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Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show…

Machine Learning · Computer Science 2019-09-04 Julius Kunze , Louis Kirsch , Hippolyt Ritter , David Barber

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…

Machine Learning · Statistics 2015-03-17 Charles A. Micchelli , Jean M. Morales , Massimiliano Pontil

Overparameterized neural networks can interpolate a given dataset in many different ways, prompting the fundamental question: which among these solutions should we prefer, and what explicit regularization strategies will provably yield…

Machine Learning · Statistics 2026-01-28 Julia Nakhleh , Robert D. Nowak

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

Statistics Theory · Mathematics 2021-08-10 Ilsang Ohn , Yongdai Kim

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel…

Information Theory · Computer Science 2014-05-09 Omid Taheri , Sergiy A. Vorobyov

The robustness and anomaly detection capability of neural networks are crucial topics for their safe adoption in the real-world. Moreover, the over-parameterization of recent networks comes with high computational costs and raises questions…

Machine Learning · Computer Science 2022-07-12 Morgane Ayle , Bertrand Charpentier , John Rachwan , Daniel Zügner , Simon Geisler , Stephan Günnemann

In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including…

Machine Learning · Computer Science 2023-01-31 Tomer Galanti , Mengjia Xu , Liane Galanti , Tomaso Poggio

In this paper, we consider one dimensional (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained. First, we mathematically show that for such networks L2-regularized regression…

Machine Learning · Computer Science 2023-10-05 Jakob Heiss , Josef Teichmann , Hanna Wutte

Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to…

Machine Learning · Statistics 2025-10-14 Brendan van Rooyen , Aditya Krishna Menon , Robert C. Williamson

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…

Optimization and Control · Mathematics 2017-04-05 Martin Benning , Guy Gilboa , Joana Sarah Grah , Carola-Bibiane Schönlieb

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Machine Learning · Statistics 2012-08-14 Lorenzo Rosasco , Silvia Villa , Sofia Mosci , Matteo Santoro , Alessandro verri

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…

Numerical Analysis · Mathematics 2018-01-17 Zenith Purisha , Juho Rimpeläinen , Tatiana Bubba , Samuli Siltanen

We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as…

Neural and Evolutionary Computing · Computer Science 2017-01-24 Gabriel Pereyra , George Tucker , Jan Chorowski , Łukasz Kaiser , Geoffrey Hinton

Reinforcement learning (RL) is a key post-pretraining step for aligning large language models (LLMs) with complex tasks and human preferences. While it is often assumed that RL fine-tuning requires updating most of a model's parameters, we…

Machine Learning · Computer Science 2025-07-30 Andrii Balashov

Sparsification of neural networks is one of the effective complexity reduction methods to improve efficiency and generalizability. We consider the problem of learning a one hidden layer convolutional neural network with ReLU activation…

Optimization and Control · Mathematics 2020-02-26 Thu Dinh , Jack Xin

Regularization, whether explicit in terms of a penalty in the loss or implicit in the choice of algorithm, is a cornerstone of modern machine learning. Indeed, controlling the complexity of the model class is particularly important when…

Machine Learning · Statistics 2024-10-22 Matteo Vilucchio , Nikolaos Tsilivis , Bruno Loureiro , Julia Kempe

We provide a function space characterization of the inductive bias resulting from minimizing the $\ell_2$ norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting…

Machine Learning · Computer Science 2022-07-12 Meena Jagadeesan , Ilya Razenshteyn , Suriya Gunasekar

Often, what is termed algorithmic bias in machine learning will be due to historic bias in the training data. But sometimes the bias may be introduced (or at least exacerbated) by the algorithm itself. The ways in which algorithms can…

Machine Learning · Computer Science 2021-04-20 Padraig Cunningham , Sarah Jane Delany

Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and…

Machine Learning · Computer Science 2019-05-28 Sanjeev Arora , Simon S. Du , Wei Hu , Zhiyuan Li , Ruosong Wang

Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…

Machine Learning · Computer Science 2024-12-02 Yanzhe Bekkemoen , Helge Langseth