arXiv 17 Dec 2020 · Machine Learning · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2023) · 10 citations (OpenAlex)
arXiv:2012.09422 · PDF · DOI · OpenAlex · Extracted main text
The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite set of marginal moment conditions and applies the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be theoretically efficient but practically unwieldy if we use a growing sieve of moment conditions. Motivated by a variational minimax reformulation of OWGMM, we define a very general class of estimators for the conditional moment problem, which we term the variational method of moments (VMM) and which naturally enables controlling infinitely-many moments. We provide a detailed theoretical analysis of multiple VMM estimators, including ones based on kernel methods and neural nets, and provide conditions under which these are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model. We additionally provide algorithms for valid statistical inference based on the same kind of variational reformulations, both for kernel- and neural-net-based varieties. Finally, we demonstrate the strong performance of our proposed estimation and inference algorithms in a detailed series of synthetic experiments.
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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 | C. Ai and X. Chen (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions | 1.000 | 11 | 5 | 100% |
| 2 | X. Chen and D. Pouzo (2009) Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals | 1.000 | 6 | 4 | 100% |
| 3 | N. Dikkala, G. Lewis, L. Mackey, and V. Syrgkanis (2020) Minimax estimation of conditional moment models | 1.000 | 6 | 3 | 100% |
| 4 | R. Singh, M. Sahani, and A. Gretton (2019) Kernel instrumental variable regression | 1.000 | 6 | 3 | 100% |
| 5 | A. Bennett, N. Kallus, L. Li, and A. Mousavi (2021) Off-policy evaluation in infinite-horizon reinforcement learning with latent confounders | 1.000 | 5 | 3 | 100% |
| 6 | K. Muandet, A. Mehrjou, S. K. Lee, and A. Raj (2020) Dual instrumental variable regression | 1.000 | 5 | 3 | 100% |
| 7 | A. Bennett, N. Kallus, and T. Schnabel (2019) Deep generalized method of moments for instrumental variable analysis | 0.974 | 13 | 6 | 92% |
| 8 | A. Bennett and N. Kallus (2020) Efficient policy learning from surrogate-loss classification reductions | 0.965 | 10 | 6 | 90% |
| 9 | X. Chen and D. Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals | 0.928 | 5 | 5 | 80% |
| 10 | W. K. Newey and J. L. Powell (2003) Instrumental variable estimation of nonparametric models | 0.928 | 4 | 3 | 100% |
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