2 research outputs found
Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions
Consider a setting where there are heterogeneous units and
interventions. Our goal is to learn unit-specific potential outcomes for any
combination of these interventions, i.e., causal parameters.
Choosing a combination of interventions is a problem that naturally arises in a
variety of applications such as factorial design experiments, recommendation
engines, combination therapies in medicine, conjoint analysis, etc. Running experiments to estimate the various parameters is likely expensive
and/or infeasible as and grow. Further, with observational data there
is likely confounding, i.e., whether or not a unit is seen under a combination
is correlated with its potential outcome under that combination. To address
these challenges, we propose a novel latent factor model that imposes structure
across units (i.e., the matrix of potential outcomes is approximately rank
), and combinations of interventions (i.e., the coefficients in the Fourier
expansion of the potential outcomes is approximately sparse). We establish
identification for all parameters despite unobserved
confounding. We propose an estimation procedure, Synthetic Combinations, and
establish it is finite-sample consistent and asymptotically normal under
precise conditions on the observation pattern. Our results imply consistent
estimation given observations,
while previous methods have sample complexity scaling as $\min(N \times s^2p, \
\ \text{poly(r)} \times (N + 2^p))p$ items (e.g., rankings)