# Entropy Balancing for Continuous Treatments

arXiv: https://arxiv.org/abs/2001.06281 · HTML: https://mlsanity.com/paper/2001.06281/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 12 of 12)

- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [Causal Foundation Models with Continuous Treatments](https://mlsanity.com/paper/2605.15133/) (2026)
- [Sources of Gain: Decomposing Performance in Conditional Average Dose Response Estimation](https://mlsanity.com/paper/2406.08206/) (2024)
- [Policy Learning for Optimal Individualized Dose Intervals](https://mlsanity.com/paper/2202.12234/) (2022)
- [Generalized Balancing Weights via Deep Neural Networks](https://mlsanity.com/paper/2211.07533/) (2022)
- [Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression](https://mlsanity.com/paper/2604.13410/) (2026)
- [Learning sources of variability from high-dimensional observational studies](https://mlsanity.com/paper/2307.13868/) (2023)
- [Temporal-Spatial Entropy Balancing for Causal Continuous Treatment-Effect Estimation](https://mlsanity.com/paper/2312.08670/) (2023)
- [Kernel-Based Functional Balancing for Causal Inference with Compositional Treatments](https://mlsanity.com/paper/2606.17308/) (2026)
- [Causal Generalization of Continuous Treatment Effects under Covariate Shift](https://mlsanity.com/paper/2608.19383/) (2026)

## Abstract (arXiv)

This paper introduces entropy balancing for continuous treatments (EBCT) by extending the original entropy balancing methodology of Hainm"uller (2012). In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem. EBCT weights reliably eradicate Pearson correlations between covariates and the continuous treatment variable. This is the case even when other methods based on the generalized propensity score tend to yield insufficient balance due to strong selection into different treatment intensities. Moreover, the optimization procedure is more successful in avoiding extreme weights attached to a single unit. Extensive Monte-Carlo simulations show that treatment effect estimates using EBCT display similar or lower bias and uniformly lower root mean squared error. These properties make EBCT an attractive method for the evaluation of continuous treatments.