Debiased Inference on Functionals of Ill-Posed Inverses with Applications to Long-Term Causal Inference

Seminar in Mathematics

Abstract: Experimentation on digital platforms often faces a dilemma: we want rapid innovation but we also want to make decisions based on long-term impact. Usually, one resorts to looking at indices that combine multiple short-term surrogate outcomes. Constructing indices by flexible regressions of long-term metrics on short-term ones is easy with off-the-self ML but suffers bias from confounding and direct (i.e., unmediated) effects. I will discuss how to instead leverage past experiments as instrumental variables (IVs) and some surrogates as negative-control-outcome proxies, with real-world examples from Netflix. There are two key challenges to surmount to make this possible. First, past experiments characterize the right surrogate index as the nonparametric function solving an ill-posed moment restriction: it does not uniquely identify an index and approximately solving it does not translate to approximating any solution. I tackle this by developing a novel and generic debiasing method for inference on linear functionals of solutions to ill-posed moment restrictions (as average long-term effects are such functionals of the index) and adversarial ML estimators for the solution and for a functional-specific debiasing nuisance function, admitting flexible hypothesis classes such as neural nets and reproducing kernel Hilbert spaces. Second, even as we observe more past experiments, we have non-vanishing bias in estimating the moment implied by each one, since each experiment has a bounded size that is often just barely powered to detect effects, giving rise to a many-weak-instruments phenomenon. I tackle this by incorporating an instrument-splitting technique into our estimators, leading to a nonparametric analogue of the classic (linear) jackknife IV estimator (JIVE) with guarantees for flexible function classes in terms of generic functional complexity measures. Along the way, I will review the landscape of debiased ML and of long-term causal inference and my work in these areas.