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Anna KORBA (CREST) – Sampling with Mollified Interaction Energy Descent
Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 2nd october 2023
Place : 3001
Anna KORBA – Sampling with Mollified Interaction Energy Descent
Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. We present a new optimization-based method for sampling called mollified interaction energy descent (MIED), that minimizes an energy on probability measures called mollified interaction energie (MIE). The latter converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence, as the mollifiers approach Dirac deltas. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show the performance of our algorithm on both unconstrained and constrained sampling in comparison to state-of-the-art alternatives.
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)