NSF-BSF: AF: Small: Algorithmic and Information-Theoretic Challenges in Causal Inference

California Institute Of Technology, Pasadena CA

Investigators

Abstract

Scientific research is often intended to answer questions of causal effect in various domains such as public health, medicine, economic or educational policy, regulatory policy, business decisions, etc. However, precisely because so much is at stake in many of these questions, scientists are frequently precluded by ethical or other constraints from addressing them with a randomized controlled trial (RCT), the gold standard for experimental research. This has often been one of the greatest barriers to establishing cause and effect in matters of public interest. The framework of causal networks is a relatively recent elaboration of the scientific method which enables one to codify assumptions that some parts of a system have no direct effect on some others (without ruling out indirect effects). When certain assumptions are justified, one can in principle use purely observational data in lieu of RCTs to determine causal effects. However, existing methods are justified only within a narrow range of assumptions and often do not scale well to large networks. This project, to be carried out by the investigator, students, postdocs and collaborators, is dedicated to increasing the range of applicability of such methods with new algorithms and sample complexity bounds, as well as bounds on the strength of correlations that can occur in large, sparse causal networks. At a fundamental level, there are two obstacles to rigorous causal inference: latent confounding and selection bias. Latent confounding occurs because significant aspects of the system cannot (or have not) been observed. Selection bias occurs if data is recorded only under special circumstances that are correlated with the quantities of interest. The presence of a global confounder (one which affects all observables) rules out causal identification---unless additional assumptions are introduced. One such is a cardinality bound on the range of the global confounder; however, existing methods require in addition a statistical separation assumption. Work in this project aims to relax this assumption in favor of model identification in Wasserstein distance. The project also seeks to move beyond a single global confounder to efficient treatment of multiple global confounders. Another goal of the project is to apply causal networks to the analysis of time series data, a topic with a currently distinct methodology. A key goal of the project is to provide strong information inequalities: a special case, strong data processing inequalities, have been studied for concatenations of noisy channels, the simplest example of a causal network; but nothing of this type is known for networks with latent confounding and selection bias. A further goal of the project is to give methods for causal discovery (the use of statistical data rather than domain knowledge to determine network structure) that work efficiently and are robust to noise despite a cardinality-bounded global confounder. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.