生成树约束的行列式点过程很难（近似）评估
Spanning Tree Constrained Determinantal Point Processes are Hard to (Approximately) Evaluate
摘要：
本文研究了生成树约束下的决定点过程。给定图$G=(V,E)$和由$E$索引的半正定矩阵$\mathbf{A}$，生成树DPP定义了一个分布，使得仅当$S$诱导生成树时，我们才以与$\det(\mathbf{A}_S)$成比例的概率绘制$S\subseteq E$。我们证明了$\sharp\textsf{P}$ -计算生成树DPPs的归一化常数的困难，并提供了一个近似保持减少从混合判别式，FPRAS是未知的。我们显示了类似的结果，受森林约束的DPP。
英文摘要：
We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph $G=(V,E)$ and a positive semi-definite matrix $\mathbf{A}$ indexed by $E$, a spanning-tree DPP defines a distribution such that we draw $S\subseteq E$ with probability proportional to $\det(\mathbf{A}_S)$ only if $S$ induces a spanning tree. We prove $\sharp\textsf{P}$-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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
