Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation
arxiv(2023)
摘要
State-of-the-art methods for conditional average treatment effect (CATE)
estimation make widespread use of representation learning. Here, the idea is to
reduce the variance of the low-sample CATE estimation by a (potentially
constrained) low-dimensional representation. However, low-dimensional
representations can lose information about the observed confounders and thus
lead to bias, because of which the validity of representation learning for CATE
estimation is typically violated. In this paper, we propose a new,
representation-agnostic refutation framework for estimating bounds on the
representation-induced confounding bias that comes from dimensionality
reduction (or other constraints on the representations) in CATE estimation.
First, we establish theoretically under which conditions CATE is
non-identifiable given low-dimensional (constrained) representations. Second,
as our remedy, we propose a neural refutation framework which performs partial
identification of CATE or, equivalently, aims at estimating lower and upper
bounds of the representation-induced confounding bias. We demonstrate the
effectiveness of our bounds in a series of experiments. In sum, our refutation
framework is of direct relevance in practice where the validity of CATE
estimation is of importance.
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