On the Christoffel function and its links with positive polynomials
This talk is a brief introduction to the Christoffel-Darboux (CD) kernel and the Christoffel function (CF).
Even though the CD kernel and the CF are well-known tools from approximation theory and orthogonal polynomials, only recently it was realized that they could prove to be very useful (and easy-to-use) in solving some problems in data analysis (e.g outlier detection & support inference). Moreover, we will also show that a non standard use of the CD kernel can provide accurate approximations and interpolations of discontinuous functions. Last but not least we also reveal some (in the author’s opinion) surprising connections of the CF with seemingly unrelated fields (positivity certificates, Pell’s equation, convex duality).
Practical information:
Georganiseerd door:
Teacher / speaker
CNRS and Institute of Mathematics, Toulouse, France
Back to the Roots Seminar Series
The ERC research project "Back to the roots of data-driven dynamical system identification", led by Prof. Dr. Bart De Moor (KU Leuven, ESAT-STADIUS), focuses on system identification, where mathematical models are derived from observed data generated by systems such as medical monitoring, electricity consumption and industrial processes. Utilizing optimization algorithms, one seeks to identify the best model in a chosen model class. This methodology finds widespread application across thousands of use cases within the AI community. However, there is no guarantee that optimization algorithms will find the best model. Present-day optimization practices are heuristic in nature, yielding results that may not be reproducible and consequently difficult to interpret.
The main objective of the Back to the Roots project is to develop a theoretical framework that combines model classes and optimization algorithms, enabling the calculation of the optimal model within the specified model class with 100% certainty.
