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A Distributionally Robust Framework for Nuisance in Causal Effect Estimation

Akira Tanimoto

TL;DR

This paper tackles distribution shifts in observational causal inference and the instability of inverse probability weighting by introducing a distributionally robust, adversarial framework for nuisance estimation. It casts nuisance learning as a worst-case optimization over a constrained propensity set and bounds generalization error with a weighted Rademacher complexity, then instantiates the approach in two architectures: NuDRNet (DRNet) and NuSNet (SNet). The proposed NuDRNet and NuSNet demonstrate consistent improvements over strong baselines on synthetic and real-world datasets, highlighting the benefits of end-to-end, nuisance-robust weighting and representation strategies. By connecting DRO principles with causal plug-in methods, the work provides a principled path to more stable, non-asymptotic causal inference in high-dimensional settings. The framework also points to broader applicability to other multi-step causal inference tasks and invites further exploration of representation-uncertainty and adversarial training stability.

Abstract

Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods address this distribution shift through inverse probability weighting (IPW), which requires estimating propensity scores as an intermediate step. These methods face two key challenges: inaccurate propensity estimation and instability from extreme weights. We decompose the generalization error to isolate these issues--propensity ambiguity and statistical instability--and address them through an adversarial loss function. Our approach combines distributionally robust optimization for handling propensity uncertainty with weight regularization based on weighted Rademacher complexity. Experiments on synthetic and real-world datasets demonstrate consistent improvements over existing methods.

A Distributionally Robust Framework for Nuisance in Causal Effect Estimation

TL;DR

This paper tackles distribution shifts in observational causal inference and the instability of inverse probability weighting by introducing a distributionally robust, adversarial framework for nuisance estimation. It casts nuisance learning as a worst-case optimization over a constrained propensity set and bounds generalization error with a weighted Rademacher complexity, then instantiates the approach in two architectures: NuDRNet (DRNet) and NuSNet (SNet). The proposed NuDRNet and NuSNet demonstrate consistent improvements over strong baselines on synthetic and real-world datasets, highlighting the benefits of end-to-end, nuisance-robust weighting and representation strategies. By connecting DRO principles with causal plug-in methods, the work provides a principled path to more stable, non-asymptotic causal inference in high-dimensional settings. The framework also points to broader applicability to other multi-step causal inference tasks and invites further exploration of representation-uncertainty and adversarial training stability.

Abstract

Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods address this distribution shift through inverse probability weighting (IPW), which requires estimating propensity scores as an intermediate step. These methods face two key challenges: inaccurate propensity estimation and instability from extreme weights. We decompose the generalization error to isolate these issues--propensity ambiguity and statistical instability--and address them through an adversarial loss function. Our approach combines distributionally robust optimization for handling propensity uncertainty with weight regularization based on weighted Rademacher complexity. Experiments on synthetic and real-world datasets demonstrate consistent improvements over existing methods.

Paper Structure

This paper contains 27 sections, 4 theorems, 33 equations, 1 figure, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem setting
  3. Related work
  4. Inverse probability weighting with propensity scores (IPW) and its extension
  5. Representation-based method using neural networks
  6. Distributionally robust optimization
  7. Pessimism in offline reinforcement learning
  8. Nuisance-Robust Weighting Network
  9. Adversarial Reformulation of Plug-in Nuisance
  10. Nuisance-robust Doubly-robust Network (NuDRNet)
  11. Nuisance-robust Shared Representation Network (NuSNet)
  12. Experiment
  13. Settings
  14. Synthetic data generation
  15. Baseline methods
  16. ...and 12 more sections

Key Result

theorem thmcountertheorem

Suppose that the instance-wise loss is bounded by $c'$ as $w^{(n)}_\mu \ell^{(n)}(\theta)\le c'$. Then, for any $\delta>0$, with probability at least $1-\delta$ over the choice of a sample $D$, the following holds for all $\theta \in \Theta$.

Figures (1)

  • Figure 1: The training architecture of our network. Gray boxes are pre-trained and fixed. The nuisance function $\mu$ is trained to maximize the empirical loss $\hat{L}(\theta; \mu)$ while minimizing the other terms. This adversarial formulation can be presented as a joint minimization with the gradient reversal layers indicated in magenta.

Theorems & Definitions (6)

  • theorem thmcountertheorem
  • theorem thmcountertheorem
  • theorem thmcountertheorem: Theorem 4.1
  • proof
  • theorem thmcountertheorem: Theorem 4.2
  • proof