使用Givens旋转求解用于学习高斯网络的所有回归模型
Solving All Regression Models For Learning Gaussian Networks Using Givens Rotations
AI总结：
针对贝叶斯网络学习中需计算大量回归模型的问题，提出结合QR分解与Givens旋转的高效精确算法，复杂度低于现有同类算法且支持并行化加速。
摘要：
基于评分的学习（SBL）是一种很有前景的贝叶斯网络学习方法。大多数SBL算法的初始步骤是计算变量所有可能的子节点与父节点集组合的评分。对于含连续变量的贝叶斯网络，特定评分通常通过子节点对父节点集变量的回归函数来计算。待求解的回归模型数量极为庞大，因此需要设计高效的数值算法。本文提出一种算法，可高效且精确地计算所有子节点与父节点集组合的回归结果。该算法利用QR分解（QRD）来捕捉不同族系回归之间的依赖关系，并借助Givens旋转高效遍历QRD空间，从而以尽可能短的路径覆盖所有回归模型。我们将所提方法与不同算法（主要是所有子集回归问题中出现的算法）进行了复杂度对比，结果表明本文算法的算法复杂度最低。我们还说明了如何对所提方法进行并行化处理，使其运行时间可按与所用处理器数量成正比的比例缩短。
英文摘要：
Score based learning (SBL) is a promising approach for learning Bayesian networks. The initial step in the majority of the SBL algorithms consists of computing the scores of all possible child and parent-set combinations for the variables. For Bayesian networks with continuous variables, a particular score is usually calculated as a function of the regression of the child over the variables in the parent-set. The sheer number of regressions models to be solved necessitates the design of efficient numerical algorithms. In this paper, we propose an algorithm for an efficient and exact calculation of regressions for all child and parent-set combinations. In the proposed algorithm, we use QR decompositions (QRDs) to capture the dependencies between the regressions for different families and Givens rotations to efficiently traverse through the space of QRDs such that all the regression models are accounted for in the shortest path possible. We compare the complexity of the suggested method with different algorithms, mainly those arising in all subset regression problems, and show that our algorithm has the smallest algorithmic complexity. We also explain how to parallelize the proposed method so as to decrease the runtime by a factor proportional to the number of processors utilized.
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。
