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About this paper
Rui Zhang, Masaaki Imaizumi, Bernhard Schölkopf, Krikamol Muandet
MMR-IV estimates nonlinear instrumental-variable regressions by minimizing a risk that measures alignment between residuals and instrument-based test functions, rather than solving an adversarial minimax problem. Its neural-network and RKHS versions are tested on synthetic and Vitamin D data. In a low-dimensional sine-function setting, MMR-IV (Nyström) reports MSE 0.006 ± 0.002 versus SieveIV’s 0.021 ± 0.001; instrument validity remains an assumption.
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