Generalized Bayesian Likelihood-Free Inference Using Scoring Rules Estimators

Staff - Faculty of Informatics

Date: 14 December 2021 / 13:00 - 14:30

USI Campus EST, room D0.02, Sector D // online on MS Teams

This seminar is organized by Prof. Antonietta Mira, in connection with the winter doctoral school co-organized by UNIPV and USI on Contemporary methods in spatial statistics in R with applications to life science

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Speaker: Lorenzo Pacchiardi, PhD student, Department of Statistics, University of Oxford

Abstract:
After an introduction to  Likelihood-Free Inference (LFI)  we will propose a framework for Bayesian LFI based on Generalized Bayesian Inference. To define the generalized posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. As in LFI we can sample from the model (but not evaluate the likelihood), we employ SRs with easy empirical estimators. Our framework includes novel approaches and popular LFI techniques (such as Bayesian Synthetic Likelihood), which benefit from the generalized Bayesian interpretation. Our method enjoys posterior consistency in a well-specified setting when a strictly-proper SR is used (i.e., one whose expectation is uniquely minimized when the model corresponds to the data generating process). Further, we prove a finite sample generalization bound and outlier robustness for the Kernel and Energy Score posteriors, and propose a strategy suitable for the LFI setup for tuning the learning rate in the generalized posterior. We run simulations studies with pseudo-marginal Markov Chain Monte Carlo (MCMC) and compare with related approaches, which we show do not enjoy robustness and consistency. 

Biography:
Lorenzo is a PhD student in Statistics at the University of Oxford, under the supervision of Dr. Ritabrata Dutta (Uni. Warwick) and Prof. Geoff Nicholls (Uni. Oxford). His main research focus is Bayesian Likelihood-Free Inference; he is also interested in deep learning (mainly for Likelihood-Free Inference applications), generalized Bayesian inference and probabilistic weather forecasting. Before his PhD studies, he obtained a BSc in Physical Engineering from Politecnico di Torino and a joint MSc in Physics of Complex Systems from Politecnico di Torino and Université Paris Saclay.

Host: Prof. Antonietta Mira

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