Statistical Causality: Revisiting Non-parametric Granger Causality From The Viewpoint Of Unsupervised Learning
While correlation measures are used to discern statistical relationships between observed variables in almost all branches of data-driven scientific inquiry, what we are really interested in is the existence of causal dependence. Designing an efficient causality test, that may be carried out in the absence of restrictive pre-suppositions on the underlying dynamical structure of the data at hand, is non-trivial. Nevertheless, ability to computationally infer statistical prima facie evidence of causal dependence may yield a far more discriminative tool for data analysis compared to the calculation of simple correlations. In the present work, we present a new non-parametric test of Granger causality for quantized or symbolic data streams generated by ergodic stationary sources.
In contrast to state-of-art binary tests, our approach makes precise and computes the degree of causal dependence between data streams, without making any restrictive assumptions, linearity or otherwise. Additionally, without any a priori imposition of specific dynamical structure, we infer explicit generative models of causal cross-dependence, which may be then used for prediction. These explicit models are represented as generalized probabilistic automata, referred to crossed automata, and are shown to be sufficient to capture a fairly general class of causal dependence.
The proposed algorithms are computationally efficient in the PAC sense; i.e., we find good models of cross-dependence with high probability, with polynomial run-times and sample complexities.
Causality In Search Trends: The theoretical results are applied to weekly search-frequency data from Google Trends API for a chosen set of socially "charged" keywords. The causality network inferred from this dataset reveals, quite expectedly, the causal importance of certain keywords. It is also illustrated that correlation analysis fails to gather such insight.
Causality In Retroviral Mutational Dynamics: The HIV virus is highly mutagenic. Using the large database of seuquences isolated from patients over the years, we intend to capture the causality network of mutational dependencies. Our approach is intrinsically directional. Going beyond simple correlations we are able to ascertain the direction of causality flow. This allows us to infer position-specific genrative models that predict in a probabilistic sense the molecualr evolution of the retroviral genome. More importantly, this reveals locations of immunological vulnerabilities, and tells us the optimal epitope targets that would force maximum mutation rates on the virus, and hopefully push it over the error catstrophe threshold.
Causality In Global Seismicity: Our results indicate causal connections between seismic dynamics observed in California to that on the eastern edge of the Pacific plate, and additionally such hidden connections are shown to exist between events temporally separated by nearly a decade. Our technique allows for short-term statistical predictions as well, and we show that the area under the receiver operating characteristics curve is at least 0.72, establishing non-trivial performance above random decisions. Analyzing the global seismic event log, we discover a hidden causality network connecting seismic events in active zones around the world. Surprisingly, we find statistical evidence that event logs from remote locations, connected via long-range causal dependencies, are far more informative about future events compared to local history.