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Poster
Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions
Heiner Kremer · Jia-Jie Zhu · Krikamol Muandet · Bernhard Schölkopf

Tue Jul 19 03:30 PM -- 05:30 PM (PDT) @ Hall E #627

This paper investigates functional generalized empirical likelihood (FGEL) estimation, a novel extension of generalized empirical likelihood (GEL) estimation to conditional moment restrictions. Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional moment restrictions. Previous works addressed this problem by extending the generalized method of moments (GMM) to continuum moment restrictions. In contrast, GEL provides a more general framework and has been shown to enjoy favourable asymptotic properties compared to GMM-based estimators. To benefit from recent developments in machine learning, we provide a functional reformulation of GEL in which arbitrary models can be leveraged. We derive a dual formulation of the resulting infinite dimensional optimization problem and show asymptotic properties of our estimators. Finally, we provide concrete kernel and neural network based implementations of the estimators, which exhibit competitive empirical performance compared to state-of-the-art GMM-based estimators.

Author Information

Heiner Kremer (MPI for Intelligent Systems, Tübingen)
Jia-Jie Zhu (Weierstrass Institute, Berlin)
Krikamol Muandet (Max Planck Institute for Intelligent Systems)
Bernhard Schölkopf (MPI for Intelligent Systems Tübingen, Germany)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

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