Variational DAG Estimation via State Augmentation With Stochastic Permutations
This work addresses causal discovery and uncertainty quantification in Bayesian networks, but it is incremental as it builds on existing variational and permutation-based methods.
The paper tackles the problem of estimating Bayesian network structures (DAGs) from observational data by proposing a variational inference method that uses state augmentation with stochastic permutations, and it shows competitive performance compared to various benchmarks on synthetic and real datasets.
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.