Related papers: Relaxed Sparsest-Permutation Formulation for Causa…
Most constraint-based causal learning algorithms provably return the correct causal graph under certain correctness conditions, such as faithfulness. By representing any constraint-based causal learning algorithm using the notion of a…
The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…
We propose a probabilistic framework for interpreting and developing hard thresholding sparse signal reconstruction methods and present several new algorithms based on this framework. The measurements follow an underdetermined linear model,…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
Semi-structured sparsity provides a practical path to accelerate large language models (LLMs) with native hardware support, but post-training semi-structured pruning often suffers from substantial quality degradation due to strong…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
This article provides a new type of analysis of a compressed-sensing based technique for recovering column-sparse matrices, namely minimization of the $\ell_{1,2}$-norm. Rather than providing conditions on the measurement matrix which…
In this paper, we propose a general framework for designing sensing matrix $\boldsymbol{A} \in \mathbb{R}^{d\times p}$, for estimation of sparse covariance matrix from compressed measurements of the form $\boldsymbol{y} =…
We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…
In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal…