|Samples, which follow a Gaussian mixture distribution.
My research applies techniques from Algebraic Geometry and Semidefinite Programming to problems from Statistics. Gaussian mixtures have been a central theme in my research, and I am particularly interested in the problems of identifiability and parameter recovery for mixture distributions.
It is particularly fascinating to me, how classical subjects of 19th and 20th century geometry, such as the theory of Waring decompositions and Sums-of-Squares representations, are applied in cutting-edge algorithms and recovery results for high-dimensional estimation problems.
My two most recent results prove recovery guarantees for mixtures of Gaussians. In this preprint, recently presented at an Oberwolfach workshop, I show that the parameters of a general mixture of \(\Omega (n^4)\) Gaussians can be recovered from the mixture moments of degree 4 and 6. This other preprint, recently presented at FOCM, develops an algorithm to algorithmically decompose the mixture moments of centered Gaussians, where sums-of-squares representations play a crucial role to find the decomposition. You can find presentations for both results in the talks section.
Optimization for and with Machine Learning (OPTIMAL). ENW-GROOT research project funded by NWO. Collaboration between University of Amsterdam, CWI, Tilburg University, and Technical University Delft.
Part of the research group Networks and Optimization at CWI.
Organization & Service
I am a reviewer for zbMath.