Related papers: Near optimal sample complexity for matrix and tens…

Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…

In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery…

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an…

In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lam\'e parameters which are parameterized by a countably infinite number of terms in separate expansions. We estimated the…

We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

We present a smooth probabilistic reformulation of $\ell_0$ regularized regression that does not require Monte Carlo sampling and allows for the computation of exact gradients, facilitating rapid convergence to local optima of the best…

In constrained stochastic optimization, one naturally expects that imposing a stricter feasible set does not increase the statistical risk of an estimator defined by projection onto that set. In this paper, we show that this intuition can…

The Grenander estimator is a well-studied procedure for univariate nonparametric density estimation. It is usually defined as the Maximum Likelihood Estimator (MLE) over the class of all non-increasing densities on the positive real line.…

We study how to estimate a nearly low-rank Toeplitz covariance matrix $T$ from compressed measurements. Recent work of Qiao and Pal addresses this problem by combining sparse rulers (sparse linear arrays) with frequency finding (sparse…

We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…

Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…

This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…

We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…

We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social…