Related papers: Robust Sparse Estimation for Gaussians with Optima…

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

We study robust estimators of the mean of a probability measure $P$, called robust empirical mean estimators. This elementary construction is then used to revisit a problem of aggregation and a problem of estimator selection, extending…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…

We propose a learning-based approach for the sparse Gaussian Elimination. There are many hard combinatorial optimization problems in modern sparse solver. These NP-hard problems could be handled in the framework of Markov Decision Process,…

We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line…

We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…

We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…

Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and…

In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

Kernel methods are applied to many problems in pattern recognition, including subspace clustering (SC). That way, nonlinear problems in the input data space become linear in mapped high-dimensional feature space. Thereby, computationally…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…