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Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Let $\mu$ be a probability measure on $\mathbb{R}$ with cumulative distribution function $F$, $(x_{i})_{1}^{n}$ a large i.i.d. sample from $\mu$, and $F_{n}$ the associated empirical distribution function. The Glivenko-Cantelli theorem…
In this paper, we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of measure transportation. Unlike other existing proposals in…
Statistical depth functions provide measures of the outlyingness, or centrality, of the elements of a space with respect to a distribution. It is a nonparametric concept applicable to spaces of any dimension, for instance, multivariate and…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
This paper generalises inference functions (Godambe, 1960) to distributional statistical models, in which each probability measure is represented by a distribution--kernel pair $(T_\theta, \varphi) \in \mathcal S'(\mathbb R) \times \mathcal…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
We treat the problem of testing for association between a functional variable belonging to Hilbert space and a scalar variable. Particularly, we propose a distribution-free test statistic based on Kendall's Tau which is one of the most…
This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…
In this paper we develop a functorial language of probabilistic morphisms and apply it to some basic problems in Bayesian nonparametrics. First we extend and unify the Kleisli category of probabilistic morphisms proposed by Lawvere and Giry…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…