Related papers: Sparse Sliced Inverse Regression via Cholesky Matr…

We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper develops an accelerated version of RPCholesky that employs block…

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…

We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the $\ell_1$-norm penalty to filter…

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…

The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k + 1) N entry evaluations and O(k^2 N) additional arithmetic…

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…

In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…

Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a…

Gaussian processes are widely used as priors for unknown functions in statistics and machine learning. To achieve computationally feasible inference for large datasets, a popular approach is the Vecchia approximation, which is an ordered…

We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…

Sparse linear regression is a fundamental tool in data analysis. However, traditional approaches often fall short when covariates exhibit structure or arise from heterogeneous sources. In biomedical applications, covariates may stem from…