Beyond Bayesian Model Averaging over Paths in Probabilistic Programs with Stochastic Support

• URL: http://arxiv.org/abs/2310.14888v2
• Date: Fri, 12 Apr 2024 14:36:18 GMT
• Title: Beyond Bayesian Model Averaging over Paths in Probabilistic Programs with Stochastic Support
• Authors: Tim Reichelt, Luke Ong, Tom Rainforth,
• Abstract summary: We show that making predictions with this full posterior implicitly performs a Bayesian model averaging (BMA) over paths. We propose alternative mechanisms for path weighting: one based on stacking and one based on ideas from PAC-Bayes.
• Score: 20.53123189114551
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The posterior in probabilistic programs with stochastic support decomposes as a weighted sum of the local posterior distributions associated with each possible program path. We show that making predictions with this full posterior implicitly performs a Bayesian model averaging (BMA) over paths. This is potentially problematic, as BMA weights can be unstable due to model misspecification or inference approximations, leading to sub-optimal predictions in turn. To remedy this issue, we propose alternative mechanisms for path weighting: one based on stacking and one based on ideas from PAC-Bayes. We show how both can be implemented as a cheap post-processing step on top of existing inference engines. In our experiments, we find them to be more robust and lead to better predictions compared to the default BMA weights.

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