SEMINAR | Le Palaisien
SEMINAR | Le Palaisien
- 12h-12h40pm - Valentin DE BORTOLI - An introduction to Score-Based Generative Modeling and Schrodinger Bridges
- 12h40-1:20pm - Yann ISSARTEL - Seriation and 1D-localization in latent space models
- Events on the same topic
See you on July 5, 2022 at 12:00 at ENSAE, room 1004, for the Palaisien Seminar!
Animated by Valentin DE BORTOLI, who will give a talk on "An introduction to generative score-based modeling and Schrodinger bridges" and Yann ISSARTEL, on "1D seriation and localization in latent space models".
Registration is free but mandatory, subject to availability. A sandwich basket is offered.
Score-Based Generative Modeling (SGM) is a recently developed approach to probabilistic generative modeling that exhibits state-of-the-art performance on several audio and image synthesis tasks. Existing SGMs generally consist of two parts. Firstly, noise is incrementally added to the data in order to obtain a perturbed data distribution approximating an easy-to-sample prior distribution e.g. Gaussian. Secondly, a neural network is used to learn the reverse-time denoising dynamics, which when initialized at this prior distribution, defines a generative model. Song et al. (2021) have shown that one could fruitfully view the noising process as a Stochastic Differential Equation (SDE) that progressively perturbs the initial data distribution into an approximately Gaussian one. In this talk, we will introduce the basics of SGM and present some connections with stochastic control through the concept of Schrodinger bridges.
Motivated by applications in archeology for relative dating of objects, or in 2D-tomography for angular synchronization, we consider the problem of statistical seriation where one seeks to reorder a noisy disordered matrix of pairwise affinities. This problem can be recast in the powerful latent space terminology, where the affinity between a pair of items is modeled as a noisy observation of a function f(x_i,x_j) of the latent positions x_i, x_j of the two items on a one-dimensional space. This reformulation naturally leads to the problem of estimating the positions in the latent space. Under non-parametric assumptions on the affinity function f, we introduce a procedure that provably localizes all the latent positions with a maximum error of the order of the square root of log(n)/n. This rate is proven to be minimax optimal. Computationally efficient procedures are also analyzed, under some more restrictive assumptions. Our general results can be instantiated to the original problem of statistical seriation, leading to new bounds for the maximum error in the ordering.