用深度拒绝采样逼近积和式
Approximating the Permanent with Deep Rejection Sampling
摘要：
给出了非负矩阵积和式的一个随机逼近方案。我们的方案扩展了Huber和Law（SODA 2008）的递归拒绝采样方法，通过在递归树的适度大深度处用子问题边界的线性组合替换永久性的上界。这种方法，我们称之为深度拒绝采样，经验证明优于基本的深度零变体，以及Kuck等人的相关方法（NeurIPS 2019）。我们分析了随机$(0, 1)$ -矩阵的预期运行时间的计划，其中每个条目是独立的$1$概率$p$。对于$p$小于$1/5$的情况，我们的界优于之前的界，与另一个已知的界相匹配，该界在每行和每列的密度都恰好为$p$时成立。
英文摘要：
We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the upper bound for the permanent with a linear combination of the subproblem bounds at a moderately large depth of the recursion tree. This method, we call deep rejection sampling, is empirically shown to outperform the basic, depth-zero variant, as well as a related method by Kuck et al. (NeurIPS 2019). We analyze the expected running time of the scheme on random $(0, 1)$-matrices where each entry is independently $1$ with probability $p$. Our bound is superior to a previous one for $p$ less than $1/5$, matching another bound that was known to hold when every row and column has density exactly $p$.
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