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A Quantum Information Theoretic Approach to Tractable Probabilistic Models

Created by
  • Haebom

Author

Pedro Zuidberg's Martyrs

Outline

In this paper, we study machine learning models based on probabilistic circuits using the framework of quantum information theory. Probabilistic circuits have emerged as an attractive class of generative models that allow polynomial-time bounding of random variables by recursively nesting sums and products. In this work, we present Positive Unital Circuits (PUnCs), which generalize circuit evaluation for positive real-valued probabilities to circuit evaluation for positive semi-definite matrices. As a result, PUnCs generalize not only probabilistic circuits but also a class of circuits such as PSD circuits that were introduced recently.

Takeaways, Limitations

Takeaways: By analyzing probabilistic circuits from the perspective of quantum information theory and proposing a new model, PUnCs, we deepen the theoretical understanding of probabilistic circuits and provide expanded modeling capabilities. We provide a general framework that generalizes existing probabilistic circuits and PSD circuits.
Limitations: There is a lack of experimental analysis on the practical applications and performance of PUnCs. Further research on the learning algorithms and efficiency of PUnCs is needed. Since this paper focuses on the theoretical definition and generalization of PUnCs, application to real datasets and performance comparison remain as future research tasks.
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