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Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where…

Machine Learning · Computer Science 2025-03-18 Qingshi Sun , Nathan Justin , Andres Gomez , Phebe Vayanos

Machine learning models deployed on medical imaging tasks must be equipped with out-of-distribution detection capabilities in order to avoid erroneous predictions. It is unsure whether out-of-distribution detection models reliant on deep…

Computer Vision and Pattern Recognition · Computer Science 2022-06-28 Sebastian G. Popescu , David J. Sharp , James H. Cole , Konstantinos Kamnitsas , Ben Glocker

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Machine Learning · Computer Science 2025-08-26 Harrison J. Goldwyn , Mitchell Krock , Johann Rudi , Daniel Getter , Julie Bessac

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

Methodology · Statistics 2024-02-09 Ryo Okano , Masaaki Imaizumi

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

Machine Learning · Statistics 2020-10-26 Andrew Y. K. Foong , David R. Burt , Yingzhen Li , Richard E. Turner

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…

Machine Learning · Computer Science 2026-02-10 Eduardo Figueiredo , Steven Adams , Luca Laurenti

Deep neural networks achieve superior performance in semantic segmentation, but are limited to a predefined set of classes, which leads to failures when they encounter unknown objects in open-world scenarios. Recognizing and segmenting…

Computer Vision and Pattern Recognition · Computer Science 2025-12-15 Arnold Brosch , Abdelrahman Eldesokey , Michael Felsberg , Kira Maag

A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but…

Machine Learning · Statistics 2024-06-04 Benjamin Avanzi , Eric Dong , Patrick J. Laub , Bernard Wong

Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the…

Machine Learning · Computer Science 2015-12-31 Charlie Frogner , Chiyuan Zhang , Hossein Mobahi , Mauricio Araya-Polo , Tomaso Poggio

We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…

Statistics Theory · Mathematics 2022-06-22 Tudor Manole , Nhat Ho

We develop Distributionally Robust Optimization (DRO) formulations for Multivariate Linear Regression (MLR) and Multiclass Logistic Regression (MLG) when both the covariates and responses/labels may be contaminated by outliers. The DRO…

Machine Learning · Statistics 2020-06-12 Ruidi Chen , Ioannis Ch. Paschalidis

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

Machine Learning · Statistics 2025-11-12 Changyu Liu , Yuling Jiao , Junhui Wang , Jian Huang

We propose REpresentation-Aware Distributionally Robust Estimation (READ), a novel framework for Wasserstein distributionally robust learning that accounts for predictive representations when guarding against distributional shifts. Unlike…

Methodology · Statistics 2025-09-12 Zitao Wang , Nian Si , Molei Liu

This paper focuses on the Wasserstein distributionally robust mean-lower semi-absolute deviation (DR-MLSAD) model, where the ambiguity set is a Wasserstein ball centered on the empirical distribution of the training sample. This model can…

Optimization and Control · Mathematics 2024-03-04 Weimi Zhou , Yong-Jin Liu

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Machine Learning · Statistics 2019-03-11 Konstantin Posch , Jan Steinbrener , Jürgen Pilz

We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein…

Risk Management · Quantitative Finance 2025-11-13 Peng Liu , Steven Vanduffel , Yi Xia

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

Machine Learning · Computer Science 2022-10-14 Tony Tohme , Kevin Vanslette , Kamal Youcef-Toumi

Deep neural networks rely heavily on normalization methods to improve their performance and learning behavior. Although normalization methods spurred the development of increasingly deep and efficient architectures, they also increase the…

Machine Learning · Computer Science 2021-10-06 Alexander Fuchs , Christian Knoll , Franz Pernkopf

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple…

Machine Learning · Statistics 2025-06-13 Marcel Arpogaus , Thomas Kneib , Thomas Nagler , David Rügamer