Gaussian Processes for Observational Dose-Response Inference
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912046320189440 |
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| author | Dailey, Jake R. |
| author_facet | Dailey, Jake R. |
| contents | We adapt Gaussian processes for estimating the average dose-response function in observational settings, introducing a powerful complement to treatment effect estimation for understanding heterogeneous effects. We incorporate samples from a Gaussian process posterior for the propensity score into a Gaussian process response model using Girard's approach to integrating over uncertainty in training data. We show Girard's method admits a positive-definite kernel, and provide theoretical justification by identifying it with an inner product of kernel mean embeddings. We demonstrate double robustness of our approach under a misspecified response function or propensity score. We characterize and mitigate regularization-induced confounding in Gaussian process response models. We show improvement over other methods for average dose-response function estimation in terms of coverage of the dose-response function and estimation bias, with less sensitivity to misspecification across experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gaussian Processes for Observational Dose-Response Inference Dailey, Jake R. Statistics Theory We adapt Gaussian processes for estimating the average dose-response function in observational settings, introducing a powerful complement to treatment effect estimation for understanding heterogeneous effects. We incorporate samples from a Gaussian process posterior for the propensity score into a Gaussian process response model using Girard's approach to integrating over uncertainty in training data. We show Girard's method admits a positive-definite kernel, and provide theoretical justification by identifying it with an inner product of kernel mean embeddings. We demonstrate double robustness of our approach under a misspecified response function or propensity score. We characterize and mitigate regularization-induced confounding in Gaussian process response models. We show improvement over other methods for average dose-response function estimation in terms of coverage of the dose-response function and estimation bias, with less sensitivity to misspecification across experiments. |
| title | Gaussian Processes for Observational Dose-Response Inference |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2409.17043 |