English
Related papers

Related papers: On the Efficiency of ERM in Feature Learning

200 papers

Models trained with empirical risk minimization (ERM) are known to learn to rely on spurious features, i.e., their prediction is based on undesired auxiliary features which are strongly correlated with class labels but lack causal…

Machine Learning · Computer Science 2024-01-11 Phuong Quynh Le , Jörg Schlötterer , Christin Seifert

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

The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…

Machine Learning · Statistics 2019-03-04 Hiva Ghanbari , Minhan Li , Katya Scheinberg

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

A fundamental problem in robust learning is asymmetry: a learner needs to correctly classify every one of exponentially-many perturbations that an adversary might make to a test-time natural example. In contrast, the attacker only needs to…

Machine Learning · Computer Science 2024-02-14 Saba Ahmadi , Avrim Blum , Omar Montasser , Kevin Stangl

Focusing on stochastic programming (SP) with covariate information, this paper proposes an empirical risk minimization (ERM) method embedded within a nonconvex piecewise affine decision rule (PADR), which aims to learn the direct mapping…

Optimization and Control · Mathematics 2025-09-29 Yiyang Zhang , Junyi Liu , Xiaobo Zhao

In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower…

Machine Learning · Computer Science 2024-05-17 James B. Simon , Dhruva Karkada , Nikhil Ghosh , Mikhail Belkin

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

Statistics Theory · Mathematics 2016-08-14 Pascal Massart , Élodie Nédélec

The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolutionized the area of artificial intelligence, machine…

Machine Learning · Computer Science 2020-11-12 Julius Berner , Philipp Grohs , Arnulf Jentzen

Overparameterization is shown to result in poor test accuracy on rare subgroups under a variety of settings where subgroup information is known. To gain a more complete picture, we consider the case where subgroup information is unknown. We…

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

Ensemble techniques are powerful approaches that combine several weak learners to build a stronger one. As a meta-learning framework, ensemble techniques can easily be applied to many machine learning methods. Inspired by ensemble…

Machine Learning · Computer Science 2018-10-29 Hamideh Hajiabadi , Reza Monsefi , Hadi Sadoghi Yazdi

Recent advances in learning or identification of nonlinear dynamics focus on learning a suitable model within a pre-specified model class. However, a key difficulty that remains is the choice of the model class from which the dynamics will…

Systems and Control · Electrical Eng. & Systems 2023-09-29 Charis Stamouli , Evangelos Chatzipantazis , George J. Pappas

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Statistics Theory · Mathematics 2023-01-18 Wenlong Mou , Peng Ding , Martin J. Wainwright , Peter L. Bartlett

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

The tracking method based on the extreme learning machine (ELM) is efficient and effective. ELM randomly generates input weights and biases in the hidden layer, and then calculates and computes the output weights by reducing the iterative…

Machine Learning · Computer Science 2018-07-27 Jing Zhang , Huibing Wang , Yonggong Ren

In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected…

Machine Learning · Statistics 2026-01-21 Francisco Daunas , Iñaki Esnaola , Samir M. Perlaza , H. Vincent Poor

Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and…

Data Analysis, Statistics and Probability · Physics 2019-09-12 Patrick N. Raanes , Geir Evensen , Andreas S. Stordal

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

Classic supervised learning involves algorithms trained on $n$ labeled examples to produce a hypothesis $h \in \mathcal{H}$ aimed at performing well on unseen examples. Meta-learning extends this by training across $n$ tasks, with $m$…

Machine Learning · Statistics 2024-11-28 Yannay Alon , Steve Hanneke , Shay Moran , Uri Shalit