# Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights

arXiv: https://arxiv.org/abs/2406.19195 · HTML: https://mlsanity.com/paper/2406.19195/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 80 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Builds on (most cited first, 30 of 39)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Wasserstein-2 Generative Networks](https://mlsanity.com/paper/1909.13082/) (2019)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Unified Optimal Transport Framework for Universal Domain Adaptation](https://mlsanity.com/paper/2210.17067/) (2022)
- [The Information Geometry of Mirror Descent](https://mlsanity.com/paper/1310.7780/) (2013)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Optimal Transport: Fast Probabilistic Approximation with Exact Solvers](https://mlsanity.com/paper/1802.05570/) (2018)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Gromov-Wasserstein Factorization Models for Graph Clustering](https://mlsanity.com/paper/1911.08530/) (2019)
- [Learning to Re-weight Examples with Optimal Transport for Imbalanced Classification](https://mlsanity.com/paper/2208.02951/) (2022)
- [Semi-relaxed Gromov-Wasserstein divergence with applications on graphs](https://mlsanity.com/paper/2110.02753/) (2021)
- [PatchCT: Aligning Patch Set and Label Set with Conditional Transport for Multi-Label Image Classification](https://mlsanity.com/paper/2307.09066/) (2023)
- [Long-Term Effect Estimation with Surrogate Representation](https://mlsanity.com/paper/2008.08236/) (2020)
- [Entropy Balancing for Continuous Treatments](https://mlsanity.com/paper/2001.06281/) (2020)
- [Long-term Causal Effects Estimation via Latent Surrogates Representation Learning](https://mlsanity.com/paper/2208.04589/) (2022)
- [Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding](https://mlsanity.com/paper/2302.10625/) (2023)
- [Adversarially Balanced Representation for Continuous Treatment Effect Estimation](https://mlsanity.com/paper/2312.10570/) (2023)
- [Generalization bounds and algorithms for estimating conditional average treatment effect of dosage](https://mlsanity.com/paper/2205.14692/) (2022)

## Built on by (most cited first, 4 of 4)

- [Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning](https://mlsanity.com/paper/2505.05192/) (2025)
- [Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combination](https://mlsanity.com/paper/2502.18960/) (2025)
- [Long-term Causal Inference via Modeling Sequential Latent Confounding](https://mlsanity.com/paper/2502.18994/) (2025)
- [Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects](https://mlsanity.com/paper/2604.00915/) (2026)

## Abstract (arXiv)

Long-term treatment effect estimation is a significant but challenging problem in many applications. Existing methods rely on ideal assumptions, such as no unobserved confounders or binary treatment, to estimate long-term average treatment effects. However, in numerous real-world applications, these assumptions could be violated, and average treatment effects are insufficient for personalized decision-making. In this paper, we address a more general problem of estimating long-term Heterogeneous Dose-Response Curve (HDRC) while accounting for unobserved confounders and continuous treatment. Specifically, to remove the unobserved confounders in the long-term observational data, we introduce an optimal transport weighting framework to align the long-term observational data to an auxiliary short-term experimental data. Furthermore, to accurately predict the heterogeneous effects of continuous treatment, we establish a generalization bound on counterfactual prediction error by leveraging the reweighted distribution induced by optimal transport. Finally, we develop a long-term HDRC estimator building upon the above theoretical foundations. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our approach.