Restricted Search Space Graph MCMC via Birth-Death Processes
Morris Greenberg, Kieran R Campbell, Radu Craiu

TL;DR
This paper introduces a dynamic MCMC method with birth-death processes for DAG inference that adaptively adjusts the search space, reducing approximation error compared to fixed-restriction methods.
Contribution
It derives bounds on the error of restricted search space MCMC and proposes a flexible sampler that dynamically expands or contracts the search space.
Findings
Bounds characterize when approximation error is negligible.
The proposed sampler reduces error by adaptively changing the search space.
Simulation studies demonstrate finite-sample performance improvements.
Abstract
Inferring directed acyclic graphs (DAGs) from data via Markov chain Monte Carlo (MCMC) is computationally challenging in moderate-to-high dimensional settings because their discrete sampling space grows super-exponentially with the number of nodes. To address scalability, several recent MCMC-based graph inference methods restrict the search space to a subset of edges, at the cost of introducing error into the inference procedure. In this work, we derive sharp lower and upper bounds on the total variation distance between the unrestricted posterior distribution and the posterior distribution induced by a state-of-the-art restricted search space MCMC method. These bounds characterize regimes in which the approximation error is negligible and regimes in which it is not. In order to reduce the error, we propose a flexible transdimensional MCMC sampler which allows the search space to…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
