Spanning Tree Constrained Determinantal Point Processes are Hard to (Approximately) Evaluate

02/25/2021
āˆ™
by   Tatsuya Matsuoka, et al.
āˆ™
0
āˆ™

We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph G=(V,E) and a positive semi-definite matrix š€ indexed by E, a spanning-tree DPP defines a distribution such that we draw SāŠ† E with probability proportional to (š€_S) only if S induces a spanning tree. We prove ā™Æ-hardness of computing the normalizing constant for spanning-tree DPPs and provide an approximation-preserving reduction from the mixed discriminant, for which FPRAS is not known. We show similar results for DPPs constrained by forests.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset