentioned in Table 11, for the main results, we set C = 20, Ap = 5, A = 25, = 5,
T = and a 0.005, which are highlighted gray in the tables.
Table 20, Effect of the number of proxies (C) on AgeDB-DIR. The gray highlliggl value indicates the selected setting used in our experiment. The best results are marked in bold.
MAE (L)
GM (L)
Method
All
Many
Median
Few
All
Many
Median
Few
w/o PRIME
7.42:006
6.78
8.55
10.71
4.77
4.37:20
5.73
7.39
PRIME (C- =10)
7.35++010
6.49
8.80+4.00
11.47=0046
4.65
4.09:4005
5.95
7.90+0.47
PRIME (C -20)
7.09
6.38
8.39
10.13
4.39 #0.0s
3.91
5.58
+:049
PRIME (C -30)
7.14
6.41
8.31
10.61
4.48
3.98
5.55
7.31 10.50
PRIME (C = 40)
7.16
6.37=20.05
8.41+:018
11.20
4.53
4.02:10.8
5.55
7.94
23

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PRIME; Deep Imbalanced Regression with Proxies
Table 21. Effect of Ap on AgeDB-DIR. The gray-highlighted value indicates the selected setting used in our experiment. The best results are marked bold.
MAE (L)
GM ())
Method
Many
Median
Few
Many
Median
Few
w/o PRIME
4.02
6.78
8.55
10.7140.1
4.77=0008
4.37 +.0.4
5.73
#.395
PRIME (A,, 0.5)
7.19
6.42+00.7
8.46
10,97
4.53
4.00
5.73+029
7.79#0.78
PRIME (Ap 2.5)
7.21
6.46+4.11
8.33
10.84
4.44
4.05 #:0.0
5,50+0.8
6.55
PRIME (Ap. 5.0)
7.09
6.38
8.39
10.13
4.39
3.91 +:0.0
5,58+022
6.57+t0.9
PRIME (Ap = 10.0)
7.2610006
6.49
8.58
10.91
4.63=0.10
1.09
5,83
6.83
Table 22. Effect of X, on AgeDB-DIR. The gray-highlighted value indicates the selected setting used in our experiment. The best results are marked bold.
MAE (L)
GM (L)
Method
All
Many
Median
Few
All
Many
Median
Few
w/o PRIME
7.42.20.66
6.78
8.55
10.7
4.77:108
4.37=0.14
5.73
7.39
PRIME (A, =5)
7.20=a014
6.54
8.37
10.25
4.57
4.16
5,46.0.31
6.78+t04
PRIME (Aa 10)
7.18
4..11
8.51
10.80=a62
4.63
4.10
5.83
7.68
PRIME (Aa 25)
2.00
6.3810.11
8.39
10.13
4,39
3.91:10.10
5.58
6.57:10.41
PRIME (An -50)
7.21 20.07
6.42:10.7
8.56.1026
10.94=045
4.54
4.02:10.8
5.72.0.4
7.65
Table 23. Effect of Ty AgeD The gray-highlighted value indicates the selected setting used in our experiment. The best results are marked bold.
MAE (L)
GM (L)
Method
Many
Median
Few
Many
Median
Few
w/o PRIME
7.42:10.6
6.78
8,55
10.71
4.77
4.37.0.4
5.73
7.3940066
PRIME (ry -0.5)
7.20
6.61 1:016
8.18
10.10.0.39
4.59
4.20
5,41
6.68
PRIME (Ty- 1.0)
7.24
6.51 10000
8.38
10.45
4.56
4.06
5.82
6.9611026
PRIME (T -20)
0.22
6.45 1:002
8.59
10.68 +0.47
4.62 #0.11
4.09
5,90
7.39
PRIME (Ty- = 5.0)
7.09:
6.38 10.11
8.39
10.33
4.39 10.08
3,91
5.58
6.57.10.99
Table 24. Effect of r. AgeDB-DIR. The gray-highlighted value indicates the selected setting used in our experiment. The best results are marked in bold.
MAE (L)
GM (L)
Method
Many
Median
Few
Many
Median
Few
w/o PRIME
7.42-20.6
6.78
8.55
10.71
4.77+008
4.37
5.73
7.394036
PRIME (7t 0.5)
7.20
6.42++0.0
8.46
11.07
4.43
4..4
5.70
7,95
PRIME (Tc 1.0)
7.16 00.08
6.44+-0.0
8.33
10.67
4.52+008
4.04
5,57
7.38
PRIME (T. 2.0)
10
6.4022012
8.60.10
10.85
4.59
4.0621077
5.79
7.634030
PRIME (7: = 5.0)
7.09 00.0k
6.38
2.39
10.13
4.39
3.91
5,58
6.57-9049
24

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PRIME; Deep Imbalanced Regression with Proxies
Table 23, Effect of a on AgeDB-DIR. The gray-highlighted value indicates selected setting used our experiment. The best results are marked in bold.
MAE (1)
GM (1)
Method
All
Many
Median
Few
All
Many
Median
Few
w/o PRIME
0.42
+.78
8.55
10.71 +0.31
4.77
2.37
2.73
a.
PRIME (a 0)
0.21
1..0
8.44
11.16:0.40
4.50
4.02
5.76
7.77-4:0.10
PRIME (o = 0.0001)
7.17=0006
6.44
8.27 38
11.03=2017
4.55
4,04
5.62
7.79:t024
PRIME (a 0.0005)
7.22=0.07
6.47
2.
11.1920.54
4.60
4. 4.102203
5.6620.2
7.76:t029
PRIME 0.001)
7.28
6.52+000
8.
10.33
4.53
4. 4.122104
5.70
6.87:1055
PRIME (a 0.005)
7.09 00008
+.38-
8.39
10.13
4.39
3.91+0.00 +0.10
5.58
6.57:+0..9
C.4. Discussion on Regression-as-Clasiiiee Approaches
Although our PRIME shares classification-lik perspective, highlight two key differences from Regression-as- Classification approaches (Rothe et al., 2015; Cao et al., 2017; Liu et al., 2019a; Xiong & Yao, 2024) that quantize continuous targets into discrete bins and treat each bin as class: (i) As samples with different target values are grouped under the same class, previous methods suffer from quantization errors. In contrast, PRIME assigns proxies based on target associations derived from target distances, as in (6), effectively mitigating quantization error. (ii) Moreover, rather than directly predicting proxy indices (i.e., classes), PRIME optimizes the model to minimize the feature distance the corre- sponding proxy. As our proxy loss Sposy in (4) enforces proxies to be well-ordered, it facilitates better regression-speecffi representation learning.
25


Reviews:
[{"review_id": "sorBX9X05a", "reviewer": "Reviewer_h5o4", "summary": "For Deep Imbalanced Regression (DIR), the authors propose Proxy-based\nRepresentation learning for IMbalanced rEgression (PRIME).\n\nThey generate synthetic proxies in the feature space and align\ninstances to the proxies.  The proxies are distributed uniformly\nacross the target values.  While the corresponding target values are\ndetermined, the proxies are learned via model parameters.  Inspired by\ntSNE, they define $p_{i,j}$ and $q_{i,j}$ to be similarities between $y_i$ and\n$y_j$ (target space) and between $z_i$ and $z_j$ (feature space).  They seek\nto minimize the KL divergence of the two distributions ($p_{i,j}$ and $q_{i,j}$).  To reduce\ntrivial solutions, they encourage distance between proxies and \"feature\nspace uniformity\" (Wang & Isola 2020).  Proxy loss ($L_{proxy}$) is the\nKL divergence and regularization.\n\nFor each instance, they calculate the association via distance and\nsoftmax to each proxy in the features space.  Similarly, they\ncalculate the association in the target space.  Alignment loss\n($L_{align}$) is the cross entropy with the two associations (similar\nto a classification loss).  The overall loss is the regression loss\nplus $L_{proxy}$ and $L_{align}$.\n\nFor evaluation they use 4 datasets and compare with 8 existing\ntechniques.  Empirical results indicate adding PRIME is somewhat\nbeneficial.  Ablation studies were performed to indicate the\ncontribution of some of the components.\n\n## update after rebuttal\n\nAfter reading and responding to the authors' rebuttal, I decided to raise my rating to Accept -- between Weak Accept and Accept to be more precise.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the constructive feedback. We have addressed all points and will revise the manuscript accordingly.\n## 1. PRIME’s effectiveness in the Few category\nWe would like to point out that PRIME alone achieves state-of-the-art performance in the Few category on three out of four datasets, outperforming existing methods by 0.7\\%, 0.5\\%, and 3.6\\% on AgeDB-DIR, NYUD2-DIR, and STS-B-DIR, respectively. Furthermore, a key contribution of PRIME lies in its ability to seamlessly integrate class imbalance techniques into regression tasks. This facilitates balanced feature learning, substantially enhancing performance in the Few category.\n\nTo further validate PRIME’s effectiveness in the Few category, we conducted an additional analysis on the test set of AgeDB-DIR, measuring the Spearman correlation between the feature similarity matrix and the label similarity matrix. A higher correlation indicates that the learned features are more well-ordered and better reflect the continuity of the label space, which is crucial for learning effective representations in regression tasks.\n\nAs shown in Table 1, we compared the Spearman correlations for all samples and for samples in the Few category across PRIME, RankSim, and ConR. Results are averaged over five runs. While RankSim and ConR exhibit reasonable correlation values on the full dataset, their performance significantly degrades in the Few category. In contrast, PRIME maintains a high correlation within the Few category, indicating that it learns well-ordered feature representations, even for minority samples. This highlights the strength of our proxy-based formulation, which provides holistic guidance for feature positioning, allowing minority samples to be embedded in alignment with the overall label structure.\n\nWe will incorporate these additional results and analyses into the revised manuscript to better highlight PRIME’s effectiveness in the Few category.\n\n**Table 1.** Spearman correlation between feature and label similarities.\n|Method|All|Few|\n|---|---|---|\n|RankSim|0.804$\\pm$0.008|0.587$\\pm$0.036|\n|ConR|0.790$\\pm$0.024|0.614$\\pm$0.043|\n|PRIME|**0.942**$\\pm$0.008|**0.828**$\\pm$0.020|\n## 2. Feature space uniformity\nThe second term in Eq. (4) encourages proxies to be repelled from one another, as it increases the angle between $\\mathbf{z}_i^p$ and $\\mathbf{z}_j^p$, thereby inducing a more dispersed (i.e., uniform) proxy distribution. Unlike the original uniformity loss (Wang & Isola, 2020), which pushes all pairs equally apart, our formulation increases the pairwise cosine distance proportionally to the label distance. This not only promotes uniformity in the proxy space but also preserves label ordinality.\n\nSince sample features are aligned to proxies via the alignment loss in Eq. (7), the proxy uniformity is naturally transferred to the feature distribution. In this way, the second term in Eq. (4) promotes feature space uniformity by shaping the proxy distribution, which in turn guides the feature distribution through alignment.\n\nTo validate this, we trained a variant of PRIME without the second term in Eq. (4) (i.e., setting $\\alpha=0$) and measured feature space uniformity on the test set of AgeDB-DIR using the $\\mathcal{L}_{\\text{uniform}}$ metric proposed by (Wang & Isola, 2020). \n\nTable 2 presents the results averaged over five runs. Removing the second term leads to higher $\\mathcal{L}_{\\text{uniform}}$ (i.e., lower uniformity), confirming that this term is critical for inducing feature space uniformity. We will include this result and discussion in the revised manuscript.\n\n**Table 2.** Feature space uniformity.\n|Method|$\\mathcal{L}_{\\text{unifrom}}$ ($\\downarrow$)|\n|---|---|\n|PRIME ($\\alpha=0$)|$-$1.458$\\pm$0.022|\n|PRIME|**$-$1.544**$\\pm$0.016|\n## 3. Larger number of proxies\nFor simplicity, we set the number of proxies $C$ such that each proxy would roughly cover a 5-year age span for AgeDB-DIR and IMDB-WIKI-DIR, and kept it fixed while tuning the other hyperparameters. As shown in Table 15 in the appendix, even without tuning, increasing the number of proxies leads to improved performance in the many and median regions. This suggests that with proper hyperparameter tuning, a larger number of proxies could further improve performance.\n\nTo support this, we conducted an additional experiment with $C = 40$, tuning the associated hyperparameters ($\\lambda_p = 1$, $\\lambda_a = 5$, $\\tau_f = 5$, $\\tau_t = 1$, $\\alpha = 0.005$), and obtained even better results, as reported in Table 3. Results are averaged over five runs. We will revise the manuscript to include this result.\n\n**Table 3.** Results with more proxies on AgeDB-DIR.\n|Method|MAE||||GM||||\n|---|---|---|---|---|---|---|---|---|\n||All|Many|Median|Few|All|Many|Median|Few|\nPRIME ($C=40$)|**7.03**$\\pm$0.08|**6.35**$\\pm$0.12|**8.24**$\\pm$0.07|**9.90**$\\pm$0.25|**4.35**$\\pm$0.09|**4.00**$\\pm$0.07|**5.29**$\\pm$0.24|**6.09**$\\pm$0.13|", "claims_and_evidence": "For evaluation they use 4 datasets and compare with 8 existing\ntechniques.  Empirical results indicate adding PRIME is somewhat\nbeneficial.  PRIME generally outperforms existing methods.  PRIME alone outperorms in 3 out of 4 datasets in the Few category.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are reasonable.", "theoretical_claims": "I am not familiar with some of the terms in Theorem 4.1 and hence did\nnot check the proof in the Appendix.", "experimental_designs_or_analyses": "Tables of results and visualization are helpful.  In the tables, since the existing methods do not have the benefit of additional methods, compare PRIME alone with the existing methods, perhaps with a different highlight.", "relation_to_broader_scientific_literature": "The proposed method is different from existing methods on\nrepresentation learning in imbalanced regression.  While the different\ncomponents are borrowed from tSNE, (Wang & Isola 2020), and\nclassification loss, the combination seems interesting.", "essential_references_not_discussed": "I am not aware of essential references that are not discussed.", "other_strengths_and_weaknesses": "While the different components are borrowed, the combination is\ninteresting.", "other_comments_or_suggestions": "More explanation on why the second term in Eq 4\ncan achieve \"feature space uniformity\" (Wang & Isola 2020)", "questions_for_authors": "1.  To be a self-contained paper, can you explain why the second term in Eq 4\ncan achieve \"feature space uniformity\" (Wang & Isola 2020)?\n\n2.  How to determine the number of proxies?  Table 15 in Appendix: any\ninsight on why C=20 seems to perform better?  I was wondering that\nmore proxies would generally improve the learned feature space.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {"ethical_review_concerns": "n/a"}}, {"review_id": "AtAx55qr7R", "reviewer": "Reviewer_h4q5", "summary": "The authors propose a novel method for imbalanced regression, leveraging learnable proxies as global reference points to achieve a balanced and well-structured feature distribution and aligning sample features with these proxies. Extensive experiments are conducted on multiple benchmarks, yielding strong and impressive results.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the constructive and insightful comments. We have addressed all points and will revise the manuscript accordingly.\n## 1. Ablation on non-learnable proxy\nAs noted by the reviewer, PRIME is flexible with respect to how proxies are constructed—proxies can be either learnable or non-learnable. Following the suggestion, we conducted an additional ablation experiment on a non-learnable variant of PRIME, where proxy features are updated as the centroids of sample features assigned to each proxy. Specifically, to ensure the proxy loss and alignment loss can be properly backpropagated, we update the proxy features within each mini-batch based on the current sample-to-proxy assignments.\n\nTable 1 compares the performance of the centroid-based proxy update with our PRIME using learnable proxies on the AgeDB-DIR dataset. Results are averaged over five runs. While the centroid-based method achieves slightly better performance than the learnable proxy in the Median category, it suffers from notable performance degradation in the other regions. In particular, we observe a significant performance drop in the Few category, indicating that the centroid-based proxies struggle under severe data sparsity.\n\nWe attribute this performance gap to the inherent limitations of the centroid-based method. Since proxies are updated as the centroids of the assigned sample features, their quality heavily depends on the number of assigned samples. When only a few samples are available—as is often the case in the Few category—the estimated centroids become unstable and unreliable. Moreover, because centroids are computed within each mini-batch, their estimates can fluctuate significantly depending on the batch composition. In contrast, learnable proxies are global parameters that are updated via backpropagation, offering greater stability and robustness, particularly in data-sparse regions.\n\nThis issue is further exacerbated in regression settings, where some proxy bins may contain no samples at all. In such cases, the centroid-based approach cannot update the corresponding proxies, leaving them inactive throughout training. In contrast, learnable proxies remain effective even without sample assignments, serving as global reference points that guide other samples and support representation learning.\n\nWe will add this ablation study and discussion to the revised manuscript.\n\n**Table 1.** Results with non-learnable proxies.\n|Method|MAE||||GM||||\n|---|---|---|---|---|---|---|---|---|\n||All|Many|Median|Few|All|Many|Median|Few|\n|Non-learnable (centroid)|7.21$\\pm$0.09|6.57$\\pm$0.10|**8.20**$\\pm$0.13|10.89$\\pm$0.33|4.67$\\pm$0.11|4.24$\\pm$0.12|**5.42**$\\pm$0.15|7.64$\\pm$0.22|\n|PRIME|**7.09**$\\pm$0.08|**6.38**$\\pm$0.11|8.39$\\pm$0.26|**10.13**$\\pm$0.36|**4.39**$\\pm$0.08|**3.91**$\\pm$0.10|5.58$\\pm$0.22|**6.57**$\\pm$0.49|\n## 2. Clarification on Figure 2(b)\nThe twisted line pattern in Figure 2(b) appears due to suboptimal alignment between features and their corresponding proxies in the Few category. Although the proxies represent a balanced feature distribution, the alignment process in Eq. (7) still faces challenges under sample imbalance. Minority samples, which occur infrequently, often fail to align properly with their proxies, resulting in distorted feature–proxy alignment.\n\nThe use of class imbalance techniques (e.g., PRW, CB, and LDAM) provides better alignment focus on minority samples, mitigating this issue. To empirically validate their effect, we conducted an additional analysis on the AgeDB-DIR dataset, measuring the Spearman correlation between the proxy–feature similarity matrix (as visualized in Figure 2(b)) and the label similarity matrix. A higher correlation indicates better alignment and reduced distortion in the learned feature space.\n\nTable 2 reports the Spearman correlation values when PRIME is combined with various class imbalance techniques. Results are averaged over five runs. Incorporating class imbalance techniques significantly improves the correlation, confirming their effectiveness in facilitating better alignment, particularly for samples in the Few category. \n\nWe will revise the manuscript to include this additional analysis and the corresponding figures alongside Figure 2(b).\n\n**Table 2.** Alignment between proxies and features.\n|Method|Spearman $\\rho$ ($\\uparrow$)|\n|---|---|\n|PRIME|0.722$\\pm$0.020|\n|PRIME + PRW|0.802$\\pm$0.021|\n|PRIME + CB|0.800$\\pm$0.023|\n|PRIME + LDAM|0.837$\\pm$0.015|", "claims_and_evidence": "Yes, I believe the claims are supported by clear evidence.", "methods_and_evaluation_criteria": "Yes, the method is evaluated on standard benchmarks alongside other representative baselines.", "theoretical_claims": "I reviewed the theoretical claims and did not find any apparent issues. However, I am not fully certain about their rigorous correctness in the supplementary material, and a more thorough verification may be necessary.", "experimental_designs_or_analyses": "Yes, I find the current experimental designs and ablation studies to be valid and sound.", "relation_to_broader_scientific_literature": "The authors have done a good job in covering the related work.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "**Strengths**: The manuscript is in a clear and easy-to-follow presentation flow. The methodology and experimentation are solid. \n\n**Weakness**: the overall idea is interesting and the demonstration is solid, but I have concerns about the proxy features. It would enhance the contribution if the authors can discuss more on the choice of proxy features. In the proposed method a learnable proxy feature bank is used, but what if the method use non-learnable proxy features? E.g. we can discretize the data points to bins like LDS in [1], and then within each bin we can have its own proxy features (e.g., the centroid of all features within the bin)? \nDo the authors have any insights? How would this type of proxy learning compare to learnable proxy learning? It would even better if the authors can do an ablation study.\n\n\nI am open to raising my score based on the authors' response.\n\n\n[1] Yang et al., Delving into Deep Imbalanced Regression, ICML 2021", "other_comments_or_suggestions": "I have one curious question about the Figure 2(b): why is there a twisted line pattern in the top right?", "questions_for_authors": "N/A", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "X4DHYhhxy7", "reviewer": "Reviewer_RZfa", "summary": "This paper presents PRIME, a method for handling regression tasks with imbalanced data distributions. PRIME introduces synthetic proxies as reference points that uniformly represent the continuous target space, aiming to mitigate representation collapse toward majority-target regions. The method uses two main loss components: a proxy loss, which positions these reference proxies in the feature space according to their relative positions in the target space, and an alignment loss, which encourages features of individual samples to move closer to appropriate proxies based on target similarities. PRIME treats each proxy like a class prototype, allowing it to adapt imbalanced classification methods.  PRIME is empirically evaluated on four benchmark datasets.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer’s comments. We have addressed all points and will revise the manuscript accordingly.\n## 1. Impact of hyperparameters\nWe have already provided detailed analyses of the impact of each hyperparameter ($\\lambda_p$, $\\lambda_a$, $\\tau_f$, $\\tau_t$, and $\\alpha$) in Tables 16–20 in the appendix. The results show that PRIME consistently outperforms the w/o PRIME baseline regardless of the choice of hyperparameters, demonstrating strong robustness and practical stability. We will revise the manuscript to make this analysis more prominent.\n## 2. Clarification on proxy initialization\nWe believe there may be a misunderstanding. PRIME does not rely on any optimal or specific initial placements of proxies. As stated on the right side of line 115 in the manuscript, all proxies are randomly initialized and jointly learned during training. Moreover, the effect of initialization randomness is already reflected in the repeated experiments with different random seeds, as reported in our main tables. The consistent performance across these runs confirms that PRIME is robust to proxy initialization. We will revise the manuscript to make this clearer and avoid potential confusion.\n## 3. Theoretical analysis under non-optimal proxy positioning\nWe note that the derivation of the generalization error bound in Theorem 4.1 remains valid regardless of whether the proxies are optimal. When proxies are not optimally positioned, the resulting discrepancy can be incorporated as an additional term in the bound, rather than invalidating the analysis. To support this, we provide a sketch of how the generalization bound can be extended to the non-optimal case. \n\nLet $\\tilde{\\mathbf{z}}_j^p$ for $j=1,\\ldots,C$ denote the optimal proxy features,\n\nand $\\tilde{p}:=\\tilde{p}_{\\theta}(\\xi|\\mathbf{x})$ be the corresponding feature association distribution.\n\nThe empirical (i.e., non-optimal) proxies can be defined as $\\mathbf{z}_j^p:=\\tilde{\\mathbf{z}}_j^p+\\epsilon_j$, \n\nwhere $\\epsilon_j$ represents the estimation error, and $p:=p_{\\theta}(\\xi|\\mathbf{x})$ denotes the corresponding feature association.\n\nWe revisit the balanced alignment risk term in Eq. (21) of the appendix, which was originally formulated based on optimally positioned proxies. To analyze the non-optimal case, we subsititue $\\log \\tilde{p}$ by applying the following identity: $\\log \\tilde{p}=\\log p + [\\log \\tilde{p} - \\log p].$\n\nThen, the first term, $\\log p$, follows the same derivation as in Theorem 4.1. The second term, $\\log\\tilde{p}-\\log p$, captures the discrepancy introduced by the deviation between the empirical and optimal proxies. Since $p$ and $\\tilde{p}$ is defined as softmax, we can bound this residual term using the inequality: $\\frac{\\sum a_i}{\\sum b_i} \\leq \\max_i \\frac{a_i}{b_i}$ for positive values $a_i$, $b_i$, which leads to:\n$|\\log\\tilde{p} - \\log p|\n\\leq \n2\\tau_f\\max_j |d_f(\\mathbf{z},\\tilde{\\mathbf{z}}_j^p + \\epsilon_j) - d_f(\\mathbf{z},\\tilde{\\mathbf{z}}_j^p)|.$\n\nFinally, applying the inequality above to Eq. (21) yields an additional bounded term, which can be directly incorporated into the generalization error bound derived in Theorem 4.1. Importantly, as training progresses and the proxies become more accurate (i.e., $\\epsilon_j$ becomes smaller), the residual decreases accordingly, leading to a tighter bound. Our empirical results also show that PRIME performs robustly with random initialization of proxies. We will include this extended derivation in the revised manuscript with a full proof.\n## 4. Distinction from classification-based methods\nTo the best of our knowledge, PRIME is the first to introduce proxies specifically designed for imbalanced regression. Moreover, as discussed in Section C.4 of the appendix, PRIME differs substantially from prior classification-based regression methods in its formulation and learning objective.\n\nFirst, existing approaches typically quantize continuous targets into discrete bins and treat each bin as a class, which inevitably introduces quantization error. In contrast, PRIME assigns proxies based on soft associations (Eq. (6)) derived from pairwise target distances, effectively mitigating such errors.\n\nSecond, instead of predicting proxy indices (i.e., classes), PRIME learns to minimize the distance between features and their associated proxies in the embedding space. This objective aligns more naturally with the continuous nature of regression and promotes representations that reflect target similarities.\n\nFurthermore, we also empirically compare PRIME with the most recent classification-based method, Hierarchical Classification Adjustment (HCA) [CVPR’24], and observe consistently superior performance, as shown in Tables 1–3 of the manuscript. We will revise the main text to better highlight these distinctions and clarify the novelty of our method.\n## 5. Related work\nAs the comment does not specify which references are missing, we would appreciate any suggestions the reviewer might have.", "claims_and_evidence": "The paper presents experimental evaluations using four benchmark datasets: AgeDB-DIR, IMDB-WIKI-DIR, NYUD2-DIR, and STS-B-DIR. However, several important baselines or combinations of existing methods appear to be missing or selectively reported. Specifically, previous methods are typically evaluated by combining multiple methods (e.g., LDS + FDS + RankSim), and other baseline are missing such as VIR (Variational Imbalanced Regression: Fair Uncertainty Quantification via Probabilistic Smoothing).", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "The paper provides theoretical generalization bounds intended to justify the effectiveness of PRIME, in Theorem 4.1. However, the theoretical analysis assumes that proxies are well-positioned, which may not always hold in practice.", "experimental_designs_or_analyses": "The paper follows standard benchmarks for evaluating imbalanced regression methods, specifically those introduced by Yang et al. (2021).", "relation_to_broader_scientific_literature": "NA", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths:\n- The paper is clearly written, logically structured, and easy to follow.\n- It includes extensive experimental analyses, with a thorough exploration of the approach through ablation studies and evaluations across multiple benchmarks.\n- Introducing synthetic proxies to guide feature learning and achieve a balanced representation in regression tasks is innovative and conceptually clear.\n\nWeaknesses:\n\n- Although the paper provides a sensitivity analysis, PRIME introduces several hyperparameters (e.g., \nλ \np\n ,\nλ\na , \nτ\nf\n , \nτ\nt\n , \nα). The detailed impact of these parameters is not thoroughly explored, raising concerns about the robustness and practicality of tuning the method for different datasets.\n- The initialization of proxies plays a central role in PRIME’s success, yet the paper does not adequately investigate how different initialization strategies affect performance. Without this, the claimed advantages might be overly dependent on optimal initial placements of proxies.\n- The theoretical analysis relies heavily on the assumption that proxies are optimally positioned, an assumption that may not hold in practical scenarios. The robustness of PRIME under deviations from this ideal condition is not discussed.\n- Leveraging concepts from classification for regression problems, such as the use of class prototypes or proxies, is not entirely novel. The paper should clarify and distinguish more explicitly how PRIME significantly differs from prior approaches that adopt classification techniques in regression contexts.\n- The related work section is missing references-", "other_comments_or_suggestions": "NA", "questions_for_authors": "Please see weaknesses \n\n[1] The theoretical analysis assumes that proxies are well-positioned (i.e., \nL proxy=0). How does PRIME perform in scenarios where this assumption does not hold? Is there empirical evidence to support the robustness of PRIME under such conditions?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "q6LNSHWQYn", "reviewer": "Reviewer_SddV", "summary": "The paper introduces PRIME, a novel representation learning method for deep imbalanced regression tasks. PRIME leverages synthetic reference points called \"proxies\" to guide the learning of balanced and well-ordered feature representations, even for minority samples. Unlike previous methods that rely solely on sample relationships within individual batches, PRIME utilizes proxies as global anchors to shape the desired feature distribution. PRIME also enables the seamless application of class imbalance techniques from classification to regression setups, bridging the gap between the two tasks. Proposed experiments demonstrate the effectiveness of PRIME, achieving good performance on various real-world regression benchmarks.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer’s feedback and the opportunity to clarify our claim regarding state-of-the-art (SOTA) performance. Below, we provide detailed comparisons with VIR and IM-Context, along with additional experiments to ensure a fair evaluation.\n## 1. Comparison with VIR\nOur claim of achieving SOTA performance is based on evaluations under a unified experimental protocol: using the same train/val/test splits, backbone (vanilla ResNet-50), and training settings as in prior works such as LDS, RankSim, and ConR. This setup allows for a fair and controlled comparison that isolates the contribution of the proposed PRIME framework.\n\nIn contrast, VIR uses a different data split and a more complex model architecture, incorporating a calibration network and reconstruction modules. These differences make direct comparisons of reported performance potentially misleading, as the results reflect not only the learning objective but also auxiliary components and dataset configurations.\n\nIn response to the reviewer’s suggestion, we conducted an additional experiment comparing PRIME to VIR under VIR’s official setting. Since the code and data splits for VIR are only publicly available for AgeDB-DIR, we focused our comparison on this dataset. We trained PRIME using the same train/val/test splits as VIR, while keeping all other settings unchanged. We then compared our results against the official pre-trained VIR model provided by the authors. For PRIME, results are averaged over five runs. As shown in Table 1, PRIME consistently outperforms VIR across all evaluation metrics under this setting. \n\nWe will revise the manuscript to include this experiment and clarify the scope of our SOTA claim accordingly.\n\n**Table 1.** Comparison with VIR.\n|Method|MAE||||GM||||\n|---|---|---|---|---|---|---|---|---|\n||All|Many|Med.|Few|All|Many|Med.|Few|\n|VIR (author-provided)|7.12|6.69|7.73|9.59|4.56|4.26|5.11|6.29|\n|PRIME|**7.06**|**6.44**|**7.61**|**9.28**|**4.39**|**4.08**|**4.93**|**6.00**|\n\n## 2. Comparison with IM-Context\nWe thank the reviewer for bringing IM-Context to our attention.\n\nFirst, we note that IM-Context is built upon a substantially different model configuration. It employs a pre-trained CLIP image encoder to extract visual features, followed by in-context learning using large-scale models such as GPT-2 and PFN. In contrast, PRIME uses a ResNet-50 backbone trained from scratch, without leveraging any pre-trained models. Therefore, direct comparisons may not be meaningful, as the two approaches differ significantly in both model capacity (i.e., CLIP, GPT-2, PFN vs. ResNet-50) and training paradigm (i.e., leveraging pre-trained models vs. training from scratch).\n\nSecond, we emphasize that PRIME is a proxy-based representation learning framework designed to be independent of model architecture. Indeed, our method is broadly applicable and can benefit from stronger backbones. We expect that using more powerful models would further improve performance.\n\nTo examine this, we conducted additional experiments using the pre-trained CLIP image encoder (ViT-B/32) as the backbone, which is also used in IM-Context. Specifically, we fine-tuned the CLIP backbone together with a two-layer MLP regression head and trained the model using the PRIME loss. To ensure robustness, we report the average performance of PRIME over five independent runs. We then compared our results on AgeDB-DIR and IMDB-WIKI-DIR with those reported by IM-Context. \n\nAs shown in Tables 2 and 3, PRIME substantially outperforms both PFN-localized and GPT2-localized across all evaluation metrics. These findings confirm that PRIME remains effective even on top of strong pre-trained models, demonstrating its flexibility across backbone choices. We believe these additional experiments further support our SOTA claim under a unified and fair evaluation protocol. \n\nWe will revise the manuscript to include these results and reflect the comparison with IM-Context.\n\n**Table 2.** Results for AgeDB-DIR.\n|Method|MAE||||GM||||\n|---|---|---|---|---|---|---|---|---|\n||All|Many|Med.|Few|All|Many|Med.|Few|\n|PFN-localized|6.58|5.61|8.49|10.49|4.29|3.58|6.30|8.19|\n|GPT2-localized|6.05|5.67|6.71|7.83|3.79|3.59|4.17|4.90|\n|PRIME|**5.47**|**5.46**|**5.48**|**5.57**|**3.48**|**3.45**|**3.64**|**3.35**|\n\n**Table 3.** Results for IMDB-WIKI-DIR.\n|Method|MAE||||GM||||\n|---|---|---|---|---|---|---|---|---|\n||All|Many|Med.|Few|All|Many|Med.|Few|\n|PFN-localized|8.96|8.71|10.79|16.33|5.26|5.17|6.00|9.42|\n|GPT2-localized|7.76|7.35|11.15|17.71|4.29|4.13|5.96|11.00|\n|PRIME|**6.42**|**5.98**|**9.92**|**16.28**|**3.49**|**3.33**|**5.17**|**9.41**|", "claims_and_evidence": "not all. Authors assert that PRIME achieve the SOTA performance, but it seems that authors ignore the current best model which have better performance than PRIME.", "methods_and_evaluation_criteria": "yes", "theoretical_claims": "yes", "experimental_designs_or_analyses": "The paper mentions that the authors followed the \"same experimental setup\" and \"previous state-of-the-art methods\" for each dataset, indicating that they have adopted well-established experimental protocols.\n\nHowever, several SOTA baselines are missed in the paper, and I listed partial of them below.\n\nBy reviewing the VIR paper, it is evident that VIR outperforms PRIME in all shot settings on AgeDB-DIR and surpasses all other methods on IMDB-WIKI-DIR. Why did the authors not report this?  \n\nAdditionally, the paper *\"IM-Context: In-Context Learning for Imbalanced Regression Tasks\"* outperforms both VIR and ConR across all metrics, establishing it as the current state-of-the-art (SOTA) method. However, the authors did not mention this approach.  \n\nDoes this imply that PRIME is unable to outperform VIR, PFN-localized, and GPT2-localized?", "relation_to_broader_scientific_literature": "​The PRIME method, as presented in the paper, addresses a significant gap in the existing literature on imbalanced regression by introducing the concept of proxy learning into this domain for the first time. It leverages novel ideas surrounding sample-proxy relationships and integrates these with established imbalanced learning techniques to achieve state-of-the-art performance across various regression benchmarks.", "essential_references_not_discussed": "By reviewing the VIR paper, it is evident that VIR outperforms PRIME in all shot settings on AgeDB-DIR and surpasses all other methods on IMDB-WIKI-DIR. Why did the authors not report this?  \n\nAdditionally, the paper *\"IM-Context: In-Context Learning for Imbalanced Regression Tasks\"* outperforms both VIR and ConR across all metrics, establishing it as the current state-of-the-art (SOTA) method. However, the authors did not mention this approach.  \n\nDoes this imply that PRIME is unable to outperform VIR, PFN-localized, and GPT2-localized?", "other_strengths_and_weaknesses": "The main concern is why the authors assert that PRIME achieves state-of-the-art (SOTA) performance while not reporting the results of prior methods that outperform PRIME. I believe the authors need to address this issue.", "other_comments_or_suggestions": "None, but authors need to report the mentioned performance.", "questions_for_authors": "I find this paper interesting, and the proposed method is novel. However, the claim of \"demonstrating state-of-the-art performance on four real-world regression benchmarks across diverse target domains\" needs further justification.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper has received scores 4,3,3,2. There were various concerns and detailed discussions focusing primarily on confirming the state-of-the-art performance of the method over previous baselines. For example, there have been particular concerns from Reviewers SddV and RZfa about missing comparisons to recent methods. The authors appear to have responded adequately to this by presenting additional experiments in the rebuttal, overall confirming improvements over other methods.

Unfortunately, there has been no further discussion on more foundational merits and interpretations of the method itself nor of the claimed theoretical support. From the discussions, it looks clear that there is agreement on improved practical performance of the algorithm over baselines. On the other hand, I can't help but note that in my view, the method itself lacks particular clarity and insights on its conceptual components - it combines two regularization loss terms which are also further combined with classification losses. It does appear to gives gains, but I am not sure how much real new ideas can be brought up from this.

The theory provided is rather disappointing on that front: There is some bound derived on balanced loss, but its unwieldy form of the involved terms does not make it particularly useful (in my opinion) for explaining the specific roles of the 'align' or 'proxy' loss terms and the specific choices to model these. Instead, it simply seems to capture that the loss is (in upper bound) proportional to a very rough term that measures imbalance (eq. 15). Unfortunately, none of the reviewers appears to have really read or commented on the theory and its value.

Given these limitations in conceptual clarity and theoretical contribution, coupled with the late addition of experimental results during the rebuttal period, and after consultation with senior area chairs, I recommend a borderline reject. I encourage the authors to incorporate the feedback to strengthen a future submission by considering moving the current theoretical analysis to the appendix or strengthening it, enhancing the discussion of the method's components and their interactions, and including the additional experiments, comparisons, and discussions from the rebuttal.
Decision: Accept (poster)