Related papers: Adaptive Mean Estimation in the Hidden Markov sub-…
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while…
In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…
We study infinite-horizon Discounted Markov Decision Processes (DMDPs) under a generative model. Motivated by the Algorithm with Advice framework Mitzenmacher and Vassilvitskii 2022, we propose a novel framework to investigate how a…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…
Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum…
Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even…
We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known)…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…
Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…
This paper studies density estimation under pointwise loss in the setting of contamination model. The goal is to estimate $f(x_0)$ at some $x_0\in\mathbb{R}$ with i.i.d. observations, $$ X_1,\dots,X_n\sim (1-\epsilon)f+\epsilon g, $$ where…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom…