高维阶乘隐马尔可夫模型中局部性的利用
Exploiting locality in high-dimensional factorial hidden Markov models
摘要：
我们提出了近似滤波和平滑算法在高维阶乘隐马尔可夫模型。近似涉及以原则性的方式根据与发射分布相关联的因子图中的局部性的概念丢弃似然因子。这允许避免精确滤波和平滑的指数维度成本。我们证明了近似精度，在当地的总变差范数测量，是“无量纲”的意义上说，作为模型的整体尺寸的增加，我们得出的误差范围不一定会降低。分析中的一个关键步骤是量化贝叶斯规则更新中局部化似然函数所引入的误差。当数据具有已知的空间或网络结构时，我们利用的似然函数的阶乘结构自然出现。我们证明了新的算法合成的例子和伦敦地铁客流问题，其中的因素图是有效地由训练网络。
英文摘要：
We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.
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