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We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…
We prove a limit shape theorem describing the asymptotic shape of bumping routes when the Robinson-Schensted algorithm is applied to a finite sequence of independent, identically distributed random variables with the uniform distribution…
In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a…
In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample…
This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…
The Johnson-Lindenstrauss Lemma (J-L Lemma) is a cornerstone of dimension reduction techniques. We study it in the one-bit context, namely we consider the unit sphere $ \mathbb S ^{N-1}$, with normalized geodesic metric, and map a finite…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…
This paper studies finite-horizon stochastic linear-quadratic optimal control problems with random coefficients and Poisson jumps, where the weighting matrices may be random and indefinite. Under a uniform convexity condition on the cost…
This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…
Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
Consider an m by N matrix Phi with the Restricted Isometry Property of order k and level delta, that is, the norm of any k-sparse vector in R^N is preserved to within a multiplicative factor of 1 +- delta under application of Phi. We show…
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…