Automatic debiasing of neural networks via moment-constrained learning (2409.19777v1)

Abstract: Causal and nonparametric estimands in economics and biostatistics can often be viewed as the mean of a linear functional applied to an unknown outcome regression function. Naively learning the regression function and taking a sample mean of the target functional results in biased estimators, and a rich debiasing literature has developed where one additionally learns the so-called Riesz representer (RR) of the target estimand (targeted learning, double ML, automatic debiasing etc.). Learning the RR via its derived functional form can be challenging, e.g. due to extreme inverse probability weights or the need to learn conditional density functions. Such challenges have motivated recent advances in automatic debiasing (AD), where the RR is learned directly via minimization of a bespoke loss. We propose moment-constrained learning as a new RR learning approach that addresses some shortcomings in AD, constraining the predicted moments and improving the robustness of RR estimates to optimization hyperparamters. Though our approach is not tied to a particular class of learner, we illustrate it using neural networks, and evaluate on the problems of average treatment/derivative effect estimation using semi-synthetic data. Our numerical experiments show improved performance versus state of the art benchmarks.

• The paper presents a novel moment-constrained learning approach to estimate Riesz representers for automatic debiasing in neural network models.
• It improves robustness by reducing sensitivity to hyperparameters and controlling for extreme out-of-sample predictions.
• Empirical results on IHDP and BHP datasets demonstrate superior performance in estimating average treatment and derivative effects compared to state-of-the-art methods.

Overview of "Automatic Debiasing of Neural Networks via Moment-Constrained Learning"

"Automatic Debiasing of Neural Networks via Moment-Constrained Learning," authored by Christian L. Hines and Oliver J. Hines, explores a novel approach to enhancing the robustness of bias correction in machine learning models used for causal inference and biostatistics. The paper addresses shortcomings in existing methods by proposing a moment-constrained learning approach for estimating Riesz representers (RRs) to achieve more efficient and unbiased estimators for various economic and biostatistical estimands.

Causal Inference and Debiased Estimation

The paper begins by outlining relevant problems in causal inference where estimands can be expressed as the mean of a linear functional of an unknown regression function. Traditional naive methods often produce biased estimators because they inadequately manage biases in the subsequent estimation process. The debiasing approach traditionally involves learning the RR, a function that corrects for these biases.

Moment-Constrained Learning Approach

The proposed method introduces a new framework for learning RRs, called moment-constrained learning. The RR is learned by constraining predicted moments, improving robustness to optimization hyperparameters. The moment-constrained learning approach capitalizes on the property that certain known functions (denoted as $\beta$) satisfy $h(\beta) \neq 0$; this facilitates the construction of efficient moment-constrained estimators.

Theoretical Contributions

Theoretical underpinnings of the method include leveraging the properties of Hilbert spaces and the projection theorem to provide robust bias correction mechanisms. The authors derive estimators that decompose the moment-constrained function $\beta_\perp$, which minimizes the mean squared error in predicting the known function $\beta$ subject to certain constraints.

Key Results and Methodological Innovations:

1. Improved Robustness: The proposed approach yields RR estimates that better control for extreme out-of-sample predictions, showing less sensitivity to optimization hyperparameters.
2. Automatic Debiasing: The method preserves the 'automatic' nature of debiasing, making it adaptable across a wide range of estimands without requiring the derivation of functional forms of RRs.
3. Empirical Validation: Numerical experiments show that moment-constrained learning outperforms state-of-the-art benchmarks in average treatment effect (ATE) and average derivative effect (ADE) estimation using semi-synthetic data.

Implications and Future Directions

Practical Implications

The moment-constrained learning approach holds practical promise for improving the reliability and accuracy of causal inference in complex settings, particularly those involving neural networks. By ensuring that RRs are less dependent on tuning parameters and more resilient to errors in estimation, this method can be applied to high-stakes fields like econometrics and biostatistics with greater confidence.

Theoretical Implications

From a theoretical perspective, this paper strengthens the connection between debiased estimation and constrained optimization, suggesting that further extensions of this method could encompass other types of stochastic constraints. The proposed method also paves the way for using similar approaches in generalized regression models.

Numerical Performance

The paper reports on comprehensive numerical experiments showing that the new method offers significant improvements over existing methods. Specifically, the moment-constrained DR estimator demonstrates superior empirical performance in both the IHDP and BHP datasets, suggesting enhanced model robustness and efficacy.

Key Datasets and Results:

• IHDP Dataset: In the semi-synthetic IHDP data, the MADNet DR estimator outperformed previous methods such as DragonNet and RieszNet in terms of mean absolute error (MAE).
• BHP Dataset: Similar improvements were observed in the BHP dataset for ADE estimation, confirming the robustness of the proposed method across different types of causal estimands.

Conclusion

The paper "Automatic Debiasing of Neural Networks via Moment-Constrained Learning" advances the state of the art in causal inference and debiased estimation. By introducing a novel moment-constrained learning approach, the authors manage to mitigate some of the intrinsic challenges in bias correction while maintaining automatic adaptability across various types of estimands. Future developments could see this method extended to more complex inference tasks, making it a valuable tool in the arsenal of researchers working on causal inference and machine learning with structured bias correction needs.