We consider the analysis of probability distributions through their associated covariance
operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy …

The Christoffel-Darboux kernel, a central object in approximation theory, is shown to have
many potential uses in modern data analysis, including applications in machine learning …

Consider the problem of minimizing a polynomial f over a compact semialgebraic set
X⊆R^n. Lasserre introduces hierarchies of semidefinite programs to approximate this hard …

We provide a new method to approximate a (possibly discontinuous) function using
Christoffel–Darboux kernels. Our knowledge about the unknown multivariate function is in …

We present an algorithm for data-driven reachability analysis that estimates finite-horizon
forward reachable sets for general nonlinear systems using sub-level sets of a certain class …

Nous fournissons d'abord une interprétation particulière de l'équation polynomiale de Pell
satisfaite par les polynômes de Chebyshev. Pour chaque degré t, il en découle une …

Most common optimal transport (OT) solvers are currently based on an approximation of
underlying measures by discrete measures. However, it is sometimes relevant to work only …

We show that the Christoffel function (CF) factorizes (or can be disintegrated) as the product
of two Christoffel functions, one associated with the marginal and the another related to the …

Persistent homology has been widely used to study the topology of point clouds in $\mathbb
{R}^ n $. Standard approaches are very sensitive to outliers, and their computational …

These are lecture notes for a mini-course course given in October 2023 at Institut Henri
Poincaré, Paris, in the scope of the research programme “Recent trends in computer …