Integrating Transformations in Probabilistic Circuits

TL;DR

This paper enhances probabilistic circuits by integrating transformations, enabling higher likelihoods and more efficient sampling, with applications demonstrated in robotic scenarios and benchmark datasets.

Contribution

It introduces a novel extension of joint probability trees with transformations, improving likelihoods and parameter efficiency in probabilistic models.

Findings

Higher likelihoods achieved with fewer parameters.

Effective integration of transformations into tree-based learning.

Enables efficient sampling and approximate inference.

Abstract

This study addresses the predictive limitation of probabilistic circuits and introduces transformations as a remedy to overcome it. We demonstrate this limitation in robotic scenarios. We motivate that independent component analysis is a sound tool to preserve the independence properties of probabilistic circuits. Our approach is an extension of joint probability trees, which are model-free deterministic circuits. By doing so, it is demonstrated that the proposed approach is able to achieve higher likelihoods while using fewer parameters compared to the joint probability trees on seven benchmark data sets as well as on real robot data. Furthermore, we discuss how to integrate transformations into tree-based learning routines. Finally, we argue that exact inference with transformed quantile parameterized distributions is not tractable. However, our approach allows for efficient sampling and approximate inference.