Adjustment for Confounding using Pre-Trained Representations

Abstract: There is growing interest in extending average treatment effect (ATE) estimation to incorporate non-tabular data, such as images and text, which may act as sources of confounding. Neglecting these effects risks biased results and flawed scientific conclusions. However, incorporating non-tabular data necessitates sophisticated feature extractors, often in combination with ideas of transfer learning. In this work, we investigate how latent features from pre-trained neural networks can be leveraged to adjust for sources of confounding. We formalize conditions under which these latent features enable valid adjustment and statistical inference in ATE estimation, demonstrating results along the example of double machine learning. We discuss critical challenges inherent to latent feature learning and downstream parameter estimation arising from the high dimensionality and non-identifiability of representations. Common structural assumptions for obtaining fast convergence rates with additive or sparse linear models are shown to be unrealistic for latent features. We argue, however, that neural networks are largely insensitive to these issues. In particular, we show that neural networks can achieve fast convergence rates by adapting to intrinsic notions of sparsity and dimension of the learning problem.

• The paper establishes that pre-trained neural representations can validly adjust for confounding when they meet P-validity criteria, ensuring accurate ATE estimation.
• It demonstrates that non-identifiability up to invertible linear transformations challenges typical high-dimensional convergence assumptions in causal models.
• Empirical results confirm that leveraging intrinsic low dimensionality in complex data allows neural networks to outperform traditional confounder adjustment methods.

Adjustment for Confounding using Pre-Trained Representations

This paper focuses on the intersection of causal inference and machine learning, specifically investigating the use of pre-trained neural network representations to adjust for confounding in Average Treatment Effect (ATE) estimation. Confounding variables—factors that affect both the treatment and outcome—are critical in observational studies since they can bias causal inference. Pre-trained representations offer a promising avenue for adjusting non-tabular data (such as text and images) that may serve as confounders. The main contribution of this work is to provide a theoretical framework for using these representations in ATE estimation while addressing practical challenges such as high dimensionality and non-identifiability.

Key Contributions and Findings

The authors formalize conditions under which pre-trained representations can be effectively used to adjust for confounding in ATE estimation:

1. Sufficiency of Representations: The paper establishes that pre-trained representations can be used for adjustment in the causal estimation context when they are $P$-valid, $P$-Outcome Mean Sufficient (P-OMS), or $P$-Outcome Distribution Sufficient (P-ODS). They emphasize that $P$-validity is necessary and sufficient for ensuring that representations serve as valid confounder adjustments.
2. Non-Identifiability and Convergence Challenges: Due to their non-identifiability up to invertible linear transformations (ILTs), pre-trained features challenge common structural assumptions like sparsity and additivity that are typically leveraged for fast convergence rates in high-dimensional settings. These assumptions do not hold under ILTs, complicating the use of popular methods such as lasso and tree-based models in this context.
3. Intrinsic Dimension and Neural Networks: The authors advocate leveraging the intrinsic low dimensionality inherent in complex data modalities like images and text, proposing that neural networks can adapt to these low intrinsic dimensions and thereby achieve optimal convergence rates. They build on recent theoretical studies showing that neural networks efficiently approximate functions defined on low-dimensional manifolds.
4. Validation through Experiments: Empirical results validate the proposed framework, showing that neural networks effectively utilize pre-trained representations for adjusting confounding. The paper compares several ATE estimators, illustrating that Double Machine Learning (DML) with appropriate nuisance estimation surpasses naive and traditional approaches in confounded non-tabular data settings.

Implications for Machine Learning and Causal Inference

This research bridges causal inference with modern machine learning by highlighting the potential of neural networks to adjust for unobserved confounding using pre-trained representations. As such, it pushes the conventional boundaries of causal inference methods, particularly in applications involving complex data types. The findings underscore that neural networks' ability to adapt to intrinsic data properties is crucial for efficient nuisance function estimation and valid statistical inference.

Future Directions

The paper opens several avenues for future research:

1. Multi-Modality Confounding: Extending these methods to settings with multiple modality sources of confounding could reveal new insights and present new challenges, such as the coordination of multiple pre-trained models.
2. Applicability to Other Causal Parameters: While this work focuses on ATE, exploring its applicability to other causal parameters like the Average Treatment Effect on the Treated (ATT) or Conditional ATE (CATE) could broaden its utility.
3. Intricacies with Data Augmentation: Considering how data augmentation practices in machine learning impact the quality and validity of confounder adjustment using pre-trained representations presents another line of investigation.

In conclusion, this paper provides a theoretical backbone and empirical investigation into integrating pre-trained neural representations for confounding adjustment in causal inference, setting the stage for future explorations that blend machine learning advancements with causal reasoning.