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Adapting Neural Networks for the Estimation of Treatment Effects
Claudia Shi, David M. Blei, Victor Veitch
TL;DR
The paper asks how neural networks used in observational treatment-effect estimation can be adapted to improve the final effect estimate, rather than only predictive accuracy. It introduces Dragonnet and targeted regularization, and reports substantially improved estimation quality on benchmark datasets compared with existing neural-network approaches. The paper also identifies settings and procedures where these intuitions or practices may not transfer directly.
Problem
The paper asks how neural-network design and training can improve downstream treatment-effect estimation from observational data, where confounding must be addressed.
Method
The paper introduces Dragonnet, which couples outcome and propensity-score modeling, and targeted regularization, which modifies training using non-parametric estimating-equation theory.
Results
The methods substantially improve estimation quality on benchmark datasets compared with existing neural-network approaches, even when predictive performance degrades.
Takeaways & Limitations
Treatment-effect estimation may benefit from adapting neural-network representations and objectives to causal-estimation requirements rather than optimizing predictive performance alone.
Takeaways & Limitations
The Dragonnet intuition may break down in randomized trials, where covariates can affect outcomes without affecting treatment and adjustment may increase power.
Abstract
from arXiv · showhide
This paper addresses the use of neural networks for the estimation of treatment effects from observational data. Generally, estimation proceeds in two stages. First, we fit models for the expected outcome and the probability of treatment (propensity score) for each unit. Second, we plug these fitted models into a downstream estimator of the effect. Neural networks are a natural choice for the models in the first step. The question we address is: how can we adapt the design and training of the neural networks used in the first step in order to improve the quality of the final estimate of the treatment effect? We propose two adaptations based on insights from the statistical literature on the estimation of treatment effects. The first is a new architecture, the Dragonnet, that exploits the sufficiency of the propensity score for estimation adjustment. The second is a regularization procedure, targeted regularization, that induces a bias towards models that have non-parametrically optimal asymptotic properties `out-of-the-box`. Studies on benchmark datasets for causal inference show these adaptations outperform existing methods. Code is available at github.com/claudiashi57/dragonnet.
1 Introduction
The paper studies treatment-effect estimation from observational data, where confounding must be addressed under a no-hidden-confounding assumption. It asks how neural-network design and training can improve downstream treatment-effect estimates.
- Motivation: Observational treatment-effect estimation requires adjusting for confounders using covariates that contain all confounding variables.The paper focuses on the no-hidden-confounding setting.
- Estimation pipeline: The estimation pipeline fits conditional-outcome and propensity-score models before plugging them into a downstream effect estimator.The conditional outcome is Q(t, x) = E[Y | t, x], while the propensity score is g(x) = P(T = 1|x).
- Neural-network models: Neural networks are used to model both the conditional outcome and propensity score because of their strong predictive performance.The paper notes that predictive performance alone may not optimize downstream causal estimation.
- Contributions: The paper contributes Dragonnet, targeted regularization, and benchmark experiments showing improved estimation quality over existing neural-network approaches.The reported improvement can occur even when predictive performance degrades.
- Research question: The central question is how to modify neural-network design and training so that the resulting treatment-effect estimate is accurate.The question concerns the quality of the downstream estimate rather than only predictive performance.
2 Dragonnet
Dragonnet uses a shared representation with treatment and outcome heads to exploit propensity-score sufficiency. Its end-to-end training can trade predictive quality for a representation that improves treatment-effect estimation.
- Propensity-score sufficiency: Propensity-score sufficiency means adjusting for g(X) can suffice when adjustment for X identifies the average treatment effect.The relevant information in X is the part that predicts treatment.
- Propensity-score sufficiency: Information predictive of the outcome but not treatment can act as adjustment noise and may hurt finite-sample treatment-effect estimation.The paper therefore motivates discarding such information, even if outcome prediction worsens.
- Architecture: Dragonnet jointly predicts treatment and both potential outcomes from a shared representation Z(X), using a simple propensity-score head and neural outcome heads.The propensity head is a linear map followed by a sigmoid, while each outcome head is a two-hidden-layer network.
- Architecture: The propensity-score head tightly couples the shared representation to estimated treatment-assignment probabilities.This design operationalizes the sufficiency-based motivation within one end-to-end model.
- Empirical behavior: Empirically, Dragonnet trades off prediction quality to represent the propensity score, improving ATE estimation even with an outcome-only downstream estimator.Removing the propensity-score head yields an architecture essentially equivalent to TARNET.
3 Targeted Regularization
Targeted regularization modifies neural-network training so fitted outcome, propensity, and effect estimates satisfy a non-parametric estimating equation. This connects finite-sample stability with desirable asymptotic properties.
- Motivation: Targeted regularization modifies the neural-network objective using non-parametric estimation theory.The goal is a fitted model with desirable asymptotic properties under a suitable downstream estimator.
- Theory: Non-parametric theory links estimating-equation satisfaction and consistent nuisance models to robustness and asymptotic efficiency.The estimator can converge quickly even when outcome and propensity models converge slowly, and can attain the lowest asymptotic variance among consistent estimators.
- Relation to existing estimators: Unlike A-IPTW, whose propensity-score denominators can be unstable in finite samples, TMLE uses a perturbed outcome model with a stable outcome-based estimator.Targeted regularization is inspired by TMLE but adapts the entire model rather than only selecting the perturbation parameter.
- Method: The method adds a parameter ϵ and regularization term to the training objective, then defines a targeted estimator from the fitted model.The modification is designed to be differentiable and compatible with neural-network models.
- Method: Minimizing the targeted term forces the fitted outcome, propensity, and effect estimates to satisfy the required non-parametric estimating equation.The targeted estimator consequently inherits the stated asymptotic properties when the nuisance models are consistent.
- Properties: Targeted-regularization estimates retain double robustness: consistency holds if either the modified outcome model or propensity score is consistent.Both targeted regularization and TMLE are designed for stable finite-sample behavior and strong asymptotic guarantees.
4 Related Work
The paper connects Dragonnet to representation-learning approaches for causal inference and targeted regularization to semi-parametric and double-machine-learning theory. These connections position the methods as complementary to existing causal-estimation strategies.
- Representations for causal inference: Dragonnet resembles TARNET, while other representation-learning methods seek balanced covariate representations across treatment and outcome groups.TARNET is described as Dragonnet without the propensity head.
- Non-parametric estimation and machine learning: Targeted regularization is inspired by TMLE and complements double-machine-learning theory by addressing finite-sample estimation behavior.The paper uses asymptotic results for motivation while adapting training to the finite-sample setting.
- Non-parametric estimation and machine learning: Double-machine-learning results provide fast-rate guarantees when suitable estimating equations hold, even with slowly converging nuisance models.Neural networks are theoretically justified as models for propensity scores and conditional expected outcomes when they converge sufficiently quickly.
5 Experiments
Experiments on IHDP and ACIC 2018 evaluate Dragonnet and targeted regularization against neural-network baselines, focusing on treatment-effect estimation rather than prediction alone. Across these studies, the methods improve estimation on average, with benefits tied to propensity-relevant representations and finite-sample behavior.
- ACIC 2018: The ACIC analysis excludes datasets with heldout Dragonnet treatment accuracy above 90%, leaving 101 datasets because overlap violations are outside the paper’s focus.High treatment-classification accuracy is used as a heuristic for strong separation between treated and control populations.
- IHDP: Dragonnet with targeted regularization is state-of-the-art among neural-network methods on the IHDP benchmark.The authors caution that IHDP’s small sample size and limited simulation settings make broad conclusions difficult.
- ACIC 2018: On ACIC 2018, Dragonnet improves estimation relative to TARNET, and targeted regularization improves it further.The comparison uses mean absolute error over the included datasets.
- ACIC 2018: Dragonnet and targeted regularization help about half the time; improvements are substantial when present, while degradations are mild.This analysis separates datasets where each method improves or degrades estimation relative to the baseline.
- Why does Dragonnet work?: The end-to-end Dragonnet produces more accurate estimates than NEDnet, its multi-stage alternative.NEDnet first learns treatment-prediction representations, freezes them, and then trains an outcome-prediction network.
- Effect on Treatment Estimation: Dragonnet sacrifices outcome-prediction performance relative to TARNET but improves estimation, including with the propensity-independent Q-only estimator.This suggests the shared representation adapts to treatment prediction at a predictive-performance cost.
- Effect on Treatment Estimation: Dragonnet’s advantage increases with more covariates affecting only the outcome and is more significant with smaller datasets.Such covariates are treated as noise for causal adjustment, while the finite-data comparison supports greater data efficiency.
- When does targeted regularization work?: When the initial estimator is poor, TMLE significantly degrades estimation quality, whereas targeted regularization does not.When the initial estimator is good, the two methods behave similarly; the authors attribute the difference to adapting training to the non-parametric estimating equation, without a satisfactory theoretical explanation.
6 Discussion
The discussion identifies unresolved limits around extending and choosing Dragonnet-type methods, and reports that routine data-splitting is not supported by the experiments.
- Dragonnet’s covariate-selection intuition may break down outside the large-data observational setting with unknown propensity scores.In randomized trials, adjustment can increase power when covariates affect outcomes but not treatment.
- Practical guidelines are still needed for choosing covariates and understanding trade-offs in Dragonnet-type black-box adjustment models.The discussion notes good estimation accuracy alongside unclear trade-offs.
- The experiments do not support routine data-splitting for effect estimation because it significantly degrades performance.The authors also report this pattern in preliminary K-fold experiments.
Appendix A
Appendix experiments examine Dragonnet’s finite-sample advantage: its error gap over TARNET narrows with more data, while initial estimates are already near perfect.
- TARNET and Dragonnet converge in estimation error as the amount of data increases.The initial estimates are described as close to perfect.
- The difference between Dragonnet and TARNET’s estimation error becomes smaller as the amount of data increases.This comparison uses subsamples from two 50k ACIC 2018 datasets.
Appendix B
Appendix B shows that propensity-score trimming affects methods differently, so estimator performance depends on the chosen truncation level.
- The trimming parameter affects effect estimation for both the simple estimator and the doubly robust TMLE estimator.
- Truncation level has different effects across methods and estimators when computing ATE estimation errors.The comparison averages Δ_all across included ACIC 2018 datasets using all data for training and estimation.
- TARNET performs better with steeper truncation, whereas Dragonnet methods perform better when more data are retained.
- TMLE performance improves with steeper truncation.