Conditional Chow-Liu Tree Structures for Modeling Discrete-Valued Vector Time Series

TL;DR

This paper introduces Conditional Chow-Liu tree models for discrete vector time series, capturing temporal and variable dependencies, and demonstrates their effectiveness in precipitation forecasting and interpretation.

Contribution

The paper extends Chow-Liu trees to conditional models for vector time series, providing new learning algorithms and applications in meteorology.

Findings

Effective in modeling precipitation data

Improved forecasting accuracy over alternatives

Enhanced interpretability of meteorological data

Abstract

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.