Dual Instrumental Variable Regression
This work addresses a bottleneck in real-world applications of instrumental variable regression, offering a simpler and competitive method, though it appears incremental as it builds on existing two-stage approaches.
The paper tackles the problem of non-linear instrumental variable regression by introducing DualIV, a novel algorithm that reformulates two-stage methods as a convex-concave saddle-point problem, eliminating the need for first-stage regression; empirical results show it is competitive with existing algorithms.
We present a novel algorithm for non-linear instrumental variable (IV) regression, DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that two-stage procedures for non-linear IV regression can be reformulated as a convex-concave saddle-point problem. Our formulation enables us to circumvent the first-stage regression which is a potential bottleneck in real-world applications. We develop a simple kernel-based algorithm with an analytic solution based on this formulation. Empirical results show that we are competitive to existing, more complicated algorithms for non-linear instrumental variable regression.