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

02/25/2021

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by   Tatsuya Matsuoka, et al.

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We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph G=(V,E) and a positive semi-definite matrix 𝐀 indexed by E, a spanning-tree DPP defines a distribution such that we draw S⊆ E with probability proportional to (𝐀_S) only if S induces a spanning tree. We prove ♯-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.