A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queries
This work provides a unified framework for tractable inference in machine learning, generalizing existing results and enabling new scenarios, though it is incremental in building on prior circuit-based methods.
The paper tackles the problem of performing complex inference tasks on tractable circuit models by showing that these tasks can be represented as modular operations over circuits, with results including novel hardness proofs for cases where structural constraints are not met.
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine learning -- from computing the expectations of decision tree ensembles to information-theoretic divergences of deep mixture models -- can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability of a vocabulary of simple transformations -- sums, products, quotients, powers, logarithms, and exponentials -- in terms of sufficient structural constraints of the circuits they operate on, and present novel hardness results for the cases in which these properties are not satisfied. Building on these operations, we derive a unified framework for reasoning about tractable models that generalizes several results in the literature and opens up novel tractable inference scenarios.