# Kernel Optimal Orthogonality Weighting: A Balancing Approach to Estimating Effects of Continuous Treatments

arXiv: https://arxiv.org/abs/1910.11972 · HTML: https://mlsanity.com/paper/1910.11972/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [End-to-End Balancing for Causal Continuous Treatment-Effect Estimation](https://mlsanity.com/paper/2107.13068/) (2021)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Policy Learning for Optimal Individualized Dose Intervals](https://mlsanity.com/paper/2202.12234/) (2022)
- [De-confounding Representation Learning for Counterfactual Inference on Continuous Treatment via Generative Adversarial Network](https://mlsanity.com/paper/2307.12625/) (2023)
- [Fast Uncertainty Quantification for Kernel-Based Estimators in Large-Scale Causal Inference](https://mlsanity.com/paper/2603.13662/) (2026)

## Abstract (arXiv)

Many scientific questions require estimating the effects of continuous treatments. Outcome modeling and weighted regression based on the generalized propensity score are the most commonly used methods to evaluate continuous effects. However, these techniques may be sensitive to model misspecification, extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality Weighting (KOOW), a convex optimization-based method, for estimating the effects of continuous treatments. KOOW finds weights that minimize the worst-case penalized functional covariance between the continuous treatment and the confounders. By minimizing this quantity, KOOW successfully provides weights that orthogonalize confounders and the continuous treatment, thus providing optimal covariate balance, while controlling for extreme weights. We valuate its comparative performance in a simulation study. Using data from the Women's Health Initiative observational study, we apply KOOW to evaluate the effect of red meat consumption on blood pressure.