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The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is presented under mild conditions on $f$. Under such conditions, the optimal measure is shown to be unique. Examples of the solution for particular…

Machine Learning · Statistics 2024-10-25 Francisco Daunas , Iñaki Esnaola , Samir M. Perlaza , H. Vincent Poor

Let $\mathcal{F}$ be a class of measurable functions $f:S\mapsto [0,1]$ defined on a probability space $(S,\mathcal{A},P)$. Given a sample (X_1,...,X_n) of i.i.d. random variables taking values in S with common distribution P, let P_n…

Statistics Theory · Mathematics 2011-11-10 Vladimir Koltchinskii

We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…

Machine Learning · Statistics 2024-06-24 Matteo Vilucchio , Emanuele Troiani , Vittorio Erba , Florent Krzakala

We consider the problem of low probability estimation: given a machine learning model and a formally-specified input distribution, how can we estimate the probability of a binary property of the model's output, even when that probability is…

Machine Learning · Computer Science 2025-02-07 Gabriel Wu , Jacob Hilton

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of…

Machine Learning · Computer Science 2013-11-26 Hsiang-Fu Yu , Prateek Jain , Purushottam Kar , Inderjit S. Dhillon

In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve…

Machine Learning · Computer Science 2018-02-15 Di Wang , Minwei Ye , Jinhui Xu

Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…

Machine Learning · Computer Science 2021-03-30 Elan Rosenfeld , Pradeep Ravikumar , Andrej Risteski

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

Statistics Theory · Mathematics 2016-11-18 XuanLong Nguyen , Martin J. Wainwright , Michael I. Jordan

Empirical risk minimization stands behind most optimization in supervised machine learning. Under this scheme, labeled data is used to approximate an expected cost (risk), and a learning algorithm updates model-defining parameters in search…

Machine Learning · Statistics 2023-05-25 James Schmidt

The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…

Machine Learning · Statistics 2023-06-06 Wenlu Tang , Zicheng Liu

We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative…

Machine Learning · Computer Science 2024-05-24 Yuyang Deng , Mingda Qiao

Motivated by several examples, we consider a general framework of learning with linear loss functions. In this context, we provide excess risk and estimation bounds that hold with large probability for four estimators: ERM, minmax MOM and…

Statistics Theory · Mathematics 2023-10-27 Guillaume Lecué , Lucie Neirac

We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data,…

Econometrics · Economics 2025-11-04 Xuelin Yang , Licong Lin , Susan Athey , Michael I. Jordan , Guido W. Imbens

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

In the paper we argue that performance of the classifiers based on Empirical Risk Minimization (ERM) for positive unlabeled data, which are designed for case-control sampling scheme may significantly deteriorate when applied to a…

Machine Learning · Computer Science 2026-04-08 Jan Mielniczuk , Adam Wawrzeńczyk

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or…

Statistics Theory · Mathematics 2018-12-18 Luis Mendo

Supervised classification techniques use training samples to learn a classification rule with small expected 0-1 loss (error probability). Conventional methods enable tractable learning and provide out-of-sample generalization by using…

Machine Learning · Statistics 2023-08-21 Santiago Mazuelas , Mauricio Romero , Peter Grünwald

Machine learning models (e.g., speech recognizers) are usually trained to minimize average loss, which results in representation disparity---minority groups (e.g., non-native speakers) contribute less to the training objective and thus tend…

Machine Learning · Statistics 2018-08-01 Tatsunori B. Hashimoto , Megha Srivastava , Hongseok Namkoong , Percy Liang

Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…

Machine Learning · Computer Science 2024-12-06 Disha Ghandwani , Neeraj Sarna , Yuanyuan Li , Yang Lin

This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance…

Machine Learning · Computer Science 2021-03-26 Yaqi Duan , Chi Jin , Zhiyuan Li