[ibayesclub.beta] invitation: Bayes club 19th of February, 3-5 pm, zoom

[Szabo, B.T.]

Dear Colleagues,


The first (International) Bayes club (https://www.math.vu.nl/thebayesclub/)  meeting of this semester will take place on the 19th of February (Friday) from 3 pm until 5 pm. We have two speakers: David Rossell (Barcelona) and Veronika Rockova (Chicago), please find below the titles and the abstracts of the talks. The seminar will be on zoom:


Topic: International Bayes club
Time: Feb 19, 2021 03:00 PM Amsterdam

Join Zoom Meeting
https://vu-live.zoom.us/j/97567928223?pwd=Vm1SOTRuTzVsbjNrZkdBVHg1MTFrZz09

Meeting ID: 975 6792 8223
Passcode: 504799

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The program of the whole semester is available online (https://www.math.vu.nl/thebayesclub/).

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3pm Speaker: David Rossell (Univ. Pompeu Fabra in Barcelona)
Title: Approximate Laplace approximation

Bayesian model selection has desirable properties to recover structure, e.g. we discuss strong control of frequentist error probabilities in hypothesis tests. However, BMS requires evaluating integrals to assign posterior model probabilities to each candidate model. The computation is cumbersome when the integral has no closed-form, particularly when the sample size or the number of models are large. We present a simple yet powerful idea based on the Laplace approximation (LA) to an integral. LA uses a quadratic Taylor expansion at the mode of the integrand and is typically quite accurate, but requires cumbersome likelihood evaluations (for large n) an optimization (for large p). We propose the approximate Laplace approximation (ALA), which uses an Taylor expansion at the null parameter value. ALA brings significant speed-ups by avoiding optimizations altogether, and evaluating likelihoods via sufficient statistics. ALA is an approximate inference method equipped with strong model selection properties in the family of non-linear GLMs, attaining comparable rates to exact computation that also hold when all models are misspecified. In fact, it is questionable whether one should target exact calculations when (inevitably) the model is never exactly corret. We show examples in non-linear Gaussian regression with non-local priors, for which no closed-form integral exists, as well as non-linear logistic, Poisson and survival regression.



4pm Speaker: Veronika Rockova (Univ. Chicago Booth)
Title: Metropolis-Hastings Via Classification

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative Adversarial Networks (GAN) of Goodfellow et al. (2014), we reframe the likelihood function estimation problem as a classification problem. Pitting a Generator, who simulates fake data, against a Classifier, who tries to distinguish them from the real data, one obtains likelihood (ratio) estimators which can be plugged into the Metropolis-Hastings algorithm. The resulting Markov chains generate, at a steady state, samples from an approximate posterior whose asymptotic properties we characterize. Drawing upon connections with empirical Bayes and Bayesian mis-specification, we quantify the convergence rate in terms of the contraction speed of the actual posterior and the convergence rate of the Classifier. Asymptotic normality results are also provided which justify inferential potential of our approach. We illustrate the useful- ness of our approach on simulated data. (Joint work with Tetsuya Kaji)


Best wishes,
Botond (on behalf of the organising team)
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