Related papers: Fast and Adaptive Sparse Precision Matrix Estimati…
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while keeping data decentralized. In this paper, we propose a federated sparse sliced inverse…
Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…
We propose a method for the construction of preconditioners of parameter-dependent matrices for the solution of large systems of parameter-dependent equations. The proposed method is an interpolation of the matrix inverse based on a…
We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the error estimate of hyperbolic cross (HC) approximations with…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…