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Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of…

Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound).…

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

Uncertainty quantification is a key pillar of trustworthy machine learning. It enables safe reactions under unsafe inputs, like predicting only when the machine learning model detects sufficient evidence, discarding anomalous data, or…

We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of…

An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…

Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…

When making important decisions such as choosing health insurance or a school, people are often uncertain what levels of attributes will suit their true preference. After choice, they might realize that their uncertainty resulted in a…

In the domain of physics experiments, data fitting is a pivotal technique for extracting insights from both experimental and simulated datasets. This article presents an approximation method designed to estimate the systematic errors…

Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…

The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…

We study a physical system which, while devoid of the complexity one usually associates with proteins, nevertheless displays a remarkable array of protein-like properties. The constructive hypothesis that this striking resemblance is not…

Likelihood-based inference, central in modern particle physics data analysis requires the extensive evaluation of a likelihood function that depends on set of parameters defined by the statistical model under consideration. If an analytical…

The adaptation and use of Machine Learning (ML) in our daily lives has led to concerns in lack of transparency, privacy, reliability, among others. As a result, we are seeing research in niche areas such as interpretability, causality, bias…