In particular, we introduce the notion of a hierarchical route distribution and show how they can be leveraged to construct tractable PSDDs over route distributions, allowing them to scale to larger maps.

PSDD, and then multiply them.

These properties are used implicitly in exact inference, but are difficult to harness for approximate inference.

Finally, we illustrate how our framework can be used for exploratory data analysis.

We study the task of smoothing a circuit, i.e., ensuring that all children of a

Thank you all for the helpful reviews. "and the goal is to figure out what type of object each pixel corresponds to" [Forouzan, 2015]. As suggested, we will run and report experiments on more networks, for a more comprehensive picture of our algorithm. We will focus more on the real-world networks. Segmentation-11 details... See above section on experiments .

These properties are used implicitly in exact inference, but are difficult to harness for approximate inference.

We study the task of smoothing a circuit, i.e., ensuring that all children of a

Tractable learning aims to learn probabilistic models where inference is guaranteed to be efficient. However, the particular class of queries that is tractable depends on the model and underlying representation. Usually this class is MPE or conditional probabilities Pr(x |y) for joint assignments x, y . We propose a tractable learner that guarantees efficient inference for a broader class of queries. It simultaneously learns a Markov network and its tractable circuit representation, in order to guarantee and measure tractability. Our approach differs from earlier work by using Sentential Decision Diagrams (SDD) as the tractable language instead of Arithmetic Circuits (AC). SDDs have desirable properties, which more general representations such as ACs lack, that enable basic primitives for Boolean circuit compilation. This allows us to support a broader class of complex probability queries, including counting, threshold, and parity, in polytime.