A Quantum Information Theoretic Approach to Tractable Probabilistic Models
This work provides a novel theoretical framework for generative models, potentially enabling more expressive tractable probabilistic modeling, though it appears incremental as it builds on existing circuit classes.
The authors tackled the problem of generalizing probabilistic circuits by introducing positive unital circuits (PUnCs), which extend evaluations from real-valued probabilities to positive semi-definite matrices, resulting in a strict generalization that includes probabilistic circuits and PSD circuits.
By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.