论文标题
不使用分区树的贝叶斯多尺度建模
Bayesian Multi-scale Modeling of Factor Matrix without using Partition Tree
论文作者
论文摘要
多尺度因子模型对于分析矩阵或张量值数据特别有吸引力，因为它们对局部几何形状和直观解释的适应性。但是，对二进制树的依赖在参数空间中创造了很高的复杂性，因此量化其不确定性极为挑战。在本文中，我们发现了一种使用简单矩阵操作生成多尺度矩阵的替代方法：从随机矩阵开始，每列具有两个唯一的值，其Cholesky Whitening Transform Transform obeys obeys obeys递归分区结构。这使我们能够考虑在常见的多尺度因子模型上具有大量支持的生成分布，并通过汉密尔顿蒙特卡洛（Monte Carlo）进行有效的后验计算。我们在多尺度因素模型中证明了它的潜力，以找到人脑连接性的更广泛的兴趣区域。
The multi-scale factor models are particularly appealing for analyzing matrix- or tensor-valued data, due to their adaptiveness to local geometry and intuitive interpretation. However, the reliance on the binary tree for recursive partitioning creates high complexity in the parameter space, making it extremely challenging to quantify its uncertainty. In this article, we discover an alternative way to generate multi-scale matrix using simple matrix operation: starting from a random matrix with each column having two unique values, its Cholesky whitening transform obeys a recursive partitioning structure. This allows us to consider a generative distribution with large prior support on common multi-scale factor models, and efficient posterior computation via Hamiltonian Monte Carlo. We demonstrate its potential in a multi-scale factor model to find broader regions of interest for human brain connectivity.
