New research explores complexity of succinct conditional distribution compatibility

This paper explores the complexity of determining compatibility between conditional probability distributions when they are represented succinctly, such as through arithmetic circuits. The research demonstrates that for these succinct representations, the compatibility problem becomes intractable. Specifically, when all probabilities are non-zero, the problem is co-NP-complete, and when probabilities can be zero, several versions of the problem are PSPACE-complete. The findings also suggest that compatible succinct conditionals may exist whose joint distribution cannot be succinctly expressed, with implications for high-dimensional probabilistic modeling and machine learning. AI

IMPACT This research could impact how high-dimensional probabilistic models, including neural networks, are designed and analyzed for compatibility.

RANK_REASON The item is a research paper submitted to arXiv cs.LG. [lever_c_demoted from research: ic=1 ai=1.0]

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