Learning causal effects from many randomized experiments using regularized instrumental variables
This addresses a practical challenge for data scientists analyzing large collections of experiments, offering a simple, usable method for improved causal inference.
The paper tackles the problem of learning causal effects from many randomized experiments with small effects and missing metadata, showing that standard two-stage least squares is biased and proposing a sparsity-inducing l0 regularization that reduces bias and error in interventional predictions.
Scientific and business practices are increasingly resulting in large collections of randomized experiments. Analyzed together, these collections can tell us things that individual experiments in the collection cannot. We study how to learn causal relationships between variables from the kinds of collections faced by modern data scientists: the number of experiments is large, many experiments have very small effects, and the analyst lacks metadata (e.g., descriptions of the interventions). Here we use experimental groups as instrumental variables (IV) and show that a standard method (two-stage least squares) is biased even when the number of experiments is infinite. We show how a sparsity-inducing l0 regularization can --- in a reversal of the standard bias--variance tradeoff in regularization --- reduce bias (and thus error) of interventional predictions. Because we are interested in interventional loss minimization we also propose a modified cross-validation procedure (IVCV) to feasibly select the regularization parameter. We show, using a trick from Monte Carlo sampling, that IVCV can be done using summary statistics instead of raw data. This makes our full procedure simple to use in many real-world applications.