Related papers: Maximum likelihood degree of variance component mo…

Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

We express the maximum likelihood (ML) degrees of a family toric varieties in terms of Mobius invariants of matroids. The family of interest are those parametrized by monomial maps given by Lawrence lifts of totally unimodular matrices with…

The fusion of independently obtained stochastic maps by collaborating mobile agents is considered. The proposed approach includes two parts: matching of stochastic maps and maximum likelihood alignment. In particular, an affine invariant…

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…

We propose a classification of all one-dimensional discrete statistical models with maximum likelihood degree one based on their rational parametrization. We show how all such models can be constructed from members of a smaller class of…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…

We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…

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…

Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation,…

Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential…

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…

This paper presents the formulation and analysis of a novel distributed maximum likelihood algorithm that utilizes a first-order optimization scheme. The proposed approach utilizes a static average consensus algorithm to reach agreement on…

We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based…

The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…

Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…

A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…