SEMINARS IN STATISTICS @ COLLEGIO CARLO ALBERTO https://www.google.com/url?q=https://www.carloalberto.org/events/category/seminars/seminars-in-statistics/page/2/?tribe-bar-date%3D2019-09-01&source=gmail-imap&ust=1732719071000000&usg=AOvVaw1_VfRy4qDP_HHioNc49JU_

Venerdì 14/03/2025, presso il Collegio Carlo Alberto, in Piazza Arbarello 8, Torino, si terrà il seguente doppio seminario:

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11.00-12.00

Speaker: Sahani PATHIRAJA (UNSW SYDNEY)

Title: ON CONNECTIONS BETWEEN SEQUENTIAL BAYESIAN INFERENCE AND EVOLUTIONARY DYNAMICS

Abstract: It has long been posited that there is a connection between the dynamical equations describing birth-death & evolutionary processes in biology (so-called ``replicator-mutator’’ dynamics) and sequential Bayesian learning methods. This talk describes new research in which this precise connection is rigorously established in the continuous time setting. Here we focus on a class of interacting particle methods for solving the sequential Bayesian inference problem which are characterised by a McKean-Vlasov Stochastic differential equation. Of particular importance is a piecewise smooth approximation of the observation path from which the discrete time filtering equations are shown to converge to a Stratonovich interpretation of the Kushner equation. This smooth formulation will then be used to draw precise connections between nonlinear filtering and replicator-mutator dynamics. Additionally, gradient flow formulations will be investigated as well as a particular form of replicator-mutator dynamics which is shown to be beneficial for filtering with misspecified models. It is hoped this work will spur further research into exchanges between sequential learning and evolutionary biology and to inspire new algorithms in filtering and sampling.

12.00-13.00

Speaker: Quan ZHOU (TEXAS AMU)

Title: GENERATIVE MODELING USING SOFT-CONSTRAINED SCHRODINGER BRIDGE

Abstract: Schrodinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We propose to generalize this problem by allowing the terminal distribution to differ from the target but penalizing the Kullback-Leibler divergence between the two distributions. We call this new control problem soft-constrained Schrodinger bridge (SSB). The main contribution of this work is a theoretical derivation of the solution to SSB, which shows that the terminal distribution of the optimally controlled process is a geometric mixture of the target and some other distribution. This result is further extended to a time series setting. One application is the development of robust generative diffusion models. We propose a score matching-based algorithm for sampling from geometric mixtures and showcase its use via a numerical example for the MNIST data set. Joint work with J. Garg and X. Zhang. ------------------------------------------------

Sarà possibile il seminario anche in streaming: chiunque volesse collegarsi è pregato di inviare una email entro *mercoledì 12/03/2025* a matteo.giordano@unito.it mailto:matteo.giordano@unito.it

Il webinar è organizzato dalla "de Castro" Statistics Initiative (www.carloalberto.org/stats http://www.carloalberto.org/stats) in collaborazione con il Collegio Carlo Alberto.

Cordiali saluti,

Matteo Giordano Assistant Professor (RTDA) Department of Economics, Social Studies, Applied Mathematics and Statistics (ESOMAS) www.matteogiordano.weebly.com https://matteogiordano.weebly.com/