Próximas Charlas

Dia 2022-10-07 10:30:00-03:00
Hora 2022-10-07 10:30:00-03:00

Solving Inverse Problems in Imaging by Posterior Sampling with Auto-Encoding Prior

Mario González (DMEL-Cenur Litoral Norte)

 In Bayesian statistics, prior knowledge about the unobserved signal of interest is expressed as a prior distribution which, combined with observational data in the form of a likelihood function allows to determine the posterior distribution. This posterior can be used to derive point estimates such as the MAP or MMSE estimators, but also to estimate uncertainty in these predictions, e.g. in the form of confidence intervals. Most of the work using generative models such as Generative Adversarial Networks (GAN) or Variational AutoEncoders (VAE) as image priors focus on computing point estimates. On the other hand, MCMC methods for sampling from the posterior distribution permit the exploration of the solution space and computing point estimates as well as other statistics about the solutions such as uncertainty estimates. However, the performance of widely used methods like Metropolis-Hastings depends on having precise proposal distributions which can be challenging to define in high-dimensional spaces. In this talk, we present a Gibbs-like posterior sampling algorithm that exploits the bidirectional nature of VAE networks. Thanks to the GPU's parallelization capability, we efficiently run multiple chains which explore more rapidly the posterior distribution and also give more accurate convergence tests. To accelerate the burn-in period we explore the adaptation of the annealed importance sampling with resampling method.

Dia 2022-10-07 11:15:00-03:00
Hora 2022-10-07 11:15:00-03:00
LugarSala de Seminarios del IMERL y a través de Zoom

Singularity categories, Leavitt path algebras and Hochschild homology.

Bernhard Keller (Université Paris Cité)

The singularity category of a noetherian (non commutative) algebra is the quotient of its bounded by its perfect derived category. This construction goes back to Buchweitz (1986) in this setting and, independently, to Orlov (2003) in a geometric setting. We will recall the description of the singularity category of a radical-square zero quiver algebra using a graded Leavitt path algebra following work of Paul Smith, Xiao-Wu Chen, Dong Yang and others. We will then combine this with a localization theorem for Hochschild homology to obtain a simple description of the Hochschild homology of these singularity categories (with their canonical differential graded enhancement) and of the corresponding Leavitt path algebras. Finally, we will report on recent work of Xiao-Wu Chen and Zhengfang Wang which yields a generalization from radical-square zero to arbitrary finite-dimensional algebras (over an algebraically closed field).

This is mainly a survey talk. The original parts are based on joint work with Umamaheswaran Arunachalam and Yu Wang.