mlsanityData to 7 Oct 2026

Instrument Space Selection for Kernel Maximum Moment Restriction

arXiv 2106.03340 ↗First posted 7 Jun 2021cs.LGcited by 2

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Abstract (arXiv)

Kernel maximum moment restriction (KMMR) recently emerges as a popular framework for instrumental variable (IV) based conditional moment restriction (CMR) models with important applications in conditional moment (CM) testing and parameter estimation for IV regression and proximal causal learning. The effectiveness of this framework, however, depends critically on the choice of a reproducing kernel Hilbert space (RKHS) chosen as a space of instruments. In this work, we presents a systematic way to select the instrument space for parameter estimation based on a principle of the least identifiable instrument space (LIIS) that identifies model parameters with the least space complexity. Our selection criterion combines two distinct objectives to determine such an optimal space: (i) a test criterion to check identifiability; (ii) an information criterion based on the effective dimension of RKHSs as a complexity measure. We analyze the consistency of our method in determining the LIIS, and demonstrate its effectiveness for parameter estimation via simulations.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 19 of its 82 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

19 of 82 references.

References · 19

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2016Generalized Random Forestscited by 309
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7 more
  1. 2021Instrumental Variable Value Iteration for Causal Offline Reinforcement Learningcited by 35
  2. 2018Adversarial Generalized Method of Momentscited by 34
  3. 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
  4. 2020Valid Causal Inference with (Some) Invalid Instrumentscited by 19
  5. 2020Kernel Conditional Moment Test via Maximum Moment Restrictioncited by 18
  6. 2020Ivy: Instrumental Variable Synthesis for Causal Inferencecited by 17
  7. 2016An Adaptive Test of Independence with Analytic Kernel Embeddingscited by 13

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Citing papers per year: 2022: 2.

2 papers.

  1. 2022Fast Instrument Learning with Faster Ratescited by 6
  2. 2022RFFNet: Large-Scale Interpretable Kernel Methods via Random Fourier Featurescited by 0