Minimax Structured Neural Tangent Kernel in Estimating Average Treatment Effect Confounded by Image Covariate Público

Abstract

Estimating the average treatment effect (ATE) in observational studies is challenging, particularly when confounding arises from high-dimensional image co-variates. Traditional inverse probability weighting (IPW) methods could fall under the issue of the reliance on knowledge of propensity scores and their high variability in estimation caused by extreme propensity values. Thus, a minimax optimization framework is proposed that minimizes the maximum bias in treatment effect estimation. This thesis aims to propose a Minimax structured Neural Tangent Kernel to minimize the maximal of the bias. To simulate real-world conditions where direct patient data is limited, three semi-synthetic data generation frameworks are introduced—ranging from simple image brightness measures to more complex labeling and filtering techniques—to mimic treatment assignments and outcomes based on lung X-ray images. Empirical evaluations using those semi-synthetic data demonstrate that these advanced techniques yield estimates closely aligned with the true ATE, highlighting their promise for robust causal inference in complex, image-driven settings. 

Table of Contents

Contents

1 Introduction 1

1.1 EmpiricalProblem ............................ 3

1.2 OverviewofChapters........................... 4

2 Semi-Synthetic Data Generation 6

2.1 Framework1:ASimpleOne....................... 6

2.2 Framework2:Labeling.......................... 8

2.3 Framework3:ImageFiltering ...................... 10

3 Inverse Probability Weighting 13

3.1 IPWI:StandardIPWwithTruePropensityScores . . . . . . . . . . 13

3.2 IPW II: Logistic Regression Estimation of Propensity Scores . . . . . 14

3.3 IPWIII:WeightedPixelbyLassoRegression . . . . . . . . . . . . . 15

4 A Minimax Approach 18

4.1 LinearConditionalMeanFunctions................... 18

5 RBF Kernelized Minimax Approach 22

5.1 RBF Kernel and MinimaxApproach .................. 22

6 Neural Tangent Kernel Mini-Max 25

6.1 NeuralNetworkStructure ........................ 25

6.2 NTK-BasedMinimax........................... 26

6.3 TheAIPWEstimator........................... 27

6.4 Non-ParametricVarianceEstimation .................. 28

6.5 Implementation.............................. 29

7 Oracle and Non-Oracle Estimators 30

7.1 OracleEstimators............................. 30

7.2 Non-OracleEstimators.......................... 31

8 Empirical Performances 33

8.1 EvaluationTechniques .......................... 34

8.2 Results................................... 35

9 Discussion and Conclusion 37

9.1 InterpretationofFindings ........................ 37

9.1.1 TableResults ........................... 37

9.1.2 VisualResults........................... 38

9.2 Discussion................................. 40

9.3 FutureWork................................ 41

Appendix A Plots of Simulation Results 42

Appendix B Parameter Tuning Selection 50

Bibliography 53 

About this Honors Thesis

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School	Emory College
Department	Quantitative Science
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Computer Science Statistics Applied Mathematics
Palavra-chave	Average Treatment Effect Neural Tangent Kernel Minimax Optimization Lung X-ray Images Image Confounding Variable Inverse Probability Weighting Balancing Weights
Committee Chair / Thesis Advisor	David Hirshberg, Emory University
Committee Members	Abhishek Ananth, Emory University Kevin McAlister, Emory University

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