# Integrating Transformations in Probabilistic Circuits

arXiv: https://arxiv.org/abs/2310.04354 · HTML: https://mlsanity.com/paper/2310.04354/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 4 of 4)

- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [Explainable boosted linear regression for time series forecasting](https://mlsanity.com/paper/2009.09110/) (2020)
- [Regression-Enhanced Random Forests](https://mlsanity.com/paper/1904.10416/) (2019)
- [Joint Probability Trees](https://mlsanity.com/paper/2302.07167/) (2023)

## Abstract (arXiv)

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.