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We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof…
The computation of the maximum likelihood (ML) estimator for heteroscedastic regression models is considered. The traditional Newton algorithms for the problem require matrix multiplications and inversions, which are bottlenecks in modern…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
This work has its origin in intuitive physical and statistical considerations. The problem of optimizing an artificial neural network is treated as a physical system, composed of a conservative vector force field. The derived scalar…
In this paper, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We approach this problem…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the…
Suppose we are given observations, where each observation is drawn independently from one of $k$ known distributions. The goal is to match each observation to the distribution from which it was drawn. We observe that the maximum likelihood…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…
The exponential family random graph modeling (ERGM) framework provides a flexible approach for the statistical analysis of networks. As ERGMs typically involve normalizing factors that are costly to compute, practical inference relies on a…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
In this paper, we develop a new technique which we call representation theory of the real hyperrectangle, which describes how to compute the eigenvectors and eigenvalues of certain matrices arising from hyperrectangles. We show that these…
In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…
We study the consistency and optimality of the maximum marginal likelihood estimate (MMLE) in the hyperparameter inference for large-degree-of-freedom models. We perform main analyses within the exponential family, where the natural…
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…
Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it…
We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…