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Adversarial Generalized Method of Moments

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  • Greg Lewis
  • Vasilis Syrgkanis

Abstract

We provide an approach for learning deep neural net representations of models described via conditional moment restrictions. Conditional moment restrictions are widely used, as they are the language by which social scientists describe the assumptions they make to enable causal inference. We formulate the problem of estimating the underling model as a zero-sum game between a modeler and an adversary and apply adversarial training. Our approach is similar in nature to Generative Adversarial Networks (GAN), though here the modeler is learning a representation of a function that satisfies a continuum of moment conditions and the adversary is identifying violating moments. We outline ways of constructing effective adversaries in practice, including kernels centered by k-means clustering, and random forests. We examine the practical performance of our approach in the setting of non-parametric instrumental variable regression.

Suggested Citation

  • Greg Lewis & Vasilis Syrgkanis, 2018. "Adversarial Generalized Method of Moments," Papers 1803.07164, arXiv.org, revised Apr 2018.
  • Handle: RePEc:arx:papers:1803.07164
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    File URL: http://arxiv.org/pdf/1803.07164
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    References listed on IDEAS

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    1. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Chen, Xiaohong & Liao, Zhipeng, 2015. "Sieve semiparametric two-step GMM under weak dependence," Journal of Econometrics, Elsevier, vol. 189(1), pages 163-186.
    4. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    5. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    6. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
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    Cited by:

    1. Jason Hartford & Victor Veitch & Dhanya Sridhar & Kevin Leyton-Brown, 2020. "Valid Causal Inference with (Some) Invalid Instruments," Papers 2006.11386, arXiv.org.
    2. Krikamol Muandet & Arash Mehrjou & Si Kai Lee & Anant Raj, 2019. "Dual Instrumental Variable Regression," Papers 1910.12358, arXiv.org, revised Oct 2020.
    3. Luyang Chen & Markus Pelger & Jason Zhu, 2019. "Deep Learning in Asset Pricing," Papers 1904.00745, arXiv.org, revised May 2020.
    4. Andrew Bennett & Nathan Kallus, 2020. "The Variational Method of Moments," Papers 2012.09422, arXiv.org.
    5. Krikamol Muandet & Wittawat Jitkrittum & Jonas Kubler, 2020. "Kernel Conditional Moment Test via Maximum Moment Restriction," Papers 2002.09225, arXiv.org, revised Jun 2020.

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