Ziyu Wang, Yuhao Zhou, Jun Zhu
arXiv 22 May 2022 · Statistics — Machine Learning
arXiv:2205.10772 · PDF · DOI · OpenAlex · Extracted main text
We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.
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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 | R. Zhang, M. Imaizumi, B. Schölkopf, and K. Muandet, “Maximum moment… (2020) Maximum moment restriction for instrumental variable regression | 0.941 | 6 | 4 | 83% |
| 2 | K. Muandet, A. Mehrjou, S. K. Lee, and A. Raj, “Dual instrumental va… (2020) Dual instrumental variable regression | 0.894 | 7 | 5 | 71% |
| 3 | R. Singh, M. Sahani, and A. Gretton, “enKernel Instrumental variable… (2019) enKernel Instrumental variable regression | 0.874 | 12 | 6 | 67% |
| 4 | K. Kato, “enQuasi-Bayesian analysis of nonparametric instrumental va… (2013) enQuasi-Bayesian analysis of nonparametric instrumental variables models | 0.843 | 4 | 3 | 75% |
| 5 | A. Bennett, N. Kallus, and T. Schnabel, “Deep generalized method of… (2019) Deep generalized method of moments for instrumental variable analysis | 0.843 | 10 | 4 | 60% |
| 6 | B. Ghorbani, S. Mei, T. Misiakiewicz, and A. Montanari, “Limitations… (2019) Limitations of lazy training of two-layers neural networks | 0.843 | 3 | 3 | 100% |
| 7 | C. Wei, J. D. Lee, Q. Liu, and T. Ma, “Regularization matters: Gener… (2019) Regularization matters: Generalization and optimization of neural nets v.s. their induced kernel | 0.843 | 3 | 3 | 100% |
| 8 | N. Dikkala, G. Lewis, L. Mackey, and V. Syrgkanis, “Minimax estimati… (2020) Minimax estimation of conditional moment models | 0.825 | 32 | 8 | 56% |
| 9 | J. Hartford, G. Lewis, K. Leyton-Brown, and M. Taddy, “Deep IV: A fl… (2017) Deep IV: A flexible approach for counterfactual prediction | 0.794 | 10 | 5 | 50% |
| 10 | J. Schmidt-Hieber, “Nonparametric regression using deep neural netwo… (2020) Nonparametric regression using deep neural networks with ReLU activation function | 0.773 | 13 | 5 | 46% |
Showing the top 10 of 93 scored citations.