Events

Math & Data (MaD) Seminar: Christoffel-Darboux Polynomial Kernel for High-Dimensional Anomaly Detection in Satellite Telemetry

Speaker: Didier Henrion

Location: 60 Fifth Avenue, Room 7th floor open space

Date: Thursday, April 23, 2026

Abstract: This work is motivated by satellite housekeeping telemetry for CNES, the French space agency. The goal is short- to medium-term anomaly detection on streams of health-and-status data a satellite sends about itself, including battery and solar-panel voltages, temperatures at various locations, and reaction-wheel speeds for attitude control. In this setting, one seeks anomaly scores that are both explainable and frugal, while remaining effective in high dimension. We introduce a scalable variant of the Christoffel-Darboux (CD) polynomial kernel based on a simple but powerful observation. Instead of evaluating the classical multivariate CD kernel at a query point, we push the data distribution forward by the squared-distance map. This produces a univariate measure, depending on the query point, and hence a univariate CD kernel evaluated at the origin. The resulting score retains geometric information through its dependence on the query point, while replacing a high-dimensional polynomial problem by a scalar one. We show that this univariate CD kernel preserves the fundamental on/off-support dichotomy of the classical CD construction: it grows at most polynomially when the query point lies in the support of the distribution, and at least exponentially outside the support. Thus it remains a principled anomaly score, with the same qualitative separation mechanism as the multivariate kernel. The main gain is computational. The classical CD kernel requires manipulating moment matrices of size which quickly becomes prohibitive. By contrast, our method only requires building and inverting a univariate moment matrix from moments of squared distances to the query point. This yields a lightweight, numerically stable, and easily implementable procedure, suitable for large-scale or streaming settings. Joint work with Florian Grivet, Clément Hinderer, Jean Bernard Lasserre, Louise Travé-Massuyès and Lionel Vintenat. 

Bio: Didier Henrion is a senior researcher at the Laboratory of Analysis and Architecture of Systems (LAAS) of the National Center for Scientific Research (CNRS) in Toulouse, France. He is also a Professor at the Department of Control Engineering of the Faculty of Electrical Engineering of the Czech Technical University in Prague. His main research interest I am interested in polynomial optimization, a branch of applied mathematics dealing with difficult, non-linear, typically non-convex optimization problems with polynomial data. He has contributed to the foundations of polynomial optimization as well as its engineering applications, and especially in systems control and non-linear differential equations. In 2004 he was awarded the Bronze Medal from CNRS, for his achievements in systems control theory. In 2005 he was awarded, jointly with Fredrik Kahl, the David Marr Prize for the best paper at the International Conference on Computer Vision. In 2012 he was awarded, jointly with Jérôme Malick, the Charles Broyden prize for the best paper in the journal Optimization Methods and Software. In 2016 he was awarded, jointly with Cédric Josz, the Optimization Letters Best Paper Award. He is the recipient of the IFAC French NMO Award 2020.