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Conformal Diffusion Models for Individual Treatment Effect Estimation and Inference

Hengrui Cai, Huaqing Jin, Lexin Li

TL;DR

A novel conformal diffusion model-based approach that integrates the highly flexible diffusion modeling, the model-free statistical inference paradigm of conformal inference, along with propensity score and covariate local approximation that tackle distributional shifts is proposed.

Abstract

Estimating treatment effects from observational data is of central interest across numerous application domains. Individual treatment effect offers the most granular measure of treatment effect on an individual level, and is the most useful to facilitate personalized care. However, its estimation and inference remain underdeveloped due to several challenges. In this article, we propose a novel conformal diffusion model-based approach that addresses those intricate challenges. We integrate the highly flexible diffusion modeling, the model-free statistical inference paradigm of conformal inference, along with propensity score and covariate local approximation that tackle distributional shifts. We unbiasedly estimate the distributions of potential outcomes for individual treatment effect, construct an informative confidence interval, and establish rigorous theoretical guarantees. We demonstrate the competitive performance of the proposed method over existing solutions through extensive numerical studies.

Conformal Diffusion Models for Individual Treatment Effect Estimation and Inference

TL;DR

A novel conformal diffusion model-based approach that integrates the highly flexible diffusion modeling, the model-free statistical inference paradigm of conformal inference, along with propensity score and covariate local approximation that tackle distributional shifts is proposed.

Abstract

Estimating treatment effects from observational data is of central interest across numerous application domains. Individual treatment effect offers the most granular measure of treatment effect on an individual level, and is the most useful to facilitate personalized care. However, its estimation and inference remain underdeveloped due to several challenges. In this article, we propose a novel conformal diffusion model-based approach that addresses those intricate challenges. We integrate the highly flexible diffusion modeling, the model-free statistical inference paradigm of conformal inference, along with propensity score and covariate local approximation that tackle distributional shifts. We unbiasedly estimate the distributions of potential outcomes for individual treatment effect, construct an informative confidence interval, and establish rigorous theoretical guarantees. We demonstrate the competitive performance of the proposed method over existing solutions through extensive numerical studies.
Paper Structure (19 sections, 3 theorems, 49 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 19 sections, 3 theorems, 49 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Problem setup
  4. Individual treatment effects
  5. Conformal inference with sample splitting
  6. Conformal diffusion models for ITE
  7. Modeling potential outcome distribution via deep generative learning
  8. Adjusting covariate distributional shifts
  9. Weighted conformal inference for ITE
  10. Theory
  11. Simulation studies
  12. Simulation setup
  13. Comparison with alternative solutions
  14. Sensitivity analysis
  15. Data application
  16. ...and 4 more sections

Key Result

Theorem 1

Let $n_{\rm train} = \left| \mathcal{D}_{\text{train}}\right|$, and $n_{\rm cal} = \left|\mathcal{D}_{\text{cal}}\right|$. Let $\widehat{C}(X)$ be the resulting confidence interval from Algorithm alg:1. Then under Assumptions cons to bnd_weights, we have that, Furthermore, if $\lim_{n_{\rm train}, n_{\rm cal} \rightarrow \infty} \mathbb{E}\left| {\widehat{w} (X)}- {w(X) }\right|=0$, where $\wideh

Figures (4)

  • Figure 1: Empirical coverage probability of the 95% interval estimate for ITE (left column), and the corresponding interval length (right column) for the homoscedastic case, with a standard Gaussian, Gamma, and non-local moment noise, and the covariate dimension $d=10$ (upper row) and $d=300$ (lower row). Six methods: CDM (ours), CDM-nolocal, MLP, CQR, naive, and causal forest methods, are compared. The red horizontal line indicates the nominal coverage probability $0.95$.
  • Figure 2: Empirical coverage probability of the 95% interval estimate for ITE (left column), and the corresponding interval length (right column) for the heteroscedastic case, with a standard Gaussian, Gamma, and non-local moment noise, and the covariate dimension $d=10$ (upper row) and $d=300$ (lower row). Six methods: CDM (ours), CDM-nolocal, MLP, CQR, naive, and causal forest methods, are compared. The red horizontal line indicates the nominal coverage probability $0.95$.
  • Figure 3: Empirical coverage probability of the 95% interval estimate for ITE (left column), and the corresponding interval length (right column) for the homoscedastic case, with a standard Gaussian noise, and the covariate dimension $d=10$ (upper row) and $d=300$ (lower row), under the varying number of random samples $M$ and the bandwidth factor $c$.
  • Figure 4: Empirical coverage probability of the 95% interval estimate for ITE (left column), and the corresponding interval length (right column) for the heteroscedastic case, with a standard Gaussian noise, and the covariate dimension $d=10$ (upper row) and $d=300$ (lower row), under the varying number of random samples $M$ and the bandwidth factor $c$.

Theorems & Definitions (3)

  • Theorem 1
  • Lemma 1
  • Lemma 2