Related papers: Probabilistic Inference from Arbitrary Uncertainty…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
Mixture models postulate the overall population as a mixture of finite subpopulations with unobserved membership. Fitting mixture models usually requires large sample sizes and combining data from multiple sites can be beneficial. However,…
Existing frameworks for probabilistic inference assume the quantity of interest is the parameter of a posited statistical model. In machine learning applications, however, often there is no statistical model/parameter; the quantity of…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are…
Regression mixture models are widely studied in statistics, machine learning and data analysis. Fitting regression mixtures is challenging and is usually performed by maximum likelihood by using the expectation-maximization (EM) algorithm.…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…
Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…
We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
Recommender systems leverage product and community information to target products to consumers. Researchers have developed collaborative recommenders, content-based recommenders, and (largely ad-hoc) hybrid systems. We propose a unified…
This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
Identifying pure components in mixtures is a common yet challenging problem. The associated unmixing process requires the pure components, also known as endmembers, to be sufficiently spectrally distinct. Even with this requirement met,…