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We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up…

Machine Learning · Statistics 2018-06-25 Christos Louizos , Max Welling , Diederik P. Kingma

Pruning the weights of neural networks is an effective and widely-used technique for reducing model size and inference complexity. We develop and test a novel method based on compressed sensing which combines the pruning and training into a…

Computer Vision and Pattern Recognition · Computer Science 2021-04-08 Jonathan W. Siegel , Jianhong Chen , Pengchuan Zhang , Jinchao Xu

Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…

Computer Vision and Pattern Recognition · Computer Science 2019-12-18 Kevin Bui , Fredrick Park , Shuai Zhang , Yingyong Qi , Jack Xin

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

Machine Learning · Computer Science 2017-07-31 Carlo Ciliberto , Alessandro Rudi , Lorenzo Rosasco

Empirical evidence shows that ensembles, such as bagging, boosting, random and rotation forests, generally perform better in terms of their generalization error than individual classifiers. To explain this performance, Schapire et al.…

Machine Learning · Statistics 2019-06-10 Waldyn Martinez , J. Brian Gray

Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we…

Machine Learning · Computer Science 2023-11-07 Danil Akhtiamov , Reza Ghane , Babak Hassibi

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

Machine Learning · Computer Science 2015-06-05 Paolo Di Lorenzo , Ali H. Sayed

Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…

Machine Learning · Statistics 2024-10-10 Vassilis Apidopoulos , Tomaso Poggio , Lorenzo Rosasco , Silvia Villa

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

Machine Learning · Statistics 2017-11-07 Jason Xu , Eric C. Chi , Kenneth Lange

Combining predictions from different models is a central problem in Bayesian inference and machine learning more broadly. Currently, these predictive distributions are almost exclusively combined using linear mixtures such as Bayesian model…

Machine Learning · Statistics 2023-05-15 Yuling Yao , Luiz Max Carvalho , Diego Mesquita , Yann McLatchie

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular…

In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…

Machine Learning · Computer Science 2017-11-28 Pengtao Xie , Hongbao Zhang , Eric P. Xing

In M-open problems where no true model can be conceptualized, it is common to back off from modeling and merely seek good prediction. Even in M-complete problems, taking a predictive approach can be very useful. Stacking is a model…

Statistics Theory · Mathematics 2016-02-17 Tri Le , Bertrand Clarke

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…

Methodology · Statistics 2016-12-23 Marbac Matthieu , Sedki Mohammed

Video summarization methods are usually classified into shot-level or frame-level methods, which are individually used in a general way. This paper investigates the underlying complementarity between the frame-level and shot-level methods,…

Computer Vision and Pattern Recognition · Computer Science 2022-07-05 Yubo An , Shenghui Zhao , Guoqiang Zhang

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

Machine Learning · Computer Science 2023-10-13 Mengyuan Zhang , Kai Liu

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

Methodology · Statistics 2014-02-26 Minh-Ngoc Tran

Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD,…

Machine Learning · Computer Science 2019-02-26 Pavel Izmailov , Dmitrii Podoprikhin , Timur Garipov , Dmitry Vetrov , Andrew Gordon Wilson

Finding neural network weights that generalize well from small datasets is difficult. A promising approach is to learn a weight initialization such that a small number of weight changes results in low generalization error. We show that this…

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…

Optimization and Control · Mathematics 2014-02-11 Zhiwei Qin , Donald Goldfarb