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.

翻译：多面体中的非负整数格点集（也称为线性映射的纤维）在优化和统计等多个应用中均有涉及。我们利用三个要素解决该集合的采样问题：约束矩阵的易计算格基、基于贝叶斯框架的偏置采样算法以及逐步选择方法。算法中嵌入的偏置通过更新采样器参数，在每步从先前发现的元素中选择，从而提高纤维发现率。我们通过多个实例展示了该算法的性能，包括现有最先进马尔可夫基采样器无法处理的纤维情况。