Related papers: Explicit Maximum Likelihood Loss Estimator in Mult…

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…

The tensor Ising model is a discrete exponential family used for modeling binary data on networks with not just pairwise, but higher-order dependencies. A particularly important class of tensor Ising models are the tensor Curie-Weiss…

In this letter, we revisit the problem of maximum likelihood estimation (MLE) of parameters of Gaussian Mixture Model (GMM) and show a new derivation for its parameters. The new derivation, unlike the classical approach employing the…

We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting,…

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…

We introduce a new class of mean regression estimators -- penalized maximum tangent likelihood estimation -- for high-dimensional regression estimation and variable selection. We first explain the motivations for the key ingredient, maximum…

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex…

We explore past and recent developments in rare-event probability estimation with a particular focus on a novel Monte Carlo technique Empirical Likelihood Maximization (ELM). This is a versatile method that involves sampling from a sequence…

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 import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation produces a perturbation of sample data, which we call a…

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…

The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual…

The traditional maximum likelihood estimator (MLE) is often of limited use in complex high-dimensional data due to the intractability of the underlying likelihood function. Maximum composite likelihood estimation (McLE) avoids full…

We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are…

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…

Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…

Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…

We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on…

Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood…