Data-Driven Learning of Large Causal Structures “QuICly” using Quotient Graphical Independence Models

In the era of big data, industry and public policy are able to make use of large amounts of data for policy decisions. The proliferation of cheap sensors and fast communication

enables policy makers to consider complex networks as a whole, using time series data from many sources to model the system. Of particular interest is a representation

of the dependence of various time series on one another, the so-called “structure” of the system, which is not always known and needs to be learned from passively obtained

data. The Input/Output structures of such systems are helpful in understanding how they work and designing new control laws. Such structures can be learned from passively

obtained data as well, which is beneficial as it avoids the need to perform costly or risky experiments. When not all variables are measured, however, the Input/Output

structure is no longer valid, and a new notion of structure needs to be developed. Such systems have an ancestral graph structure, but these are very large for dynamical

systems and existing methods for learning ancestral graphs are infeasible when they have so many nodes. We note how existing methods for some related problems exhibit

similar behavior in their treatment of irrelevant or redundant associations. Inspired by these methods, we present the Partial Quotient Graph model. We show when such

graphs act as independence models and present the Quotient Inductive Causation—or “QuIC”—algorithm for learning them from data. The thesis concludes with some example implementations of QuIC, which we test on simulated dynamical systems. Where the systems we test have instantaneous causality or latent variables which cause prior methods to produce incorrect results, QuIC instead recovers the structures correctly.