Approximate arithmetic circuits

Approximate Inference by Compilation to Arithmetic Circuits

Arithmetic circuits (ACs) exploit context-specific independence and determinism to allow exact inference even in networks with high treewidth. In this paper, we introduce the first ever approximate inference methods using ACs, for domains where exact inference remains intractable. We propose and evaluate a variety of techniques based on exact compilation, forward sampling, AC structure learning...

Design of Energy - Efficient Approximate Arithmetic Circuits

Learning Arithmetic Circuits

Graphical models are usually learned without regard to the cost of doing inference with them. As a result, even if a good model is learned, it may perform poorly at prediction, because it requires approximate inference. We propose an alternative: learning models with a score function that directly penalizes the cost of inference. Specifically, we learn arithmetic circuits with a penalty on the ...

Lazy Arithmetic Circuits

Compiling a Bayesian network into a secondary structure, such as a junction tree or arithmetic circuit allows for offline computations before observations arrive, and quick inference for the marginal of all variables. However, query-based algorithms, such as variable elimination and recursive conditioning, that compute the posterior marginal of few variables given some observations, allow pruni...

Algorithms for Arithmetic Circuits

Given a multivariate polynomial f(X) ∈ F[X] as an arithmetic circuit we would like to efficiently determine: 1. Identity Testing. Is f(X) identically zero? 2. Degree Computation. Is the degree of the polynomial f(X) at most a given integer d . 3. Polynomial Equivalence. Upto an invertible linear transformation of its variables, is f(X) equal to a given polynomial g(X). The algorithmic complexit...