标题： 关于图模型的一类更广泛的先验分布 显示英文标题

标题： On a wider class of prior distributions for graphical models

摘要： 高斯图模型是推断多元随机变量条件独立结构的有用工具。不幸的是，由于$\mathcal{G}_n$（所有顶点为$n$的图的集合）呈指数增长，潜图结构的贝叶斯推断具有挑战性。为了解决这个问题，有人提出了一种方法，即将搜索限制在$\mathcal{G}_n$的子集上。本文研究了以循环空间$\mathcal{C}_n$为主例的向量子空间。我们基于循环基元的线性组合提出了一个关于$\mathcal{C}_n$的新先验，并介绍了其理论性质。利用这个先验，我们实现了一个马尔可夫链蒙特卡洛算法，结果显示：(i) 使用我们的技术计算出的后验边包含估计与标准技术的结果相当，尽管搜索的是更小的图空间；(ii) 向量空间视角使得马尔可夫链蒙特卡洛算法的实现变得简单直接。 显示英文摘要

摘要： Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of $\mathcal{G}_n$, the set of all graphs in $n$ vertices. One approach that has been proposed to tackle this problem is to limit search to subsets of $\mathcal{G}_n$. In this paper, we study subsets that are vector subspaces with the cycle space $\mathcal{C}_n$ as main example. We propose a novel prior on $\mathcal{C}_n$ based on linear combinations of cycle basis elements and present its theoretical properties. Using this prior, we implement a Markov chain Monte Carlo algorithm, and show that (i) posterior edge inclusion estimates computed with our technique are comparable to estimates from the standard technique despite searching a smaller graph space, and (ii) the vector space perspective enables straightforward implementation of MCMC algorithms.