在高斯图模型中学习块结构图
Learning block structured graphs in Gaussian graphical models
AI总结：
本文提出一种在高斯图模型中学习块结构图的方法，通过双可逆跳跃MCMC算法在G-Wishart先验下实现块结构学习，并应用于函数型数据的平滑与条件独立结构估计。
摘要：
在高斯图模型的框架下，我们引入了一个关于底层图的先验分布，以诱导图的邻接矩阵产生块结构，并学习固定变量组之间的关系。我们开发了一种名为“双可逆跳跃马尔可夫链蒙特卡洛”的新型采样策略，用于在共轭G-Wishart先验下进行块结构学习。该算法提出的移动不仅添加或删除单个链接，而是添加或删除整组边。随后，该方法被应用于平滑函数型数据。通过将图模型置于基展开系数上，经典平滑过程得到改进，从而提供了其条件独立结构的估计。由于B样条基的元素具有紧支撑，该独立结构反映在定义明确的定义域部分上。我们利用函数域的一个已知划分来研究化合物中各物质之间的关系。
英文摘要：
Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for block structural learning, under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single link but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional independence structure. Since the elements of a B-Spline basis have compact support, the independence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among the substances within the compound.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
