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Boyan Beronov

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UAI Conference 2021 Conference Paper

Sequential core-set Monte Carlo

  • Boyan Beronov
  • Christian Weilbach
  • Frank Wood
  • Trevor Campbell

Sequential Monte Carlo (SMC) is a general-purpose methodology for recursive Bayesian inference, and is widely used in state space modeling and probabilistic programming. Its resample-move variant reduces the variance of posterior estimates by interleaving Markov chain Monte Carlo (MCMC) steps for particle “rejuvenation”; but this requires accessing all past observations and leads to linearly growing memory size and quadratic computation cost. Under the assumption of exchangeability, we introduce sequential core-set Monte Carlo (SCMC), which achieves constant space and linear time by rejuvenating based on sparse, weighted subsets of past data. In contrast to earlier approaches, which uniformly subsample or throw away observations, SCMC uses a novel online version of a state-of-the-art Bayesian core-set algorithm to incrementally construct a nonparametric, data- and model-dependent variational representation of the unnormalized target density. Experiments demonstrate significantly reduced approximation errors at negligible additional cost.

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NeurIPS Conference 2019 Conference Paper

Sparse Variational Inference: Bayesian Coresets from Scratch

  • Trevor Campbell
  • Boyan Beronov

The proliferation of automated inference algorithms in Bayesian statistics has provided practitioners newfound access to fast, reproducible data analysis and powerful statistical models. Designing automated methods that are also both computationally scalable and theoretically sound, however, remains a significant challenge. Recent work on Bayesian coresets takes the approach of compressing the dataset before running a standard inference algorithm, providing both scalability and guarantees on posterior approximation error. But the automation of past coreset methods is limited because they depend on the availability of a reasonable coarse posterior approximation, which is difficult to specify in practice. In the present work we remove this requirement by formulating coreset construction as sparsity-constrained variational inference within an exponential family. This perspective leads to a novel construction via greedy optimization, and also provides a unifying information-geometric view of present and past methods. The proposed Riemannian coreset construction algorithm is fully automated, requiring no problem-specific inputs aside from the probabilistic model and dataset. In addition to being significantly easier to use than past methods, experiments demonstrate that past coreset constructions are fundamentally limited by the fixed coarse posterior approximation; in contrast, the proposed algorithm is able to continually improve the coreset, providing state-of-the-art Bayesian dataset summarization with orders-of-magnitude reduction in KL divergence to the exact posterior.

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