Related papers: Relaxed Sparsest-Permutation Formulation for Causa…

Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing attention has recently been devoted to…

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…

The problem of finding the sparsest solution to a linear underdetermined system of equations, often appearing, e.g., in data analysis, optimal control, system identification, or sensor selection problems, is considered. This non-convex…

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

$\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity (the size of the support set), under which with high probability a sparse signal…

Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…

We address the problem of recovering a sparse $n$-vector within a given subspace. This problem is a subtask of some approaches to dictionary learning and sparse principal component analysis. Hence, if we can prove scaling laws for recovery…

Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…

Leveraging deep learning for causal discovery in time series remains challenging because existing neural methods predominantly rely on component-wise architectures that fail to capture shared system dynamics or employ decoupled post-hoc…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

This paper shows that causal model discovery is not an NP-hard problem, in the sense that for sparse graphs bounded by node degree k the sound and complete causal model can be obtained in worst case order N^{2(k+2)} independence tests, even…

The sparse Mixture-of-Experts (Sparse-MoE) framework efficiently scales up model capacity in various domains, such as natural language processing and vision. Sparse-MoEs select a subset of the "experts" (thus, only a portion of the overall…

We study how reliably sparse autoencoders (SAEs) support claims about reasoning-related internal features in large language models. We first give a stylized analysis showing that sparsity-regularized decoding can preferentially retain…

This work introduces a novel estimation method, called LOVE, of the entries and structure of a loading matrix A in a sparse latent factor model X = AZ + E, for an observable random vector X in Rp, with correlated unobservable factors Z \in…

We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…

This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…

We take a new perspective on identification in structural dynamic models: rather than imposing restrictions alone, we optimize an objective. While definitive structural identification ultimately requires exogenous economic insight, a…