论文标题
固定边缘二进制矩阵的不均匀采样
Non-Uniform Sampling of Fixed Margin Binary Matrices
论文作者
论文摘要
二元矩阵形式的数据集在科学领域之间无处不在，研究人员通常有兴趣识别和量化值得注意的结构。一种方法是将观察到的数据与在零模型下可能获得的数据进行比较。在这里，我们考虑从满足一组边缘行和列总和的二进制矩阵空间进行采样。尽管现有的采样方法集中在该空间的均匀采样上，但我们引入了两个元素交换算法的修改版本，这些算法根据由权重矩阵定义的非均匀概率分布进行采样，这给出了每个条目的相对概率。我们证明，重量矩阵中的零值，即结构零，通常对于交换算法是有问题的，除非它们具有特殊的单调结构。我们通过仿真研究探讨了算法的特性，并说明了使用经典的鸟类居住数据集使用不均匀的无效模型的潜在影响。
Data sets in the form of binary matrices are ubiquitous across scientific domains, and researchers are often interested in identifying and quantifying noteworthy structure. One approach is to compare the observed data to that which might be obtained under a null model. Here we consider sampling from the space of binary matrices which satisfy a set of marginal row and column sums. Whereas existing sampling methods have focused on uniform sampling from this space, we introduce modified versions of two elementwise swapping algorithms which sample according to a non-uniform probability distribution defined by a weight matrix, which gives the relative probability of a one for each entry. We demonstrate that values of zero in the weight matrix, i.e. structural zeros, are generally problematic for swapping algorithms, except when they have special monotonic structure. We explore the properties of our algorithms through simulation studies, and illustrate the potential impact of employing a non-uniform null model using a classic bird habitation dataset.
