Related papers: Consistency of the MLE under mixture models
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…
The hallmark of effective language use lies in consistency: expressing similar meanings in similar contexts and avoiding contradictions. While human communication naturally demonstrates this principle, state-of-the-art language models (LMs)…
We study the likelihood ratio test in general mixture models where the base density is parametric, the null is a known fixed mixing distribution, and the alternative is a general mixing distribution supported on a bounded parameter space.…
Accurately gauging the confidence level of Large Language Models' (LLMs) predictions is pivotal for their reliable application. However, LLMs are often uncalibrated inherently and elude conventional calibration techniques due to their…
Many real-world classification problems are significantly class-imbalanced to detriment of the class of interest. The standard set of proper evaluation metrics is well-known but the usual assumption is that the test dataset imbalance equals…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
We characterise the unbiasedness of the score function, viewed as an inference function for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number…
P values or risk ratios from multiple, independent studies, observational or randomized, can be computationally combined to provide an overall assessment of a research question in meta-analysis. There is a need to examine the reliability of…
The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty…
Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…
In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
When do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…