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Title: Robust generalised Bayesian inference for intractable likelihoods Authors:  Chris Oates - Newcastle University (United Kingdom) [presenting]
Francois-Xavier Briol - University College London (United Kingdom)
Takuo Matsubara - The Alan Turing Institute / Newcastle University (United Kingdom)
Jeremias Knoblauch - University College London (United Kingdom)
Abstract: Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. We consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the normalisation constant and produces generalised posteriors that are either closed form or accessible using the standard Markov chain Monte Carlo. On a theoretical level, we show consistency, asymptotic normality, and bias-robustness of the generalised posterior, highlighting how these properties are impacted by the choice of Stein discrepancy. Then, we provide numerical experiments on a range of intractable distributions, including applications to kernel-based exponential family models and non-Gaussian graphical models.