论文标题
改进了具有给定的行和列总和的非阴性整数矩阵数量的估计值
Improved estimates for the number of non-negative integer matrices with given row and column sums
论文作者
论文摘要
具有给定的行和列总和的非阴性整数矩阵的数量出现在数学和统计中的各种问题中，但尚无封闭形式的表达，因此我们依靠各种类型的近似值。在这里，我们描述了一个新的近似值，这是由考虑非全列数量的矩阵统计数据所激发的。可以在矩阵的大小上进行线性评估该估计值，并返回准确性的结果，比广泛的设置范围内的现有线性时间近似值一样好或更好。我们还使用此新估计值作为改进的数值方法的起点，用于使用顺序重要性采样来计数或采样矩阵。提供了实施我们方法的代码。
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we describe a new such approximation, motivated by consideration of the statistics of matrices with non-integer numbers of columns. This estimate can be evaluated in time linear in the size of the matrix and returns results of accuracy as good as or better than existing linear-time approximations across a wide range of settings. We also use this new estimate as the starting point for an improved numerical method for either counting or sampling matrices using sequential importance sampling. Code implementing our methods is provided.
