Nonparametric Mixture of Sparse Regressions on Spatio-Temporal Data -- An Application to Climate Prediction
Yumin Liu, Junxiang Chen, Auroop Ganguly and Jennifer Dy
Climate prediction is a very challenging problem. Many institutes around the world try to predict climate variables by building climate models called General Circulation Models (GCMs), which are based on mathematical equations that describe the physical processes. The prediction abilities of different GCMs may vary dramatically across different regions and time. Motivated by the need of identifying which GCMs are more useful for a particular region and time, we introduce a clustering model combining Dirichlet Process (DP) mixture of sparse linear regression with Markov Random Fields (MRFs). This model incorporates DP to automatically determine the number of clusters, imposes MRF constraints to guarantee spatio-temporal smoothness, and selects a subset of GCMs that are useful for prediction within each spatio-temporal cluster with a spike-and-slab prior. We derive an effective Gibbs sampling method for this model. Experimental results are provided for both synthetic and real-world climate data.
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