Related papers: Picasso: A Sparse Learning Library for High Dimens…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not strictly convex, and hence it may not have a…
The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision matrix and improves upon the popular graphical LASSO method.…
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…
While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of…
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…
Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters.…
Dealing with biased data samples is a common task across many statistical fields. In survey sampling, bias often occurs due to unrepresentative samples. In causal studies with observational data, the treated versus untreated group…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
There have been many attempts to identify high-dimensional network features via multivariate approaches. Specifically, when the number of voxels or nodes, denoted as p, are substantially larger than the number of images, denoted as n, it…
Sparse mapping has been a key methodology in many high-dimensional scientific problems. When multiple tasks share the set of relevant features, learning them jointly in a group drastically improves the quality of relevant feature selection.…