Causal Risk Minimization for High-Dimensional Treatments

2026-05-26

AI Summary

This work addresses the challenge of causal effect estimation under high-dimensional treatments—such as text—where traditional methods fail due to their reliance on the strong assumption that all treatment variants are observable. Reformulating causal inference as a learning problem, the authors propose an optimization framework based on higher-moment balancing errors under the standard unconfoundedness assumption. By decomposing the causal estimation error and directly minimizing a tight upper bound, the method enhances estimation accuracy. Furthermore, it projects high-dimensional treatment effects into a low-dimensional attribute space, enabling a single model to generalize across multiple causal queries. Experiments on semi-synthetic data derived from Amazon Reviews—including textual, discrete, and continuous treatments—demonstrate that the proposed approach significantly outperforms baseline methods, with projected estimates matching the performance of attribute-specific estimators.

Abstract

Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains. However, classical causal estimators tend to assume that all possible interventions are observed, which is infeasible when interventions vary widely, for instance, in the space of all text strings. We adapt a well-known approach of recasting causal inference as a learning problem, to address high-dimensional treatment spaces. Specifically, under standard assumptions like no unobserved confounding, we show that causal error decomposes into a series of moment-balancing errors of increasing order, and design objectives that directly improve causal estimation. We also show how to project the effect of a high-dimensional treatment onto lower-dimensional treatment attributes, which allows a single model to answer several causal questions without additional attribute-specific training. We empirically evaluate our estimators in settings with high-dimensional continuous, discrete, and text treatments, the last of which used a semi-synthetic dataset of Amazon Reviews. Our experiments demonstrate the benefit of higher-order balance error optimization and competitive performance of projected causal estimates with attribute-specific estimators.

Problem

• causal inference
• high-dimensional treatments
• treatment effect estimation
• text interventions
• moment balancing

Innovation

• Causal Risk Minimization
• High-Dimensional Treatments
• Moment Balancing
• Treatment Projection
• Causal Inference