mlsanityData to 7 Oct 2026

Deep Neural Networks for Estimation and Inference

arXiv 1809.09953 ↗First posted 26 Sep 2018econ.EM cs.LG math.STcited by 62

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Abstract (arXiv)

We study deep neural networks and their use in semiparametric inference. We establish novel rates of convergence for deep feedforward neural nets. Our new rates are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second-step inference after first-step estimation with deep learning, a result also new to the literature. Our estimation rates and semiparametric inference results handle the current standard architecture: fully connected feedforward neural networks (multi-layer perceptrons), with the now-common rectified linear unit activation function and a depth explicitly diverging with the sample size. We discuss other architectures as well, including fixed-width, very deep networks. We establish nonasymptotic bounds for these deep nets for a general class of nonparametric regression-type loss functions, which includes as special cases least squares, logistic regression, and other generalized linear models. We then apply our theory to develop semiparametric inference, focusing on causal parameters for concreteness, such as treatment effects, expected welfare, and decomposition effects. Inference in many other semiparametric contexts can be readily obtained. We demonstrate the effectiveness of deep learning with a Monte Carlo analysis and an empirical application to direct mail marketing.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Sep 2018.

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Citing papers per year: 2021: 17; 2022: 19; 2023: 16; 2024: 5; 2025: 4; 2026: 1.

62 papers.

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  1. 2021VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatmentscited by 59
  2. 2022Criteria for Classifying Forecasting Methodscited by 48
  3. 2022Deep Nonparametric Estimation of Operators between Infinite Dimensional Spacescited by 45
  4. 2021RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forestscited by 42
  5. 2021Uncertainty quantification in the Bradley-Terry-Luce modelcited by 28
  6. 2022How do noise tails impact on deep ReLU networks?cited by 25
  7. 2023Deep Operator Learning Lessens the Curse of Dimensionality for PDEscited by 18
  8. 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
  9. 2021Generating Synthetic Text Data to Evaluate Causal Inference Methodscited by 9
  10. 2023Testing for the Markov Property in Time Series via Deep Conditional Generative Learningcited by 9
  11. 2024DoubleMLDeep: Estimation of Causal Effects with Multimodal Datacited by 8
  12. 2021Sample Complexity of Offline Reinforcement Learning with Deep ReLU Networkscited by 7
38 more
  1. 2023RCT Rejection Sampling for Causal Estimation Evaluationcited by 7
  2. 2021Calibrating multi-dimensional complex ODE from noisy data via deep neural networkscited by 6
  3. 2022Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networkscited by 6
  4. 2023Sup-Norm Convergence of Deep Neural Network Estimator for Nonparametric Regression by Adversarial Trainingcited by 6
  5. 2021Estimation of a regression function on a manifold by fully connected deep neural networkscited by 5
  6. 2022Covariate-Balancing-Aware Interpretable Deep Learning models for Treatment Effect Estimationcited by 5
  7. 2022On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimationcited by 5
  8. 2025Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimandscited by 5
  9. 2022Unlabeled Data Help: Minimax Analysis and Adversarial Robustnesscited by 4
  10. 2023Deep Gaussian Mixture Ensemblescited by 4
  11. 2023Distributionally Robust Learning for Multi-source Unsupervised Domain Adaptationcited by 4
  12. 2024Improving the Finite Sample Estimation of Average Treatment Effects using Double/Debiased Machine Learning with Propensity Score Calibrationcited by 4
  13. 2021Estimation and Applications of Quantiles in Deep Binary Classificationcited by 3
  14. 2022Individual Treatment Effect Estimation Through Controlled Neural Network Training in Two Stagescited by 3
  15. 2022Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networkscited by 3
  16. 2022Bayesian Neural Networks for Macroeconomic Analysiscited by 3
  17. 2021Nonasymptotic theory for two-layer neural networks: Beyond the bias-variance trade-offcited by 2
  18. 2022The boosted HP filter is more general than you might thinkcited by 2
  19. 2022Heterogeneous Synthetic Learner for Panel Datacited by 2
  20. 2023Semiparametric Regression for Spatial Data via Deep Learningcited by 2
  21. 2023On Heterogeneous Treatment Effects in Heterogeneous Causal Graphscited by 2
  22. 2023Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimatorscited by 2
  23. 2023From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networkscited by 2
  24. 2024Off-policy Evaluation with Deeply-abstracted Statescited by 2
  25. 2024Causal Invariance Learning via Efficient Nonconvex Optimizationcited by 2
  26. 2021Calibrated Optimal Decision Making with Multiple Data Sources and Limited Outcomecited by 1
  27. 2021GEAR: On Optimal Decision Making with Auxiliary Datacited by 1
  28. 2021The Bias-Variance Tradeoff of Doubly Robust Estimator with Targeted L1 regularized Neural Networks Predictionscited by 1
  29. 2021Normalized Augmented Inverse Probability Weighting with Neural Network Predictionscited by 1
  30. 2021Searching for Minimal Optimal Neural Networkscited by 1
  31. 2022Deep Sufficient Representation Learning via Mutual Informationcited by 1
  32. 2023Matched Machine Learning: A Generalized Framework for Treatment Effect Inference With Learned Metricscited by 1
  33. 2023Econometrics of Machine Learning Methods in Economic Forecastingcited by 1
  34. 2023Non-linear dimension reduction in factor-augmented vector autoregressionscited by 1
  35. 2025Bayesian Semi-supervised Inference via a Debiased Modeling Approachcited by 1
  36. 2021Predicting Inflation with Recurrent Neural Networkscited by 0
  37. 2021An Interpretable Neural Network for Parameter Inferencecited by 0
  38. 2021Structural Sievescited by 0

50 most cited of 62 All 62 (JSON)