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In this work, we discuss a general class of the estimators for the cumulative distribution function (CDF) based on judgment post stratification (JPS) sampling scheme which includes both empirical and kernel distribution functions.…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little…
Few-shot image classification remains challenging due to the scarcity of labeled training examples. Augmenting them with synthetic data has emerged as a promising way to alleviate this issue, but models trained on synthetic samples often…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
The functional empirical process is a very powerful tool for deriving asymptotic laws for almost any kind of statistics whenever we know how to express them into functions of the sample. Since this method seems to be applied more and more…
Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…
A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
Distributed aggregation allows the derivation of a given global aggregate property from many individual local values in nodes of an interconnected network system. Simple aggregates such as minima/maxima, counts, sums and averages have been…
The evolution of skyline and ranking queries has created new archetypes like flexible skylines, which have proven to be an efficient method to select relevant data from large datasets using multi objective optimization. This paper aims to…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
Many clustering algorithms when the data are curves or functions have been recently proposed. However, the presence of contamination in the sample of curves can influence the performance of most of them. In this work we propose a robust,…
Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the…
This paper studies the large sample asymptotics of data analysis procedures based on the optimization of functionals defined on $k$-NN graphs on point clouds. The paper is framed in the context of minimization of balanced cut functionals,…
Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…
The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand…