Interventional Processes for Causal Uncertainty Quantification
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913178317750272 |
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| author | Dance, Hugh Orbanz, Peter Gretton, Arthur |
| author_facet | Dance, Hugh Orbanz, Peter Gretton, Arthur |
| contents | Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_14483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interventional Processes for Causal Uncertainty Quantification Dance, Hugh Orbanz, Peter Gretton, Arthur Machine Learning Methodology Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation. |
| title | Interventional Processes for Causal Uncertainty Quantification |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2410.14483 |