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In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…

Machine Learning · Computer Science 2016-12-07 Yi Xu , Haiqin Yang , Lijun Zhang , Tianbao Yang

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in…

Machine Learning · Statistics 2024-09-05 Ben Dai

We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be…

Optimization and Control · Mathematics 2024-09-17 Eric Luxenberg , Dhruv Malik , Yuanzhi Li , Aarti Singh , Stephen Boyd

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

Machine Learning · Statistics 2025-07-09 William Kengne , Modou Wade

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…

Machine Learning · Statistics 2023-12-01 Matthew J. Holland , Kazuki Tanabe

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The…

Information Theory · Computer Science 2020-06-25 Namrata Vaswani , Thierry Bouwmans , Sajid Javed , Praneeth Narayanamurthy

We consider the problem of regression learning for deterministic design and independent random errors. We start by proving a sharp PAC-Bayesian type bound for the exponentially weighted aggregate (EWA) under the expected squared empirical…

Applications · Statistics 2012-06-27 Arnak Dalalyan , Alexandre B. Tsybakov

We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second.…

Machine Learning · Statistics 2026-02-02 Hugo Cui , Yue M. Lu

Metric learning has attracted a lot of interest over the last decade, but the generalization ability of such methods has not been thoroughly studied. In this paper, we introduce an adaptation of the notion of algorithmic robustness…

Machine Learning · Computer Science 2019-01-25 Aurélien Bellet , Amaury Habrard

It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birg\'e and Massart, 1993). In this paper, we prove that, under relatively mild assumptions, the suboptimality…

Statistics Theory · Mathematics 2025-11-04 Gil Kur , Eli Putterman , Alexander Rakhlin

In performative prediction, a predictive model impacts the distribution that generates future data, a phenomenon that is being ignored in classical supervised learning. In this closed-loop setting, the natural measure of performance named…

Machine Learning · Computer Science 2022-10-24 Yulai Zhao

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in…

Machine Learning · Computer Science 2022-10-25 Pranjal Awasthi , Abhimanyu Das , Weihao Kong , Rajat Sen

Empirical Risk Minimization (ERM) is a standard technique in machine learning, where a model is selected by minimizing a loss function over constraint set. When the training dataset consists of private information, it is natural to use a…

Machine Learning · Computer Science 2016-11-22 Kunal Talwar , Abhradeep Thakurta , Li Zhang

Invariant risk minimization (IRM) aims to enable out-of-distribution (OOD) generalization in deep learning by learning invariant representations. As IRM poses an inherently challenging bi-level optimization problem, most existing approaches…

Machine Learning · Computer Science 2025-05-26 Kotaro Yoshida , Konstantinos Slavakis

In this paper we consider learning in passive setting but with a slight modification. We assume that the target expected loss, also referred to as target risk, is provided in advance for learner as prior knowledge. Unlike most studies in…

Machine Learning · Computer Science 2013-05-21 Mehrdad Mahdavi , Rong Jin

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is…

Statistics Theory · Mathematics 2015-10-13 Andreas Christmann , Ding-Xuan Zhou

We propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. We first show that adversarial risk is equivalent to the risk induced by a distributional adversarial…

Machine Learning · Statistics 2023-09-06 Changyu Liu , Yuling Jiao , Junhui Wang , Jian Huang

Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address…

Machine Learning · Computer Science 2021-03-18 Tian Li , Ahmad Beirami , Maziar Sanjabi , Virginia Smith

In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover,…

Optimization and Control · Mathematics 2015-06-09 Dominik Csiba , Peter Richtárik

Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution…

Machine Learning · Statistics 2021-11-30 Vincent Plassier , François Portier , Johan Segers