Variational DAG Estimation via State Augmentation With Stochastic Permutations

• URL: http://arxiv.org/abs/2402.02644v3
• Date: Tue, 28 May 2024 05:30:01 GMT
• Title: Variational DAG Estimation via State Augmentation With Stochastic Permutations
• Authors: Edwin V. Bonilla, Pantelis Elinas, He Zhao, Maurizio Filippone, Vassili Kitsios, Terry O'Kane,
• Abstract summary: Estimating the structure of a Bayesian network from observational data is a statistically and computationally hard problem. From a probabilistic inference perspective, the main challenges are (i) representing distributions over graphs that satisfy the DAG constraint and (ii) estimating a posterior over the underlying space. We propose an approach that addresses these challenges by formulating a joint distribution on an augmented space of DAGs and permutations.
• Score: 16.57658783816741
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Estimating the structure of a Bayesian network, in the form of a directed acyclic graph (DAG), from observational data is a statistically and computationally hard problem with essential applications in areas such as causal discovery. Bayesian approaches are a promising direction for solving this task, as they allow for uncertainty quantification and deal with well-known identifiability issues. From a probabilistic inference perspective, the main challenges are (i) representing distributions over graphs that satisfy the DAG constraint and (ii) estimating a posterior over the underlying combinatorial space. We propose an approach that addresses these challenges by formulating a joint distribution on an augmented space of DAGs and permutations. We carry out posterior estimation via variational inference, where we exploit continuous relaxations of discrete distributions. We show that our approach performs competitively when compared with a wide range of Bayesian and non-Bayesian benchmarks on a range of synthetic and real datasets.

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