Related papers: Measuring the Discrepancy between Conditional Dist…
While machine learning (ML) architectures have evolved rapidly to account for complex data, loss functions like cross-entropy remain mostly structure-agnostic in many real-world applications. However, the `class-symmetric' nature of these…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued…
Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least $(1-\alpha)$ confidence. This…
Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…
The paper proposes a specification test based on two estimates of distribution function. One is the traditional kernel distribution function estimate and the other is a newly proposed convolution-type distribution function estimate.…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In…
Many natural and social science systems are described using probability distributions over elements that are related to each other: for instance, occupations with shared skills or species with similar traits. Standard information theory…
This article introduces novel measures of inaccuracy and divergence based on survival extropy and their dynamic forms and explores their properties and applications. To address the drawbacks of asymmetry and range limitations, we introduce…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…
Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…
Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We…
We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a Weighted…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…
We study distribution testing in the standard access model and the conditional access model when the memory available to the testing algorithm is bounded. In both scenarios, the samples appear in an online fashion and the goal is to test…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…