Related papers: Quantifying deviations from Gaussianity with appli…
Distribution shifts, where statistical properties differ between training and test datasets, present a significant challenge in real-world machine learning applications where they directly impact model generalization and robustness. In this…
Mapping data from and/or onto a known family of distributions has become an important topic in machine learning and data analysis. Deep generative models (e.g., generative adversarial networks ) have been used effectively to match known and…
Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…
The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts,…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
We investigate the evolution of the skewness of the distribution of density fluctuations in CDM models with both Gaussian and non--Gaussian initial fluctuations. We show that the method proposed by Coles \& Frenk (1991), which uses the…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
We study the problem of estimating multiple discrete unimodal distributions, motivated by search behavior analysis on a real-world platform. To incorporate prior knowledge of precedence relations among distributions, we impose stochastic…
Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed…
The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and…
The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions. In this work, we introduce an alternative definition of the…
The Jensen-Shannon divergence is a renown bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However the Jensen-Shannon divergence…
This paper introduces Gaussian Spatial Transport (GST), a novel framework that leverages Gaussian splatting to facilitate transport from the probability measure in the image coordinate space to the annotation map. We propose a Gaussian…
We study a heavily overloaded single-server queue with abandonment and derive bounds on stationary tail probabilities of the queue length. As the abandonment rate $\gamma \downarrow 0$, the centered-scaled queue length $\tilde{q}$ is known…
Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…