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Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that…

Machine Learning · Statistics 2021-08-12 Christian Brownlees , Jordi Llorens-Terrazas

While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…

Machine Learning · Statistics 2022-05-27 Avishek Ghosh , Arya Mazumdar , Soumyabrata Pal , Rajat Sen

Empirical risk minimization is perhaps the most influential idea in statistical learning, with applications to nearly all scientific and technical domains in the form of regression and classification models. To analyze massive streaming…

Machine Learning · Statistics 2020-06-26 Benjamin Coleman , Gaurav Gupta , John Chen , Anshumali Shrivastava

We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…

Machine Learning · Statistics 2018-04-23 Adarsh Prasad , Arun Sai Suggala , Sivaraman Balakrishnan , Pradeep Ravikumar

We derive upper bounds for random design linear regression with dependent ($\beta$-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp instance-optimal non-asymptotics…

Machine Learning · Computer Science 2023-10-30 Ingvar Ziemann , Stephen Tu , George J. Pappas , Nikolai Matni

There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an…

Machine Learning · Statistics 2019-05-10 Karim Abou-Moustafa , Csaba Szepesvari

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

We study Regularized Empirical Risk Minimizers (RERM) and minmax Median-Of-Means (MOM) estimators where the regularization function $\phi(\cdot)$ is an even convex function. We obtain bounds on the $L_2$-estimation error and the excess risk…

Statistics Theory · Mathematics 2019-10-16 Geoffrey Chinot

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

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

Machine Learning · Computer Science 2017-09-05 Aryan Mokhtari , Alejandro Ribeiro

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure…

Statistics Theory · Mathematics 2017-11-30 Gábor Lugosi , Shahar Mendelson

This work, based on Random Matrix Theory (RMT), introduces a novel early-stopping strategy for Transformer training dynamics. Utilizing the Power Law (PL) fit to tansformer attention matrices as a probe, we demarcate training into three…

Machine Learning · Computer Science 2025-12-30 Jing He , Hua Jiang , Cheng Li , Siqian Xin , Shuzhen Yang

In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by…

Machine Learning · Computer Science 2025-05-26 Hongyi Henry Jin , Zijun Ding , Dung Daniel Ngo , Zhiwei Steven Wu

Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the…

Machine Learning · Computer Science 2026-04-27 Rico Angell , Raghav Singhal , Zachary Horvitz , Zhou Yu , Rajesh Ranganath , Kathleen McKeown , He He

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

Machine Learning · Statistics 2024-05-09 William Kengne , Modou Wade

We study the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass…

Machine Learning · Computer Science 2016-04-19 Amit Daniely , Sivan Sabato , Shai Ben-David , Shai Shalev-Shwartz

Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as…

Machine Learning · Computer Science 2019-01-25 Charles H. Martin , Michael W. Mahoney

We study the performance of empirical risk minimization on the $p$-norm linear regression problem for $p \in (1, \infty)$. We show that, in the realizable case, under no moment assumptions, and up to a distribution-dependent constant,…

Statistics Theory · Mathematics 2024-06-19 Ayoub El Hanchi , Murat A. Erdogdu

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

We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$, the excess risk of the empirical risk…

Statistics Theory · Mathematics 2011-02-25 Guillaume Lecué , Shahar Mendelson