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Contrastive Balancing Representation Learning for Heterogeneous Dose-Response Curves Estimation

Minqin Zhu, Anpeng Wu, Haoxuan Li, Ruoxuan Xiong, Bo Li, Xiaoqing Yang, Xuan Qin, Peng Zhen, Jiecheng Guo, Fei Wu, Kun Kuang

TL;DR

This paper theoretically demonstrate the importance of the balancing and prognostic representations for unbiased estimation of the heterogeneous dose-response curves and proposes a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves without losing the continuity of treatments.

Abstract

Estimating the individuals' potential response to varying treatment doses is crucial for decision-making in areas such as precision medicine and management science. Most recent studies predict counterfactual outcomes by learning a covariate representation that is independent of the treatment variable. However, such independence constraints neglect much of the covariate information that is useful for counterfactual prediction, especially when the treatment variables are continuous. To tackle the above issue, in this paper, we first theoretically demonstrate the importance of the balancing and prognostic representations for unbiased estimation of the heterogeneous dose-response curves, that is, the learned representations are constrained to satisfy the conditional independence between the covariates and both of the treatment variables and the potential responses. Based on this, we propose a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves without losing the continuity of treatments. Extensive experiments are conducted on synthetic and real-world datasets demonstrating that our proposal significantly outperforms previous methods.

Contrastive Balancing Representation Learning for Heterogeneous Dose-Response Curves Estimation

TL;DR

This paper theoretically demonstrate the importance of the balancing and prognostic representations for unbiased estimation of the heterogeneous dose-response curves and proposes a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves without losing the continuity of treatments.

Abstract

Estimating the individuals' potential response to varying treatment doses is crucial for decision-making in areas such as precision medicine and management science. Most recent studies predict counterfactual outcomes by learning a covariate representation that is independent of the treatment variable. However, such independence constraints neglect much of the covariate information that is useful for counterfactual prediction, especially when the treatment variables are continuous. To tackle the above issue, in this paper, we first theoretically demonstrate the importance of the balancing and prognostic representations for unbiased estimation of the heterogeneous dose-response curves, that is, the learned representations are constrained to satisfy the conditional independence between the covariates and both of the treatment variables and the potential responses. Based on this, we propose a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves without losing the continuity of treatments. Extensive experiments are conducted on synthetic and real-world datasets demonstrating that our proposal significantly outperforms previous methods.
Paper Structure (21 sections, 15 equations, 3 figures, 3 tables)

This paper contains 21 sections, 15 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Dose-Response Curve Estimation.
  4. Contrastive Representation Learning.
  5. Problem Setup
  6. Motivation
  7. Method
  8. Contrastive Regularizer
  9. Partial Distance Measure.
  10. CRNet
  11. Experiments
  12. Experimental Setup
  13. Synthetic Data Generation.
  14. Semi-synthetic Data Generation.
  15. Baselines and Evaluation.
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Contrastive regularizer. The $n$ covariates $\mathbf{X}$ undergo a transformation via the encoder $\Phi$ resulting in $\Phi(\mathbf{X})$. $\Phi(\mathbf{X})$ transforms to $g(\Phi({\mathbf{X}}))$ through projection head $g$chen2020simple. $g(\Phi({\mathbf{X}}))$ is directly constrained by $\ell^{CR}_{\Phi}(\mathbf{X}, \mathbf{T})$. To simplify notation, we use $\Phi(\mathbf{X})$ in the context to represent $g({\Phi(\mathbf{X}}))$. $D_{\Phi({\mathbf{X}})}$ and $D_{\Phi({\mathbf{X}'})}$ are partial distance measure of positive/negative samples szekely2014partial.
  • Figure 2: CRNet. For the training procedure, the representations $\Phi(\mathbf{X})$ constrained by contrastive loss $\ell^{CR}_{\Phi}(\mathbf{X},\mathbf{T})$ are concatenated and input to MLPs $h$ to obtain the estimated outcome $\hat{Y}$ by the final loss in Eq. (\ref{['finalloss']}). The final objective is to minimize the loss. For the inference procedure, the estimated HDRC is obtained by $h(\Phi(\mathbf{X}),\Psi(\mathbf{T}))$.
  • Figure 3: The sensitivity experiments (MISE $\pm$ SD) for the value of $\alpha$ and the dimension of double balancing representation $K_{\Phi({X})}$ on IHDP-1 and News-16 datasets.

Theorems & Definitions (3)

  • Definition 1: Balancing Representation Condition
  • Definition 2: Prognostic Representation Condition
  • Definition 3: Double Balancing Representation Condition