Granger Causality Analysis with Hidden Variables in Climate Science Applications

The data-centric discovery of the influence patterns in climate systems relies solely on the observation of climate quantities such as temperature, precipitation and wind speed. Compared to the traditional method of simulation of climate systems using the physical properties of the environment, the data-centric approach provides a faster and less expensive alternative solution for many climatology tasks. The data-cetric approach has been successfully applied to variety of climate science tasks such as climate change study [7], global climate dependence [11], tracking climate models [8] and drought detection [4]. The data-centric approach requires observations of all major quantities in a climate system which can be expensive or even not viable in some cases. Thus the ability to allow existence of few hidden variables in the analysis makes the analysis significantly more accurate and realistic. The hidden time series can be the quantities that are hard to measure, corrupted measurements or even immeasurable abstract entities. In this paper we study the task of identification of the influence graph in the climate systems with the assumption that there are few unobserved variables. We show how the stability of time series can help identifiability of the model and propose a convex optimization problem to find the globally optimal solution.