Related papers: On the maximum likelihood estimation in general lo…
Large Language Models (LLMs), originally developed for natural language processing (NLP), have demonstrated the potential to generalize across modalities and domains. With their in-context learning (ICL) capabilities, LLMs can perform…
We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…
Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
Simulation-based optimal design techniques are a convenient tool for solving a particular class of optimal design problems. The goal is to find the optimal configuration of factor settings with respect to an expected utility criterion. This…
The EM algorithm is a generic tool that offers maximum likelihood solutions when datasets are incomplete with data values missing at random or completely at random. At least for its simplest form, the algorithm can be rewritten in terms of…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical…
Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…
Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…
Nonlinear Mixed Effects models (NLME) models are widely used in pharmacometrics and related fields to analyze hierarchical and longitudinal data. However, as the number of parameters and random effects increases, traditional methods for…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
Objectives: Highly flexible nonparametric estimators have gained popularity in causal inference and epidemiology. Popular examples of such estimators include targeted maximum likelihood estimators (TMLE) and double machine learning (DML).…
In a regular full exponential family, the maximum likelihood estimator (MLE) need not exist in the traditional sense. However, the MLE may exist in the completion of the exponential family. Existing algorithms for finding the MLE in the…
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…
We study targeted maximum likelihood estimation (TMLE) of the average treatment effect in a semiparametric regression model whose mean function is indexed by a finite-dimensional parameter, while the additive error distribution is left…