Related papers: Invariant theory and scaling algorithms for maximu…

We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…

Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…

AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…

A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

We consider multivariate centered Gaussian models for the random variable $Z=(Z_1,\ldots, Z_p)$, invariant under the action of a subgroup of the group of permutations on $\{1,\ldots, p\}$. Using the representation theory of the symmetric…

Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…

This paper considers the maximum likelihood estimation of panel data models with interactive effects. Motivated by applications in economics and other social sciences, a notable feature of the model is that the explanatory variables are…

We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…

We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…