Related papers: A modern maximum-likelihood theory for high-dimens…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
Random-effects models are frequently used to synthesise information from different studies in meta-analysis. While likelihood-based inference is attractive both in terms of limiting properties and of implementation, its application in…
Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from…
In this paper we discuss how to evaluate the differences between fitted logistic regression models across sub-populations. Our motivating example is in studying computerized diagnosis for learning disabilities, where sub-populations based…
Regression analysis based on many covariates is becoming increasingly common. However, when the number of covariates $p$ is of the same order as the number of observations $n$, maximum likelihood regression becomes unreliable due to…
Consider a set of categorical variables $\mathcal{P}$ where at least one, denoted by $Y$, is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…
The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual least squares approach. In this paper a new derivation is given for the asymptotic…
The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the Maximum Likelihood (ML) principle indicates a unique, statistically rigorous…
There is a considerable literature in case-control logistic regression on whether or not non-confounding covariates should be adjusted for. However, only limited and ad hoc theoretical results are available on this important topic. A…
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…
Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…
Machine-Learned Likelihoods (MLL) combines machine-learning classification techniques with likelihood-based inference tests to estimate the experimental sensitivity of high-dimensional data sets. We extend the MLL method by including Kernel…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
Large Language Models (LLMs) can propose rules in natural language, sidestepping the need for a predefined predicate space in traditional rule learning. Yet many LLM-based approaches ignore interactions among rules, and the opportunity to…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…