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Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
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 study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…
Topic models provide a useful text-mining tool for learning, extracting, and discovering latent structures in large text corpora. Although a plethora of methods have been proposed for topic modeling, lacking in the literature is a formal…
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…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
One of the most common methods for statistical inference is the maximum likelihood estimator (MLE). The MLE needs to compute the normalization constant in statistical models, and it is often intractable. Using unnormalized statistical…
We study multivariate Gaussian statistical models whose maximum likelihood estimator (MLE) is a rational function of the observed data. We establish a one-to-one correspondence between such models and the solutions to a nonlinear…
Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. In this paper, MLE for statistical models with discrete data is studied from an algebraic statistics viewpoint. A reformulation of the MLE problem in…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…
In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum…
We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the…
We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the data are generated from the density function $(1-\lambda^{\ast})h_{0}(x)+\lambda^{\ast}f(x|\mu^{\ast}, \Sigma^{\ast})$ in which $h_{0}$ is a known…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…