相关论文: Rate of convergence in the maximum likelihood esti…

Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…

Some continuous optimization methods can be connected to ordinary differential equations (ODEs) by taking continuous limits, and their convergence rates can be explained by the ODEs. However, since such ODEs can achieve any convergence rate…

This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we…

Combining discrete probability distributions and combinatorial optimization problems with neural network components has numerous applications but poses several challenges. We propose Implicit Maximum Likelihood Estimation (I-MLE), a…

In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study…

The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…

In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…

Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…

Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…

For a multinomial distribution, suppose that we have prior knowledge of the sum of the probabilities of some categories. This allows us to construct a submodel in a full (i.e., no-restriction) model. Maximum likelihood estimation (MLE)…

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

We study the rms peculiar velocity of clusters as a convenient statistic to put constraints on cosmological models. This statistic is easy to compute theoretically given a model for the power spectrum; we show that with some assumptions it…

Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…