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We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…

机器学习 · 计算机科学 2012-07-03 Luis Francisco Sanchez Merchante , Yves Grandvalet , Gerrad Govaert

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

机器学习 · 统计学 2022-11-23 Lei Cheng , Feng Yin , Sergios Theodoridis , Sotirios Chatzis , Tsung-Hui Chang

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

数值分析 · 数学 2021-03-17 Yating Wang , Wei Deng , Lin Guang

Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…

机器学习 · 统计学 2016-07-12 Garret Vo , Debdeep Pati

Increasing attention has recently been given to the inference of sparse networks. In biology, for example, most molecules only bind to a small number of other molecules, leading to sparse molecular interaction networks. To achieve…

系统与控制 · 计算机科学 2019-01-04 J. Jin , Y. Yuan , A. Webb , J. Goncalves

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…

机器学习 · 计算机科学 2019-01-25 Yuan Shi , Aurélien Bellet , Fei Sha

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

最优化与控制 · 数学 2025-01-08 Dimitris Bertsimas , Jean Pauphilet , Bart Van Parys

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

数据结构与算法 · 计算机科学 2023-05-29 Jonathan Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

统计理论 · 数学 2024-06-03 Veronika Rockova

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…

This paper studies offline reinforcement learning with linear function approximation in a setting with decision-theoretic, but not estimation sparsity. The structural restrictions of the data-generating process presume that the transitions…

机器学习 · 统计学 2024-01-24 Angela Zhou

We propose a reinforcement learning based approach to tackle the cost-sensitive learning problem where each input feature has a specific cost. The acquisition process is handled through a stochastic policy which allows features to be…

机器学习 · 计算机科学 2016-07-14 Gabriella Contardo , Ludovic Denoyer , Thierry Artières

Interpretable machine learning has demonstrated impressive performance while preserving explainability. In particular, neural additive models (NAM) offer the interpretability to the black-box deep learning and achieve state-of-the-art…

机器学习 · 统计学 2022-02-28 Shiyun Xu , Zhiqi Bu , Pratik Chaudhari , Ian J. Barnett

Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…

统计方法学 · 统计学 2014-06-10 Yuancheng Zhu , Rina Foygel Barber

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…

机器学习 · 统计学 2012-08-14 Lorenzo Rosasco , Silvia Villa , Sofia Mosci , Matteo Santoro , Alessandro verri

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

机器学习 · 统计学 2021-03-09 Yan Sun , Qifan Song , Faming Liang

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

机器学习 · 统计学 2012-06-22 Tingni Sun , Cun-Hui Zhang

Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…

机器学习 · 计算机科学 2026-04-23 Xuelin Zhang , Xinyue Liu , Lingjuan Wu , Hong Chen

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

统计理论 · 数学 2021-11-30 Dominic Richards , Sahand N. Negahban , Patrick Rebeschini

We propose a novel regularization-based continual learning method, dubbed as Adaptive Group Sparsity based Continual Learning (AGS-CL), using two group sparsity-based penalties. Our method selectively employs the two penalties when learning…

机器学习 · 计算机科学 2021-06-01 Sangwon Jung , Hongjoon Ahn , Sungmin Cha , Taesup Moon