The Normalized Float Trick: Numerical Stability for Probabilistic Circuits without the LogSumExp Trick

Pedro Zuidberg Dos Martires

Keywords: probabilistic circuits, tractable probabilistic models

TL;DR: A new scheme for numerical stable computations in probabilistic circuits.

Abstract: Probabilistic circuits (PCs) are a class of tractable deep probabilistic models that compute event probabilities by recursively nesting sum and product computations. Unfortunately, this is numerically unstable. To mitigate this numerical stability issues, PCs are usually evaluated in log-space via the LogSumExp trick. In this paper we present an alternative to the ubiquitous LogSumExp trick, which we dub "normalized float trick". Experimentally, we show that by simply changing the scheme guaranteeing numerical stability (from the LogSumExp to the normalized float trick) we can consistently and considerably boost the performance of PCs on common density estimation benchmarks,

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 6244