# Observational-Interventional Priors for Dose-Response Learning

arXiv: https://arxiv.org/abs/1605.01573 · HTML: https://mlsanity.com/paper/1605.01573/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2016.

## Built on by (most cited first, 10 of 10)

- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Neural Pharmacodynamic State Space Modeling](https://mlsanity.com/paper/2102.11218/) (2021)
- [Uplift modeling with continuous treatments: A predict-then-optimize approach](https://mlsanity.com/paper/2412.09232/) (2024)
- [A causal intervention framework for synthesizing mobility data and evaluating predictive neural networks](https://mlsanity.com/paper/2311.11749/) (2023)
- [Combining Interventional and Observational Data Using Causal Reductions](https://mlsanity.com/paper/2103.04786/) (2021)
- [Causal Bias Quantification for Continuous Treatments](https://mlsanity.com/paper/2106.09762/) (2021)
- [Prescriptive maintenance with causal machine learning](https://mlsanity.com/paper/2206.01562/) (2022)
- [Nonparametric modeling of the composite effect of multiple nutrients on blood glucose dynamics](https://mlsanity.com/paper/2311.03129/) (2023)
- [Causal-driven attribution (CDA): Estimating channel influence without user-level data](https://mlsanity.com/paper/2512.21211/) (2025)

## Abstract (arXiv)

Controlled interventions provide the most direct source of information for learning causal effects. In particular, a dose-response curve can be learned by varying the treatment level and observing the corresponding outcomes. However, interventions can be expensive and time-consuming. Observational data, where the treatment is not controlled by a known mechanism, is sometimes available. Under some strong assumptions, observational data allows for the estimation of dose-response curves. Estimating such curves nonparametrically is hard: sample sizes for controlled interventions may be small, while in the observational case a large number of measured confounders may need to be marginalized. In this paper, we introduce a hierarchical Gaussian process prior that constructs a distribution over the dose-response curve by learning from observational data, and reshapes the distribution with a nonparametric affine transform learned from controlled interventions. This function composition from different sources is shown to speed-up learning, which we demonstrate with a thorough sensitivity analysis and an application to modeling the effect of therapy on cognitive skills of premature infants.