Related papers: Towards Optimal Estimation of Bivariate Isotonic M…
We consider in this paper the multivariate regression problem, when the target regression matrix $A$ is close to a low rank matrix. Our primary interest in on the practical case where the variance of the noise is unknown. Our main…
The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…
We consider the twin problems of estimating the effective rank and the Schatten norms $\|{\bf A}\|_{s}$ of a rectangular $p\times q$ matrix ${\bf A}$ from noisy observations. When $s$ is an even integer, we introduce a polynomial-time…
Many applications, including natural language processing, sensor networks, collaborative filtering, and federated learning, call for estimating discrete distributions from data collected in batches, some of which may be untrustworthy,…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
We consider the problem of estimating the covariance matrix of a random signal observed through unknown translations (modeled by cyclic shifts) and corrupted by noise. Solving this problem allows to discover low-rank structures masked by…
The problem of distributed identification of linear stochastic system with unknown coefficients over time-varying networks is considered. For estimating the unknown coefficients, each agent in the network can only access the input and the…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
Given a sample of covariate-response pairs, we consider the subgroup selection problem of identifying a subset of the covariate domain where the regression function exceeds a pre-determined threshold. We introduce a computationally-feasible…
This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In…
We consider the problem of localizing a submatrix with larger-than-usual entry values inside a data matrix, without the prior knowledge of the submatrix size. We establish an optimization framework based on a multiscale scan statistic, and…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…