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We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…
This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this…
This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown…
A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of…
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…
Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…
For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous…
Designing robust trajectories under uncertainties is an emerging technology that may represent a key paradigm shift in space mission design. As we pursue more ambitious scientific goals (e.g., multi-moon tours, missions with extensive…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
We investigate the continuous analogue of the Cholesky factorization, namely the pivoted Cholesky algorithm. Our analysis establishes quantitative convergence guarantees for kernels of minimal smoothness. We prove that for a symmetric…
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression…
We study the problem of computing a rank-$k$ approximation of a matrix using randomized block Krylov iteration. Prior work has shown that, for block size $b = 1$ or $b = k$, a $(1 + \varepsilon)$-factor approximation to the best rank-$k$…
A general many quantiles + noise model is studied in the robust formulation (allowing non-normal, non-independent observations), where the identifiability requirement for the noise is formulated in terms of quantiles rather than the…
Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is…
We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is…
In this study, we consider unsupervised clustering of categorical vectors that can be of different size using mixture. We use likelihood maximization to estimate the parameters of the underlying mixture model and a penalization technique to…
This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product…