Smoothing Structured Decomposable Circuits
This addresses a bottleneck in probabilistic inference for researchers and practitioners, though it is incremental as it builds on existing circuit structures.
The paper tackles the problem of smoothing structured decomposable circuits, which is essential for inference in probabilistic models, by proposing a near-linear time algorithm and a more efficient linear-time method for All-Marginals, with experimental validation.
We study the task of smoothing a circuit, i.e., ensuring that all children of a plus-gate mention the same variables. Circuits serve as the building blocks of state-of-the-art inference algorithms on discrete probabilistic graphical models and probabilistic programs. They are also important for discrete density estimation algorithms. Many of these tasks require the input circuit to be smooth. However, smoothing has not been studied in its own right yet, and only a trivial quadratic algorithm is known. This paper studies efficient smoothing for structured decomposable circuits. We propose a near-linear time algorithm for this task and explore lower bounds for smoothing decomposable circuits, using existing results on range-sum queries. Further, for the important case of All-Marginals, we show a more efficient linear-time algorithm. We validate experimentally the performance of our methods.