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Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
When a measurement of a physical quantity is reported, the total uncertainty is usually decomposed into statistical and systematic uncertainties. This decomposition is not only useful to understand the contributions to the total…
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical…
The research described in this paper is motivated by model checking for parametric single-index models with diverging number of predictors. To construct a test statistic, we first study the asymptotic property of the estimators of involved…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We generalize the theory of supervised contrastive learning, previously applied to physical systems at equilibrium or steady state, to systems following any dynamics described by coupled ordinary differential equations. We show that if…
Model-independent searches in particle physics aim at completing our knowledge of the universe by looking for new possible particles not predicted by the current theories. Such particles, referred to as signal, are expected to behave as a…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
Independent Component Analysis (ICA) is a statistical method often used to decompose a complex dataset in its independent sub-parts. It is a powerful technique to solve a typical Blind Source Separation problem. A fast calculation of the…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…
Graph representation learning has long been an important yet challenging task for various real-world applications. However, their downstream tasks are mainly performed in the settings of supervised or semi-supervised learning. Inspired by…
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…
[PhD thesis of FCP.] Nowadays, genetics studies large amounts of very diverse variables. Mathematical statistics has evolved in parallel to its applications, with much recent interest high-dimensional settings. In the genetics of human…