多面体中格点采样：一种带随机更新的贝叶斯偏置算法
Sampling lattice points in a polytope: a Bayesian biased algorithm with random updates
AI总结：
提出一种结合格基、贝叶斯偏置与逐步选择的多面体格点采样算法，能高效发现纤维，超越现有马尔可夫基采样器。
摘要：
多面体中的非负整数格点集合，也称为线性映射的纤维，在优化和统计等多个应用中都有出现。我们利用三个要素来解决从该集合中采样的问题：约束矩阵的易于计算的格基、具有贝叶斯框架的偏置采样算法，以及逐步选择方法。我们算法中嵌入的偏置会更新采样器参数，以提高每一步从先前发现的元素中选择的纤维发现率。我们在多个示例上展示了该算法的性能，包括最先进的马尔可夫基采样器无法处理的纤维。
英文摘要：
The set of nonnegative integer lattice points in a polytope, also known as the fiber of a linear map, makes an appearance in several applications including optimization and statistics. We address the problem of sampling from this set using three ingredients: an easy-to-compute lattice basis of the constraint matrix, a biased sampling algorithm with a Bayesian framework, and a step-wise selection method. The bias embedded in our algorithm updates sampler parameters to improve fiber discovery rate at each step chosen from previously discovered elements. We showcase the performance of the algorithm on several examples, including fibers that are out of reach for the state-of-the-art Markov bases samplers.
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