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 sum-product networks---can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability 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.

A Compositional Atlas of Tractable Circuit Operations for Probabilistic Inference / Vergari, Antonio; Choi, Yoojung; Liu, Anji; Teso, Stefano; Van den Broeck, Guy. - ELETTRONICO. - (2021). ((Intervento presentato al convegno NeurIPS tenutosi a online nel 6th Dec-14thDec 2021.

A Compositional Atlas of Tractable Circuit Operations for Probabilistic Inference

Teso, Stefano;
2021

Abstract

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 sum-product networks---can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability 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.
Advances in neural information processing systems
online
NeurIPS foundation
Vergari, Antonio; Choi, Yoojung; Liu, Anji; Teso, Stefano; Van den Broeck, Guy
A Compositional Atlas of Tractable Circuit Operations for Probabilistic Inference / Vergari, Antonio; Choi, Yoojung; Liu, Anji; Teso, Stefano; Van den Broeck, Guy. - ELETTRONICO. - (2021). ((Intervento presentato al convegno NeurIPS tenutosi a online nel 6th Dec-14thDec 2021.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/323847
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