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Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…

This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.

We prove a formula for the evaluation of expectations containing a scalar function of a Gaussian random vector multiplied by a product of the random vector components, each one raised to a non-negative integer power. Some of the powers…

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

Stationary and isotropic iteration stable random tessellations are considered, which can be constructed by a random process of cell division. The collection of maximal polytopes at a fixed time $t$ within a convex window $W\subset{\Bbb…

We give an exact formula for the value of the derivative at zero of the gap probability in finite n x n Gaussian ensembles. As n goes to infinity our computation provides an asymptotic (with an explicit constant) of the order n^(1/2). As a…

For $X(n)$ a Rademacher or Steinhaus random multiplicative function, we consider the random polynomials $$ P_N(\theta) = \frac1{\sqrt{N}} \sum_{n\leq N} X(n) e(n\theta), $$ and show that the $2k$-th moments on the unit circle $$ \int_0^1…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

A Newton--Kantorovich-type argument enables the a posteriori existence verification of a unique regular root near a computed approximation, purely from computable data. This framework allows for non-selfadjoint problems and extends the…

Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…

We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we…

In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in…

We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…

For systems of equations with an infinite set of roots, one can sometimes obtain Kushnirenko-Bernstein-Khovanskii type theorem if replace the number of roots by their asymptotic density. We consider systems of entire functions with…

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…

We obtain general estimates for exponential integrals of the form \[ E_f(y)=\int_{\mathbb{Z}_{p}^{n}}\psi(\sum_{j=1}^r y_j f_j(x))|dx|, \] where the $f_j$ are restricted power series over $\mathbb{Q}_p$, $y_j\in\mathbb{Q}_p$, and $\psi$ a…

Consider the random polytope, that is given by the convex hull of a Poisson point process on a smooth convex body in $\mathbb{R}^d$. We prove central limit theorems for continuous motion invariant valuations including the Will's functional…

We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…

Gaussian Boson Sampling (GBS), which can be realized with a photonic quantum computing model, perform some special kind of sampling tasks. In [4], we introduced algorithms that use GBS samples to approximate Gaussian expectation problems.…

In this paper we establish an estimate for the rate of convergence of the Krasnosel'ski\v{\i}-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic…