Causal Discovery Under Non-Stationary Feedback
Eric V. Strobl · D-Scholarship@Pitt (University of Pittsburgh) · 2017
Causal discovery algorithms help investigators infer causal relations between random variables using observational data. In this thesis, I relax the acyclicity and stationary distribution assumptions imposed by the Fast Causal Inference (FCI) algorithm, a constraint-based causal discovery method allowing latent common causes and selection bias. I provide two major contributions in doing so. First, I introduce a representation of causal processes called Continuous time Markov processes with Jump points (CMJs) which can model continuous time, feedback loops, and non-stationary distributions. Second, I characterize constraint-based causal discovery under the CMJ framework using a data type which I call mixture data, or data created by sampling from a variety of unknown time points from the CMJ. The CMJ may for example correspond to a disease process, and the samples in a mixture dataset to cross-sectional data of patients at different stages in the disease. I finally propose a sound modification of FCI called the Fast Causal Inference with Feedback (F2CI) algorithm which uses conditional independence testing and conditional mixture modeling to infer causal structure from mixture data even when feedback loops, non-stationary distributions, selection bias and/or latent variables are present. Experiments suggest that the F2CI algorithm outperforms FCI by a large margin in correctly identifying causal relations when non-stationary distributions and/or feedback loops exist.