SymCircuit: Bayesian Structure Inference for Tractable Probabilistic Circuits via Entropy-Regularized Reinforcement Learning
Probabilistic circuit (PC) structure learning is hampered by greedy algorithms that make irreversible, locally optimal decisions. We propose SymCircuit, which replaces greedy search with a learned generative policy trained via entropy-regularized reinforcement learning. Instantiating the RL-as-inference framework in the PC domain, we show the optimal policy is a tempered Bayesian posterior, recovering the exact posterior when the regularization temperature is set inversely proportional to the dataset size. The policy is implemented as SymFormer, a grammar-constrained autoregressive Transformer with tree-relative self-attention that guarantees valid circuits at every generation step. We introduce option-level REINFORCE, restricting gradient updates to structural decisions rather than all tokens, yielding an SNR (signal to noise ratio) improvement and >10 times sample efficiency gain on the NLTCS dataset. A three-layer uncertainty decomposition (structural via model averaging, parametric via the delta method, leaf via conjugate Dirichlet-Categorical propagation) is grounded in the multilinear polynomial structure of PC outputs. On NLTCS, SymCircuit closes 93% of the gap to LearnSPN; preliminary results on Plants (69 variables) suggest scalability.
Code (0)
등록된 구현이 없습니다.
Tasks
Reinforcement LearningSimilar Papers 제목 키워드 기반
The Libra Toolkit for Probabilistic Models
The Libra Toolkit is a collection of algorithms for learning and inference with discrete probabilistic models, including Bayesian networks, Markov networks, dependency networks, and sum-product networks. Compared to othe…
Bayesian Structure Scores for Probabilistic Circuits
Probabilistic circuits (PCs) are a prominent representation of probability distributions with tractable inference. While parameter learning in PCs is rigorously studied, structure learning is often more based on heuristi…
Tractable Uncertainty for Structure Learning
Bayesian structure learning allows one to capture uncertainty over the causal directed acyclic graph (DAG) responsible for generating given data. In this work, we present Tractable Uncertainty for STructure learning (TRU…
Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as …
Learning Credal Sum-Product Networks
Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main …