Rahul Singh, Maneesh Sahani, Arthur Gretton
arXiv 1 Jun 2019 · Machine Learning · 6 citations (OpenAlex)
arXiv:1906.00232 · PDF · DOI · OpenAlex · Extracted main text
Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X and the unmeasured confounder. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which convergence occurs at the minimax optimal rate for unconfounded, single-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric IV regression.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Marine Carrasco, Jean-Pierre Florens, and Eric Renault (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 1.000 | 5 | 4 | 100% |
| 2 | Whitney K Newey and James L Powell (2003) Instrumental variable estimation of nonparametric models | 0.928 | 10 | 6 | 80% |
| 3 | Xiaohong Chen and Timothy M Christensen (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression | 0.928 | 10 | 4 | 80% |
| 4 | Jason Hartford, Greg Lewis, Kevin Leyton-Brown, and Matt Taddy (2017) Deep IV: A flexible approach for counterfactual prediction | 0.894 | 14 | 4 | 71% |
| 5 | Zoltán Szabó, Arthur Gretton, Barnabás Póczos, and Bharath Sriperumb… (2015) Two-stage sampled learning theory on distributions self | 0.874 | 9 | 4 | 67% |
| 6 | Steffen Grünewälder, Guy Lever, Luca Baldassarre, Massimilano Pontil… (2012) Modelling transition dynamics in MDPs with RKHS embeddings self | 0.843 | 4 | 3 | 75% |
| 7 | Bharath Sriperumbudur, Kenji Fukumizu, and Gert Lanckriet (2010) On the relation between universality, characteristic kernels and RKHS embedding of measures | 0.843 | 3 | 3 | 100% |
| 8 | Zoltán Szabó, Bharath Sriperumbudur, Barnabás Póczos, and Arthur Gre… (2016) Learning theory for distribution regression self | 0.794 | 20 | 4 | 50% |
| 9 | Serge Darolles, Yanqin Fan, Jean-Pierre Florens, and Eric Renault (2011) Nonparametric instrumental regression | 0.781 | 21 | 5 | 48% |
| 10 | Le Song, Jonathan Huang, Alex Smola, and Kenji Fukumizu (2009) Hilbert space embeddings of conditional distributions with applications to dynamical systems | 0.763 | 9 | 3 | 44% |
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