Integrating Transformations in Probabilistic Circuits
Tom Schierenbeck Vladimir Vutov Thorsten Dickhaus Michael Beetz
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.