Product Monte Carlo: Expectation Under a Product of Densities

Key points

• Aggregating independently computed sub-sample inferences is a well-known challenge in large-scale Bayesian computation, federated learning, and opinion pooling.1
• The core problem is to approximate a distribution whose density is proportional to a product of individual densities.1
• We turn the intractable product expectation into a regression problem by expressing it through a family of computable conditional expectations.1
• In addition, PMC requires no density evaluation, making it applicable to simulation-based inference, as we demonstrate in an application with protein images.1

Sources (1)

• [1]Product Monte Carlo: Expectation Under a Product of Densities
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 08:33 PM

  We propose Product Monte Carlo (PMC), an algorithm for computing arbitrary expectations under a product of densities using only Monte Carlo draws from individual densities.

  Aggregating independently computed sub-sample inferences is a well-known challenge in large-scale Bayesian computation, federated learning, and opinion pooling.

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