离散向量时间序列的条件Chow-Liu树结构建模
Conditional Chow-Liu Tree Structures for Modeling Discrete-Valued Vector Time Series
摘要：
我们考虑离散值向量时间序列数据的建模问题，使用扩展的Chow-Liu树模型来捕获跨时间的依赖关系和跨变量的依赖关系。作为对标准Chow-Liu树的扩展，引入了条件Chow-Liu树模型，用于建模条件密度而不是联合密度。我们描述了这种模型的学习算法，并展示了它们如何可以用来学习隐马尔可夫模型的输出分布的简约表示。并将这些模型应用于雨量站网逐日降水量的模拟和预报这一重要问题。为了证明模型的有效性，我们比较了它们的性能与一些替代品使用历史降水数据从澳大利亚西南部和美国西部。我们说明了如何的结构和参数的模型可以用来提供一个改进的气象解释这样的数据。
英文摘要：
We consider the problem of modeling discrete-valued vector time series data using extensions of Chow-Liu tree models to capture both dependencies across time and dependencies across variables. Conditional Chow-Liu tree models are introduced, as an extension to standard Chow-Liu trees, for modeling conditional rather than joint densities. We describe learning algorithms for such models and show how they can be used to learn parsimonious representations for the output distributions in hidden Markov models. These models are applied to the important problem of simulating and forecasting daily precipitation occurrence for networks of rain stations. To demonstrate the effectiveness of the models, we compare their performance versus a number of alternatives using historical precipitation data from Southwestern Australia and the Western United States. We illustrate how the structure and parameters of the models can be used to provide an improved meteorological interpretation of such data.
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