Abstract
Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem).
Highlights
Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models
We found that in a deep neural network, the computational overhead of generating a small set of samples for prediction amounts to ∼30% of the cost of training the initial variational approximation; the refinement process is able to generate a set of high-quality posterior samples at the cost of a small computational overhead
Qref be the evidence lower bound (ELBO) accounting for the auxiliary variables, and let ELBOinit = E log p(y| x, w) − KL qφ0 (w) || p(w) qφ0 be the ELBO of the initial variational approximation
Summary
Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. By marginalizing over a posterior distribution over the parameters given the training data, Bayesian inference provides a principled approach to capturing uncertainty. The mean-field approximation is easy to train, but it fails to capture dependencies and multi-modality in the true posterior. We show that through this process, we can generate samples that capture both dependencies and multi-modality in the true posterior
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