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Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
Reliable spatial uncertainty evaluation of object detection models is of special interest and has been subject of recent work. In this work, we review the existing definitions for uncertainty calibration of probabilistic regression tasks.…
The rebmix package provides R functions for random univariate and multivariate finite mixture model generation, estimation, clustering and classification. The paper is focused on multivariate normal mixture models with unrestricted…
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…
In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is…
Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
In recent years, machine learning has witnessed extensive adoption across various sectors, yet its application in medical image-based disease detection and diagnosis remains challenging due to distribution shifts in real-world data. In…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The…
Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…