Data to 14 Oct 2026

Kernel Instrumental Variable Regression

arXiv 1906.00232 ↗First posted 1 Jun 2019cs.LG econ.EM math.FAcited by 118

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Abstract (arXiv)

Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X and the unmeasured confounder. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which convergence occurs at the minimax optimal rate for unconfounded, single-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric IV regression.

Key facts. Cited by 118 papers in the map (data through 14 Oct 2026). First posted on arXiv 1 Jun 2019.

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Citing papers per year: 2021: 22; 2022: 26; 2023: 18; 2024: 25; 2025: 17; 2026: 10.

118 papers.

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2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 40
2021Causal Effect Inference for Structured Treatmentscited by 39
2021Instrumental Variable Value Iteration for Causal Offline Reinforcement Learningcited by 35
2025Foundation Models for Causal Inference via Prior-Data Fitted Networkscited by 32
2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
2022Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimationcited by 25
2022Stochastic Causal Programming for Bounding Treatment Effectscited by 25
2021Deconditional Downscaling with Gaussian Processescited by 24
2023Sharp Bounds for Generalized Causal Sensitivity Analysiscited by 24

38 more

2021On Instrumental Variable Regression for Deep Offline Policy Evaluationcited by 22
2023Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithmcited by 22
2021BayesIMP: Uncertainty Quantification for Causal Data Fusioncited by 21
2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
2024Functional Bilevel Optimization for Machine Learningcited by 20
2021Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decompositioncited by 19
2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Surveycited by 19
2022Exploiting Independent Instruments: Identification and Distribution Generalizationcited by 18
2022Estimating individual treatment effects under unobserved confounding using binary instrumentscited by 18
2023Demystifying Causal Features on Adversarial Examples and Causal Inoculation for Robust Network by Adversarial Instrumental Variable Regressioncited by 18
2023Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencodercited by 17
2022An Analysis of Attention via the Lens of Exchangeability and Latent Variable Modelscited by 16
2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 14
2022Minimax Optimal Kernel Operator Learning via Multilevel Trainingcited by 13
2023Minimax Instrumental Variable Regression and L2 Convergence Guarantees without Identification or Closednesscited by 13
2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
2022Spectral Representation Learning for Conditional Moment Modelscited by 12
2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
2022Instrumental Variables in Causal Inference and Machine Learning: A Surveycited by 10
2023An Efficient Doubly-Robust Test for the Kernel Treatment Effectcited by 10
2021A Simple and General Debiased Machine Learning Theorem with Finite Sample Guaranteescited by 9
2022Identifiability of Sparse Causal Effects using Instrumental Variablescited by 9
2022Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approachcited by 9
2023Source Condition Double Robust Inference on Functionals of Inverse Problemscited by 9
2023Causal Strategic Learning with Competitive Selectioncited by 9
2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
2021Operationalizing Complex Causes: A Pragmatic View of Mediationcited by 8
2023Conditional Instrumental Variable Regression with Representation Learning for Causal Inferencecited by 8
2024Probabilities of Causation for Continuous and Vector Variablescited by 8
2024Transformers Handle Endogeneity in In-Context Linear Regressioncited by 8
2024Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimalcited by 8
2021Learning Causal Models from Conditional Moment Restrictions by Importance Weightingcited by 7
2021Instrumental Variable-Driven Domain Generalization with Unobserved Confounderscited by 7
2024Regularized DeepIV with Model Selectioncited by 7
2024Neural-Kernel Conditional Mean Embeddingscited by 7
2022Fast Instrument Learning with Faster Ratescited by 6
2022Constructing unbiased gradient estimators with finite variance for conditional stochastic optimizationcited by 6

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