Granger causality for time series states that a cause improves the predictability of its effect. That is, given two time series x and y, we are interested in detecting the causal relations among them considering the previous observations of both time series. Although, most of the algorithms are designed for causal inference among homogeneous processes where only time series from a specific distribution (mostly Gaussian) are given, many applications generate a mixture of various time series from different distributions. We utilize Generalized Linear Models (GLM) to propose a general information-theoretic framework for causal inference on heterogeneous data sets. We regard the challenge of causality detection as a data compression problem employing the Minimum Description Length (MDL) principle. By balancing the goodness-of-fit and the model complexity we automatically find the causal relations. Extensive experiments on synthetic and real-world data sets confirm the advantages of our algorithm ITGH (for Information-Theoretic Granger causal inference on Heterogeneous data) compared to other algorithms.

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