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We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…

Statistics Theory · Mathematics 2024-05-27 Takeyuki Sasai , Hironori Fujisawa

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

Methodology · Statistics 2018-08-24 Shrijita Bhattacharya , Michael Kallitsis , Stilian Stoev

Randomized controlled trials (RCTs) are widely regarded as the gold standard for causal inference in biomedical research. For instance, when estimating the average treatment effect on the treated (ATT), a doubly robust estimation procedure…

Methodology · Statistics 2025-09-26 Chi-Shian Dai , Chao Ying , Yang Ning , Jiwei Zhao

Covariate balance is crucial in obtaining unbiased estimates of treatment effects in observational studies. Methods based on inverse probability weights have been widely used to estimate treatment effects with observational data. Machine…

Methodology · Statistics 2021-04-08 Michele Santacatterina

We study the problem of inferring heterogeneous treatment effects from time-to-event data. While both the related problems of (i) estimating treatment effects for binary or continuous outcomes and (ii) predicting survival outcomes have been…

Machine Learning · Computer Science 2022-01-25 Alicia Curth , Changhee Lee , Mihaela van der Schaar

Long-tailed classification is challenging due to its heavy imbalance in class probabilities. While existing methods often focus on overall accuracy or accuracy for tail classes, they overlook a critical aspect: certain types of errors can…

Machine Learning · Computer Science 2025-01-27 Bolian Li , Ruqi Zhang

Understanding treatment effect heterogeneity has become an increasingly popular task in various fields, as it helps design personalized advertisements in e-commerce or targeted treatment in biomedical studies. However, most of the existing…

Methodology · Statistics 2024-07-12 Waverly Wei , Xinwei Ma , Jingshen Wang

In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…

Statistics Theory · Mathematics 2018-12-20 Jingjing Zou , Richard A. Davis , Gennady Samorodnitsky

This article introduces a general class of heavy-tailed autoregressions for modeling integer-valued time series with outliers. The proposed specification is based on a heavy-tailed mixture of negative binomial distributions that features an…

Statistics Theory · Mathematics 2019-09-09 Paolo Gorgi

In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes. We do so by extending the seminal works of Mendelson [Men15, Men18] on the analysis of ERM with…

Statistics Theory · Mathematics 2021-09-14 Abhishek Roy , Krishnakumar Balasubramanian , Murat A. Erdogdu

Measuring treatment effects in observational studies is challenging because of confounding bias. Confounding occurs when a variable affects both the treatment and the outcome. Traditional methods such as propensity score matching estimate…

Methodology · Statistics 2021-12-23 Bevan I. Smith , Charles Chimedza

Long-tailed data distributions pose challenges for a variety of domains like e-commerce, finance, biomedical science, and cyber security, where the performance of machine learning models is often dominated by head categories while tail…

Machine Learning · Computer Science 2024-10-31 Haohui Wang , Weijie Guan , Jianpeng Chen , Zi Wang , Dawei Zhou

Many estimators of the average effect of a treatment on an outcome require estimation of the propensity score, the outcome regression, or both. It is often beneficial to utilize flexible techniques such as semiparametric regression or…

Methodology · Statistics 2019-05-14 Cheng Ju , David Benkeser , Mark J. van der Laan

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…

Statistics Theory · Mathematics 2023-04-21 Linbo Liu , Danna Zhang

In this paper, we study adversarial training on datasets that obey the long-tailed distribution, which is practical but rarely explored in previous works. Compared with conventional adversarial training on balanced datasets, this process…

Machine Learning · Computer Science 2023-12-05 Guanlin Li , Guowen Xu , Tianwei Zhang

Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…

Machine Learning · Computer Science 2021-05-25 John Y. Shin

Deploying deep models in real-world scenarios entails a number of challenges, including computational efficiency and real-world (e.g., long-tailed) data distributions. We address the combined challenge of learning long-tailed distributions…

Computer Vision and Pattern Recognition · Computer Science 2024-04-02 Jihun Kim , Dahyun Kim , Hyungrok Jung , Taeil Oh , Jonghyun Choi

We propose a novel regression adjustment method designed for estimating distributional treatment effect parameters in randomized experiments. Randomized experiments have been extensively used to estimate treatment effects in various…

Econometrics · Economics 2024-07-24 Undral Byambadalai , Tatsushi Oka , Shota Yasui

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…

Computer Vision and Pattern Recognition · Computer Science 2018-05-24 Juan-Manuel Perez-Rua , Tomas Crivelli , Patrick Bouthemy , Patrick Perez

Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…

Methodology · Statistics 2017-12-27 Nehla Debbabi , Marie Kratz , Mamadou Mboup