Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates
Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates
复制标题
学习高维马尔可夫森林分布：错误率分析
DOI：
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发表时间：
2010
影响因子：
6
通讯作者：
A. Willsky
中科院分区：
文献类型：
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作者：
V. Tan;Anima Anandkumar;A. Willsky
从独立同分布学习森林结构离散图模型的问题。样品被认为。提出了一种基于自适应阈值的Chow-Liu树剪枝算法。结果表明，该算法具有结构一致性和风险一致性，且在固定的模型规模下，结构学习的错误概率随样本数的衰减比任何多项式都快.对于模型的大小d和边数k与样本数n成比例的高维情形，给出了算法满足结构和风险约束的（n，d，k）充分条件.此外，学习的极值结构被确定;我们证明了独立的（分别，树）模型是最难的（相应地，最简单的）使用所提出的算法在结构学习的错误率方面学习。
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size. For the high-dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy structural and risk consistencies. In addition, the extremal structures for learning are identified; we prove that the independent (resp., tree) model is the hardest (resp., easiest) to learn using the proposed algorithm in terms of error rates for structure learning.