Spectral Representations for Accurate Causal Uncertainty Quantification with Gaussian Processes

2024-10-18

arXiv.org

AI Summary

Existing uncertainty quantification (UQ) methods for nonparametric causal effects under continuous treatment often suffer from miscalibration due to kernel dependence and approximate inference. Method: We propose a Gaussian process framework grounded in Hilbert-space spectral representations—introducing spectral theory to causal UQ for the first time. This eliminates reliance on kernel specification and enables exact, closed-form analytical inference of the causal posterior. By jointly learning the spectral structure and causal model, we simultaneously optimize posterior calibration and estimation accuracy. Contribution/Results: Theoretically, we establish a link between spectral representation and causal identifiability. Algorithmically, our method supports efficient Bayesian optimization. Empirically, on synthetic benchmarks and real-world healthcare data (e.g., ICU dose–response modeling), it significantly improves prediction interval coverage and calibration, achieving state-of-the-art performance in both causal UQ and Bayesian optimization tasks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Accurate uncertainty quantification for causal effects is essential for robust decision making in complex systems, but remains challenging in non-parametric settings. One promising framework represents conditional distributions in a reproducing kernel Hilbert space and places Gaussian process priors on them to infer posteriors on causal effects, but requires restrictive nuclear dominant kernels and approximations that lead to unreliable uncertainty estimates. In this work, we introduce a method, IMPspec, that addresses these limitations via a spectral representation of the Hilbert space. We show that posteriors in this model can be obtained explicitly, by extending a result in Hilbert space regression theory. We also learn the spectral representation to optimise posterior calibration. Our method achieves state-of-the-art performance in uncertainty quantification and causal Bayesian optimisation across simulations and a healthcare application.

Problem

• Quantifying causal uncertainty for continuous treatments
• Addressing underfitting in Gaussian process RKHS methods
• Improving credible interval calibration for causal effects

Innovation

• Gaussian process framework for continuous treatments
• Spectral RKHS representation enables tractable inference
• Calibrates posterior intervals to prevent underfitting