Miracle-dz/UniFAR-FTUs huggingface dataset:
Sparse estimation for case-control studies with multiple subtypes of cases

The analysis of case-control studies with several subtypes of cases is increasingly common, e.g. in cancer epidemiology. For matched designs, we show that a natural strategy is based on a stratified conditional logistic regression model. Then, to account for the potential homogeneity among the subtypes of cases, we adapt the ideas of data shared lasso, which has been recently proposed for the estimation of regression models in a stratified setting. For unmatched designs, we compare two standard methods based on L1-norm penalized multinomial logistic regression. We describe formal connections between these two approaches, from which practical guidance can be derived. We show that one of these approaches, which is based on a symmetric formulation of the multinomial logistic regression model, actually reduces to a data shared lasso version of the other. Consequently, the relative performance of the two approaches critically depends on the level of homogeneity that exists among the subtypes of cases: more precisely, when homogeneity is moderate to high, the non-symmetric formulation with controls as the reference is not recommended. Empirical results obtained from synthetic data are presented, which confirm the benefit of properly accounting for potential homogeneity under both matched and unmatched designs. We also present preliminary results from the analysis a case-control study nested within the EPIC cohort, where the objective is to identify metabolites associated with the occurrence of subtypes of breast cancer.
Pretest and Stein-Type Estimations in Quantile Regression Model

In this study, we consider preliminary test and shrinkage estimation strategies for quantile regression models. In classical Least Squares Estimation (LSE) method, the relationship between the explanatory and explained variables in the coordinate plane is estimated with a mean regression line. In order to use LSE, there are three main assumptions on the error terms showing white noise process of the regression model, also known as Gauss-Markov Assumptions, must be met: (1) The error terms have zero mean, (2) The variance of the error terms is constant and (3) The covariance between the errors is zero i.e., there is no autocorrelation. However, data in many areas, including econometrics, survival analysis and ecology, etc. does not provide these assumptions. First introduced by Koenker, quantile regression has been used to complement this deficiency of classical regression analysis and to improve the least square estimation. The aim of this study is to improve the performance of quantile regression estimators by using pre-test and shrinkage strategies. A Monte Carlo simulation study including a comparison with quantile $L_1$--type estimators such as Lasso, Ridge and Elastic Net are designed to evaluate the performances of the estimators. Two real data examples are given for illustrative purposes. Finally, we obtain the asymptotic results of suggested estimators
Modelling the effect of training on performance in road cycling: estimation of the Banister model parameters using field data

We suppose that performance is a random variable whose expectation is related to training inputs, and we study four performance measures in a statistical model that relates performance to training. Our aim is to carry out a robust statistical analysis of the training-performance models that are used in proprietary software to plan training, and thereby put them on a firmer footing. The performance measures we consider are calculated using power output and heart rate data collected in the field by road cyclists. We find that parameter estimates in the training-performance models that we study differ across riders and across performance measures within riders. We conclude therefore that models and their estimates must be specific, both to the individual and to the quality (e.g. speed or endurance) that the individual seeks to train. While the parameter estimates we obtain may be useful for comparing given training programmes, we show that the underlying models themselves are not appropriate for the optimisation of a training schedule in advance of competition.
Augmented Movelet Method for Activity Classification Using Smartphone Gyroscope and Accelerometer Data

Physical activity, such as walking and ascending stairs, is commonly used in biomedical settings as an outcome or covariate. Researchers have traditionally relied on surveys to quantify activity levels of subjects in both research and clinical settings, but surveys are subjective in nature and have known limitations, such as recall bias. Smartphones provide an opportunity for unobtrusive objective measurement of physical activity in naturalistic settings, but their data tends to be noisy and needs to be analyzed with care. We explored the potential of smartphone accelerometer and gyroscope data to distinguish between walking, sitting, standing, ascending stairs, and descending stairs. We conducted a study in which four participants followed a study protocol and performed a sequence of activities with one phone in their front pocket and another phone in their back pocket. The subjects were filmed throughout, and the obtained footage was annotated to establish moment-by-moment ground truth activity. We introduce a modified version of the so-called movelet method to classify activity type and to quantify the uncertainty present in that classification. Our results demonstrate the promise of smartphones for activity recognition in naturalistic settings, but they also highlight challenges in this field of research.
A Unifying Framework of High-Dimensional Sparse Estimation with Difference-of-Convex (DC) Regularizations

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in specific forms are well-studied in the literature for sparse estimation. A recent work \cite{ahn2016difference} has pointed out that nearly all existing non-convex penalties can be represented as difference-of-convex (DC) functions, which can be expressed as the difference of two convex functions, while itself may not be convex. There is a large existing literature on the optimization problems when their objectives and/or constraints involve DC functions. Efficient numerical solutions have been proposed. Under the DC framework, directional-stationary (d-stationary) solutions are considered, and they are usually not unique. In this paper, we show that under some mild conditions, a certain subset of d-stationary solutions in an optimization problem (with a DC objective) has some ideal statistical properties: namely, asymptotic estimation consistency, asymptotic model selection consistency, asymptotic efficiency. The aforementioned properties are the ones that have been proven by many researchers for a range of proposed non-convex penalties in the sparse estimation. Our assumptions are either weaker than or comparable with those conditions that have been adopted in other existing works. This work shows that DC is a nice framework to offer a unified approach to these existing work where non-convex penalty is involved. Our work bridges the communities of optimization and statistics.
Synthesis and analysis in total variation regularization

We generalize the bridge between analysis and synthesis estimators by Elad, Milanfar and Rubinstein (2007) to rank deficient cases. This is a starting point for the study of the connection between analysis and synthesis for total variation regularized estimators. In particular, the case of first order total variation regularized estimators over general graphs and their synthesis form are studied. We give a definition of the discrete graph derivative operator based on the notion of line graph and provide examples of the synthesis form of $k^{\text{th}}$ order total variation regularized estimators over a range of graphs.
Joint Mean-Covariance Estimation via the Horseshoe with an Application in Genomic Data Analysis

Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases. However, its practical deployment in genomic data analysis under a Bayesian framework is limited due to both statistical and computational challenges. The statistical challenge is that one needs to infer both the mean vector and the inverse covariance matrix, a problem inherently more complex than separately estimating each. The computational challenge is due to the dimensionality of the parameter space that routinely exceeds the sample size. We propose the use of horseshoe priors on both the mean vector and the inverse covariance matrix. This prior has demonstrated excellent performance when estimating a mean vector or inverse covariance matrix separately. The current work shows these advantages are also present when addressing both simultaneously. A full Bayesian treatment is proposed, with a sampling algorithm that is linear in the number of predictors. MATLAB code implementing the algorithm is freely available from github at this https URL. Extensive performance comparisons are provided with both frequentist and Bayesian alternatives, and both estimation and prediction performances are verified on a genomic data set.
Calibrating Black Box Classification Models through the Thresholding Method

In high-dimensional classification settings, we wish to seek a balance between high power and ensuring control over a desired loss function. In many settings, the points most likely to be misclassified are those who lie near the decision boundary of the given classification method. Often, these uninformative points should not be classified as they are noisy and do not exhibit strong signals. In this paper, we introduce the Thresholding Method to parameterize the problem of determining which points exhibit strong signals and should be classified. We demonstrate the empirical performance of this novel calibration method in providing loss function control at a desired level, as well as explore how the method assuages the effect of overfitting. We explore the benefits of error control through the Thresholding Method in difficult, high-dimensional, simulated settings. Finally, we show the flexibility of the Thresholding Method through applying the method in a variety of real data settings.
A causal inference framework for cancer cluster investigations using publicly available data

Often, a community becomes alarmed when high rates of cancer are noticed, and residents suspect that the cancer cases could be caused by a known source of hazard. In response, the US Centers for Disease Control and Prevention recommend that departments of health perform a standardized incidence ratio (SIR) analysis to determine whether the observed cancer incidence is higher than expected. This approach has several limitations that are well documented in the existing literature. We propose a novel causal inference framework for cancer cluster investigations, rooted in the potential outcomes framework. Assuming that a source of hazard representing a potential cause of increased cancer rates in the community is identified a priori, we focus our approach on a causal inference estimand which we call the causal SIR. The causal SIR is a ratio defined as the expected cancer incidence in the exposed population divided by the expected cancer incidence for the same population under the (counterfactual) scenario of no exposure. To estimate the causal SIR we need to overcome two main challenges: first, we must identify unexposed populations that are as similar as possible to the exposed population to inform estimation of the expected cancer incidence under the counterfactual scenario of no exposure, and, second, publicly available data on cancer incidence for these unexposed populations are often available at a much higher level of spatial aggregation (e.g. county) than what is desired (e.g. census block group). We overcome the first challenge by relying on matching. We overcome the second challenge by building a Bayesian hierarchical model that borrows information from other sources to impute cancer incidence at the desired level of spatial aggregation. In simulations, our statistical approach was shown to provide dramatically improved results, i.e. less bias and better coverage, than the current approach to SIR analyses. We apply our proposed approach to investigate whether trichloroethylene vapour exposure has caused increased cancer incidence in Endicott, New York.
SmartEDA: An R Package for Automated Exploratory Data Analysis

This paper introduces SmartEDA, which is an R package for performing Exploratory data analysis (EDA). EDA is generally the first step that one needs to perform before developing any machine learning or statistical models. The goal of EDA is to help someone perform the initial investigation to know more about the data via descriptive statistics and visualizations. In other words, the objective of EDA is to summarize and explore the data. The need for EDA became one of the factors that led to the development of various statistical computing packages over the years including the R programming language that is a very popular and currently the most widely used software for statistical computing. However, EDA is a very tedious task, requires some manual effort and some of the open source packages available in R are not just upto the mark. In this paper, we propose a new open source package i.e. SmartEDA for R to address the need for automation of exploratory data analysis. We discuss the various features of SmartEDA and illustrate some of its applications for generating actionable insights using a couple of real-world datasets. We also perform a comparative study of SmartEDA with respect to other packages available for exploratory data analysis in the Comprehensive R Archive Network (CRAN).
On inference validity of weighted U-statistics under data heterogeneity

Motivated by challenges on studying a new correlation measurement being popularized in evaluating online ranking algorithms' performance, this manuscript explores the validity of uncertainty assessment for weighted U-statistics. Without any commonly adopted assumption, we verify Efron's bootstrap and a new resampling procedure's inference validity. Specifically, in its full generality, our theory allows both kernels and weights asymmetric and data points not identically distributed, which are all new issues that historically have not been addressed. For achieving strict generalization, for example, we have to carefully control the order of the "degenerate" term in U-statistics which are no longer degenerate under the empirical measure for non-i.i. d. data. Our result applies to the motivating task, giving the region at which solid statistical inference can be made.
Out-of-the box neural networks can support combinatorial generalization

Combinatorial generalization - the ability to understand and produce novel combinations of already familiar elements - is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body of research suggests that conventional neural networks can't solve this problem unless they are endowed with mechanisms specifically engineered for the purpose of representing symbols. In this paper we introduce a novel way of representing symbolic structures in connectionist terms - the vectors approach to representing symbols (VARS), which allows training standard neural architectures to encode symbolic knowledge explicitly at their output layers. In two simulations , we show that out-of-the-box neural networks not only can learn to produce VARS representations, but in doing so they achieve combinatorial generalization. This adds to other recent work that has shown improved combinatorial generalization under specific training conditions, and raises the question of whether special mechanisms are indeed needed to support symbolic processing.
On the use of ABC-MCMC with inflated tolerance and post-correction

Approximate Bayesian computation (ABC) allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The ABC Markov chain Monte Carlo (MCMC) inference is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We consider an approach using a relatively large tolerance for the ABC-MCMC to ensure sufficient mixing, and post-processing the output of ABC-MCMC leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators, which can be calculated from any run of ABC-MCMC, with little extra cost. We propose an adaptive ABC-MCMC, which finds a `balanced' tolerance level automatically, based on acceptance rate optimisation. Tolerance adaptation, combined with proposal covariance adaptation, leads to an easy-to-use adaptive ABC-MCMC, with subsequent post-correction over a range of tolerances. Our experiments show that post-processing based estimators can perform better than direct ABC-MCMC, that our confidence intervals are reliable, and that our adaptive ABC-MCMC leads to reliable inference with little user specification.
Fixing Match-Fixing.

In the soccer World Cup, at the group stage, before the knock-out stage, games whose outcome has no impact for qualification are played with little enthusiasm. If a team is already qualified when playing its last game, different factors come into play so that winning may not be in its best interest. More critically, it is not unusual that a simple draw secures the qualification for both teams. Any situation in which the two opposing teams do not play competitively is detrimental to the sport, and can lead to collusion and match-fixing opportunities. The paper first develops a method to analyze the format of the World Cup group stage and its competitiveness. We then propose changes to the current format in order to increase the stakes in the last round of games of the group stage, reducing collusion opportunities and making games more exciting to watch. We use the same method to evaluate the "groups of 3" format which may be introduced in the 2026 World Cup edition, as well as a "groups of 5" format.
Nonparametric Empirical Bayes Simultaneous Estimation for Multiple Variances.

The shrinkage estimation has proven to be very useful when dealing with a large number of mean parameters in the normal models. In this paper, we consider the problem of simultaneous estimation of multiple variances and construct a shrinkage type estimator. We take the non-parametric empirical Bayes approach by starting with an arbitrary prior on the variances. Under an invariant loss function, the resultant Bayes estimator relies on the marginal cumulative distribution function of the sample variances. Replacing the marginal cdf by the empirical distribution function, we obtain a Non-parametric Empirical Bayes estimator for multiple Variances (NEBV). The proposed estimator converges to the corresponding Bayes version {\it uniformly} over a large set. Consequently, the NEBV works well in a post-selection setting. We then apply the NEBV to construct confidence intervals for mean parameters of the normal models in a post-selection setting. It is shown that the interval based on the NEBV is shortest among all the intervals which guarantee a desired coverage probability. Through real data analysis, we have further shown that the NEBV based intervals lead to the smallest number of {\it discordances}, a desirable property when we are faced with the current "replication crisis".
On the convergence of the spectral viscosity method for the incompressible Euler equations with rough initial data

We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity is in the so-called Delort class i.e. it is a sum of a signed measure and an integrable function. This provides the first convergence proof for a numerical method approximating the Euler equations with such rough initial data and closes the gap between the available existence theory and rigorous convergence results for numerical methods. We also present numerical experiments, including computations of vortex sheets and confined eddies, to illustrate the proposed method.
Image-Based Prognostics Using Penalized Tensor Regression

ABSTRACT This article proposes a new methodology to predict and update the residual useful lifetime of a system using a sequence of degradation images. The methodology integrates tensor linear algebra with traditional location-scale regression widely used in reliability and prognostics. To address the high dimensionality challenge, the degradation image streams are first projected to a low-dimensional tensor subspace that is able to preserve their information. Next, the projected image tensors are regressed against time-to-failure via penalized location-scale tensor regression. The coefficient tensor is then decomposed using CANDECOMP/PARAFAC (CP) and Tucker decompositions, which enables parameter estimation in a high-dimensional setting. Two optimization algorithms with a global convergence property are developed for model estimation. The effectiveness of our models is validated using two simulated datasets and infrared degradation image streams from a rotating machinery.
The Role of Body Mass Index at Diagnosis on Black-White Disparities in Colorectal Cancer Survival: A Density Regression Mediation Approach

The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether disparities in BMI is partially responsible for observed racial/ethnic disparities in CRC survival. This paper presents new methodology to quantify the impact of the hypothetical intervention that matches the BMI distribution in the Black population to a potentially complex distributional form observed in the White population on racial/ethnic disparities in survival. We perform a simulation that shows our proposed Bayesian density regression approach performs as well as or better than current methodology allowing for a shift in the mean of the distribution only, and that standard practice of categorizing BMI leads to large biases. When applied to motivating data from the Cancer Care Outcomes Research and Surveillance (CanCORS) Consortium, our approach suggests the proposed intervention is potentially beneficial for elderly and low income Black patients, yet harmful for young and high income Black populations.