Related papers: Computing Maximum Likelihood Estimates for Gaussia…

We introduce the package LatticePolytopes for Macaulay2. The package provides methods for computations related to Cayley structures, local positivity and smoothness for lattice polytopes.

This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be…

Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

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…

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…

In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to…

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

We give a description of a new Macaulay2 package called SimplicialPosets. This package provides functions for working with simplicial posets and calculating their generalized Stanley-Reisner ideals. For practical purposes, we also introduce…

This introduces Rees algebras and some of their uses with illustrations via version 2.0 of the Macaulay2 package ReesAlgebra.m2.

This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…

For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern…

In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…

Maximum likelihood estimation of generalized linear mixed models(GLMMs) is difficult due to marginalization of the random effects. Computing derivatives of a fitted GLMM's likelihood (with respect to model parameters) is also difficult,…

We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matrix (ASM) varieties. The package also introduces tools for…

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…

Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…

The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…