Algorithms for Learning from Spatiotemporal Data
Open AccessIn this work we develop algorithms for incorporating spatiotemporal information into learning algorithms. We apply our algorithms to two important problems: combining the predictions of a multi-model ensemble of climate models, and combining implied volatility predictions from an ensemble of financial securities. Our techniques are particularly relevant to both of these problems, as there is often a high variance between the predictions of different members of the ensemble.We focus on settings where an ensemble of experts makes multiple predictions over space and time. We propose three methods for combining the predictions of these experts: a Markov Random Field (MRF) based framework that defines the spatial and temporal probabilistic dependencies between the best expert at different locations and times, an online learning algorithm that uses a heuristic to incorporate spatial influence (which is capable of efficiently processing massive datasets), and an approach to using additional information from multiple forecast periods to further improve results.We also propose algorithms for detecting decay of influence in MRFs. When decay of influence exists, these algorithms allow us to isolate subsets of the MRF for marginal inference, rather than processing the entire graph. These methods potentially improve the efficiency of our MRF-based framework, and may have applicability in a number of other fields.In our climate model application, we use hindcasts of climate models and historical climate observation data to evaluate our methods. Our results demonstrate that our online method is a reasonable approximation for our MRF-based method, and both of these methods that incorporate spatial influence outperform simpler methods that do not model for spatial variation and influence. We then show that our approach to incorporating information from multiple forecast periods can lead to further improvements with seasonal climate models.Our financial application focuses on predicting volatility, which is important for financial stability and monitoring. Implied volatility predictions are derived from market prices of financial options using an option pricing model. These implied volatilities can be viewed as a prediction that the market is making for the volatility of the security over the option term. As such, we apply our techniques to combine different implied volatilities into a single prediction. We show that our method for utilizing multiple forecast periods can lead to improved volatility predictions.
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