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大尺度高斯马尔可夫随机场的方差逼近

Variance Approximation in Large-Scale Gaussian Markov Random Fields
课程网址: http://videolectures.net/icml09_malioutov_itva/  
主讲教师: Dmitry Malioutov
开课单位: 麻省理工学院
开课时间: 2009-08-26
课程语种: 英语
中文简介:
在本次演讲中,我们讨论了在大规模高斯马尔可夫随机场中计算精确近似方差的框架。我们首先要激发计算GMRF差异的需求,并讨论机器学习中的相关问题。我们的方法基于构建某个低秩混叠矩阵,该矩阵利用了模型的马尔可夫图。我们首先为具有短距离相关性的模型构造这样的矩阵,然后描述基于小波的构造,用于具有长程相关的模型。该方法基于稀疏线性系统的快速求解,并且我们描述了合适的预处理器。我们还描述了该方法如何用于稀疏加低秩结构的问题,例如在具有大状态空间的近似卡尔曼滤波中。
课程简介: In this talk we discuss a framework for computing accurate approximate variances in large scale Gaussian Markov Random Fields. We start by motivating the need to compute variances in GMRFs, and discuss related problems in machine learning. Our approach is based on constructing a certain low-rank aliasing matrix which takes advantage of the Markov graph of the model. We first construct such a matrix for models with short-range correlation, and then describe a wavelet-based construction for models with long-range correlation. The approach is based on fast solution of sparse linear systems, and we describe suitable preconditioners. We also describe how the approach can be used for problems with sparse plus low-rank structure, for example in approximate Kalman filtering with large state spaces.
关 键 词: 高斯马尔可夫随机场; 精确近似方差; 器学习
课程来源: 视频讲座网
最后编审: 2019-04-23:lxf
阅读次数: 75