基于E-MS算法的高斯图模型选择

发布时间：2018-05-15 13:53

本文选题：高斯图模型 + E-MS算法　；参考：《长春工业大学》2017年硕士论文

【摘要】：图模型是处理高维复杂问题的有力工具,已被广泛应用于生物信息学、机器学习等各个领域。图模型的模型选择作为图模型研究中的一个重要而具有挑战性的问题,倍受到了广大学者的关注。针对完全数据情形,Meinshausen and Bühlmann(2006),Yuan and Lin(2007)和Friedmam,Hastie and Tibshirani(2008)等提出了一系列最大化惩罚似然的图模型选择方法。针对缺失数据情形,St?dler and Bühlmann(2012)利用EM算法最大化惩罚观测似然;Thai,Hunter and Akametalu(2014)等提出了m-CCCP算法,该算法比EM收敛速度更快。然而,Jiang,Nguyen and Rao(2015)指出传统的基于EM的模型选择方法在处理这类问题时存在一定的局限性,并提出了比基于EM的模型选择方法更为有效E-MS算法,在一定的条件下证明了其相合性。在本文中,我们将利用E-MS算法进行含缺失数据情形下的高斯图模型的模型选择。首先我们介绍E-MS算法,然后给出基于E-MS算法的模型选择的具体步骤及相应的理论推导。对于图模型顶点个数为3、4和5的情形,我们通过模拟研究,比较了E-MS算法和传统的EM结合BIC方法的效果,验证了E-MS算法在处理高斯图模型选择问题时具有更高的准确度。但随着图模型顶点个数的增加,候选模型的数量呈指数级增加。E-MS算法每一次迭代的MS步中,最佳模型很难被选出。对于高维的高斯图模型选择问题,我们将用模拟退火(SA)算法对E-MS算法的MS步进行优化,通过随机搜索的方法找出当前迭代的最佳模型。我们给出了具体的优化方法和步骤,并通过数值模拟验证了E-MS结合SA方法的可行性。
[Abstract]:Graph model is a powerful tool to deal with high dimensional complex problems. It has been widely used in many fields such as bioinformatics machine learning and so on. As an important and challenging problem in the research of graph model, the model selection of graph model has attracted the attention of many scholars. In this paper, we propose a series of graph model selection methods for complete data such as and B 眉 hlmannn 2006 / Yuan and Linn 2007 and Friedmamn Hastie and Tibshirani 2008). In this paper, we propose a new m-CCCP algorithm for missing data, such as Standler and B 眉 hlmann (2012), using EM algorithm to maximize the penalty of observed likelihood, and so on. The proposed m-CCCP algorithm is faster than EM in convergence speed. However, Jiang Nguyen and Rao / 2015) points out that the traditional model selection method based on EM has some limitations in dealing with this kind of problems, and proposes a more effective E-MS algorithm than the model selection method based on EM, and proves its consistency under certain conditions. In this paper, we will use E-MS algorithm to select the model of the Gaustmap model with missing data. First, we introduce the E-MS algorithm, then give the specific steps of model selection based on E-MS algorithm and the corresponding theoretical derivation. For the case where the number of vertices of graph model is 3 ~ 4 and 5, we compare the effect of E-MS algorithm and traditional EM combined with BIC method, and verify that E-MS algorithm has higher accuracy in dealing with the problem of model selection of Gao Si graph. However, with the increase of vertex number of graph model, the number of candidate models increases exponentially. E-MS algorithm is difficult to select the best model in each iteration of MS step. For the high-dimensional model selection problem, we will use simulated annealing algorithm to optimize the MS step of E-MS algorithm, and find out the best model of the current iteration by random search method. The specific optimization methods and steps are given, and the feasibility of E-MS combined with SA method is verified by numerical simulation.
【学位授予单位】：长春工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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