English
Related papers

Related papers: Adaptive Matrix Sparsification and Applications to…

200 papers

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM…

Optimization and Control · Mathematics 2021-07-08 Matthew Norton , Johannes O. Royset

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

We study the differentially private Empirical Risk Minimization (ERM) and Stochastic Convex Optimization (SCO) problems for non-smooth convex functions. We get a (nearly) optimal bound on the excess empirical risk and excess population loss…

Machine Learning · Computer Science 2021-03-31 Janardhan Kulkarni , Yin Tat Lee , Daogao Liu

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

We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms…

Machine Learning · Computer Science 2017-06-06 Alon Gonen , Shai Shalev-Shwartz

Let $F$ be a finite model of cardinality $M$ and denote by $\operatorname {conv}(F)$ its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over $\operatorname…

Statistics Theory · Mathematics 2013-12-17 Guillaume Lecué

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This…

Machine Learning · Computer Science 2022-11-15 Samir M. Perlaza , Gaetan Bisson , Iñaki Esnaola , Alain Jean-Marie , Stefano Rini

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

Machine Learning · Statistics 2020-07-07 Hossein Taheri , Ramtin Pedarsani , Christos Thrampoulidis

In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…

Computational Geometry · Computer Science 2018-05-01 Sariel Har-Peled , Piotr Indyk , Sepideh Mahabadi

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

Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…

Computational Complexity · Computer Science 2017-04-11 Arturs Backurs , Piotr Indyk , Ludwig Schmidt

In this paper, we study the generalization performance of global minima for implementing empirical risk minimization (ERM) on over-parameterized deep ReLU nets. Using a novel deepening scheme for deep ReLU nets, we rigorously prove that…

Machine Learning · Computer Science 2023-03-01 Shao-Bo Lin , Yao Wang , Ding-Xuan Zhou

We present an extension of Vapnik's classical empirical risk minimizer (ERM) where the empirical risk is replaced by a median-of-means (MOM) estimator, the new estimators are called MOM minimizers. While ERM is sensitive to corruption of…

Statistics Theory · Mathematics 2018-08-10 Guillaume Lecué , Matthieu Lerasle , Timothée Mathieu

This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of…

Machine Learning · Computer Science 2025-06-02 Erchi Wang , Yuqing Zhu , Yu-Xiang Wang

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…

Machine Learning · Computer Science 2023-11-10 Daniel Carmon , Roi Livni , Amir Yehudayoff

Empirical risk minimization (ERM) can be computationally expensive, with standard solvers scaling poorly even in the convex setting. We propose a novel lossless compression framework for convex ERM based on color refinement, extending prior…

Optimization and Control · Mathematics 2026-02-03 Bryan Zhu , Ziang Chen

In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…

Machine Learning · Statistics 2024-02-26 Adam Block , Alexander Rakhlin , Abhishek Shetty

We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage…

Statistics Theory · Mathematics 2017-04-06 Jianqing Fan , Han Liu , Qiang Sun , Tong Zhang

In this paper, we consider the problem of empirical risk minimization (ERM) of smooth, strongly convex loss functions using iterative gradient-based methods. A major goal of this literature has been to compare different algorithms, such as…

Machine Learning · Computer Science 2020-11-06 Ali Jadbabaie , Anuran Makur , Devavrat Shah

Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair…

Machine Learning · Statistics 2015-11-09 Kazuto Fukuchi , Jun Sakuma