
A Contrastive Divergence for Combining Variational Inference and MCMC
We develop a method to combine Markov chain Monte Carlo (MCMC) and varia...
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Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributions
We introduce a new algorithm for approximate inference that combines rep...
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MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference
In this contribution, we propose a new computationally efficient method ...
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Variational Bayes under Model Misspecification
Variational Bayes (VB) is a scalable alternative to Markov chain Monte C...
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Posterior inference unchained with EL_2O
Statistical inference of analytically nontractable posteriors is a diff...
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Newtonian Monte Carlo: singlesite MCMC meets secondorder gradient methods
Singlesite Markov Chain Monte Carlo (MCMC) is a variant of MCMC in whic...
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Identifying Invariant Factors Across Multiple Environments with KL Regression
Many datasets are collected from multiple environments (e.g. different l...
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Markovian Score Climbing: Variational Inference with KL(pq)
Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling largescale probabilistic inference in complex models. VI posits a family of approximating distributions q and then finds the member of that family that is closest to the exact posterior p. Traditionally, VI algorithms minimize the "exclusive KL" KL(qp), often for computational convenience. Recent research, however, has also focused on the "inclusive KL" KL(pq), which has good statistical properties that makes it more appropriate for certain inference problems. This paper develops a simple algorithm for reliably minimizing the inclusive KL. Consider a valid MCMC method, a Markov chain whose stationary distribution is p. The algorithm we develop iteratively samples the chain z[k], and then uses those samples to follow the score function of the variational approximation, ∇log q(z[k]) with a RobbinsMonro stepsize schedule. This method, which we call Markovian score climbing (MSC), converges to a local optimum of the inclusive KL. It does not suffer from the systematic errors inherent in existing methods, such as Reweighted WakeSleep and Neural Adaptive Sequential Monte Carlo, which lead to bias in their final estimates. In a variant that ties the variational approximation directly to the Markov chain, MSC further provides a new algorithm that melds VI and MCMC. We illustrate convergence on a toy model and demonstrate the utility of MSC on Bayesian probit regression for classification as well as a stochastic volatility model for financial data.
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