Core Concepts

Representation learning is crucial for finding desirable weights in causal inference weighting problems that do not incorporate outcome information, such as in prospective cohort studies, survey weighting, and the weighting portion of augmented weighting estimators. This paper proposes a general framework for learning suitable representations that minimize the error due to the choice of representation, without relying on outcome information.

Abstract

The paper focuses on finding "design-based weights" for causal inference, which do not incorporate any outcome information. Such weights arise in classical observational studies, prospective cohort studies, survey design, and in doubly robust methods that combine outcome and weighting models.

The authors first quantify the information lost by using a weighted estimator based on a representation, rather than the original covariates. They decompose the bias into a "confounding bias" and a "balancing score error", and provide guarantees on the resulting bias of the estimator for any (posited class of the) outcome model.

The authors then develop a method inspired by DeepMatch and RieszNet that learns representations from data, without using any outcome information. Unlike the original RieszNet, the authors do not incorporate outcome information and do not use the final Riesz representer head as the solution weight function, but instead plug the representation into a probability distance to obtain the solution weights.

The authors show promising performance of this approach on benchmark datasets in treatment effect estimation, and argue that the learnt representation can serve as a generic pre-processing method for any weighting method.

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by Oscar Clivio... at **arxiv.org** 09-26-2024

Deeper Inquiries

The proposed representation learning approach can be effectively extended to handle high-dimensional or structured covariates, such as images or text data, by leveraging advanced neural network architectures specifically designed for these data types. For instance, convolutional neural networks (CNNs) can be employed for image data to automatically learn hierarchical representations that capture spatial features, while recurrent neural networks (RNNs) or transformers can be utilized for text data to capture sequential dependencies and contextual information.
To adapt the representation learning framework, one can integrate these specialized architectures into the representation function ( \phi(x; \theta_\phi) ). The neural network can be trained to minimize the AutoDML loss, which allows for the estimation of weights without requiring outcome information. By doing so, the model can learn a low-dimensional representation that retains essential information from the high-dimensional input, thereby mitigating the curse of dimensionality.
Moreover, techniques such as transfer learning can be employed, where pre-trained models on large datasets are fine-tuned on the specific task at hand. This approach not only enhances the model's ability to generalize but also reduces the amount of labeled data required for training. Additionally, regularization techniques can be incorporated to prevent overfitting, ensuring that the learned representations are robust and generalizable across different datasets.

The theoretical guarantees on the consistency and convergence rates of the final weighted estimator derived from the proposed representation learning approach are grounded in the framework's ability to minimize the balancing score error (BSE) and the bias associated with the chosen representation. Under the assumptions outlined in the paper, including the absolute continuity of the target distribution with respect to the source distribution, the estimator is shown to be consistent as the sample size increases.
Specifically, the convergence rates can be established through the analysis of the bias decomposition, which includes terms for the bias with respect to the representation and the confounding bias. The proposed method provides a more flexible framework compared to existing methods, as it does not rely on strict assumptions about the outcome model or the representation being well-specified. This flexibility allows for better performance in practical scenarios where such assumptions may not hold.
In comparison to existing methods, such as those relying on propensity score matching or outcome regression, the proposed approach offers improved robustness against model misspecification. While traditional methods often require well-defined models for both the outcome and the treatment assignment, the representation learning framework can adaptively learn representations that minimize bias without direct access to outcome information, leading to potentially lower bias and variance in the final estimates.

Adapting the proposed framework to handle settings with unobserved confounders presents a significant challenge, as the confounding bias cannot be directly quantified without knowledge of the unobserved variables. However, the framework can be modified to incorporate sensitivity analyses that assess the robustness of the causal estimates to potential unobserved confounding.
One approach is to introduce latent variable models or instrumental variable techniques that can help account for unobserved confounders indirectly. By positing a model for the unobserved confounders, one can derive bounds on the causal estimates, allowing for a more nuanced understanding of the potential impact of these confounders on the results.
Additionally, the representation learning framework can be extended to include regularization techniques that penalize complexity in the learned representations, thereby reducing the risk of overfitting to observed data that may be influenced by unobserved confounders. This can be achieved through the use of techniques such as dropout or weight decay during the training of the neural network.
Furthermore, the framework can incorporate domain knowledge or auxiliary data that may provide insights into the potential confounding structure, allowing for a more informed estimation of the causal effects. By integrating these strategies, the representation learning approach can be made more robust to the challenges posed by unobserved confounders, ultimately leading to more reliable causal inference in complex settings.

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