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Causal Effect Estimation Using Random Hyperplane Tessellations

Abhishek Dalvi, Neil Ashtekar, Vasant Honavar

TL;DR

This work proves that the RHPT representation is an approximate balancing score -- thus maintaining the strong ignorability assumption -- and provides empirical evidence for this claim and reports results of extensive experiments showing that matching using RHPT outperforms traditional matching techniques and is competitive with state-of-the-art deep learning methods for causal effect estimation.

Abstract

Matching is one of the simplest approaches for estimating causal effects from observational data. Matching techniques compare the observed outcomes across pairs of individuals with similar covariate values but different treatment statuses in order to estimate causal effects. However, traditional matching techniques are unreliable given high-dimensional covariates due to the infamous curse of dimensionality. To overcome this challenge, we propose a simple, fast, yet highly effective approach to matching using Random Hyperplane Tessellations (RHPT). First, we prove that the RHPT representation is an approximate balancing score -- thus maintaining the strong ignorability assumption -- and provide empirical evidence for this claim. Second, we report results of extensive experiments showing that matching using RHPT outperforms traditional matching techniques and is competitive with state-of-the-art deep learning methods for causal effect estimation. In addition, RHPT avoids the need for computationally expensive training of deep neural networks.

Causal Effect Estimation Using Random Hyperplane Tessellations

TL;DR

This work proves that the RHPT representation is an approximate balancing score -- thus maintaining the strong ignorability assumption -- and provides empirical evidence for this claim and reports results of extensive experiments showing that matching using RHPT outperforms traditional matching techniques and is competitive with state-of-the-art deep learning methods for causal effect estimation.

Abstract

Matching is one of the simplest approaches for estimating causal effects from observational data. Matching techniques compare the observed outcomes across pairs of individuals with similar covariate values but different treatment statuses in order to estimate causal effects. However, traditional matching techniques are unreliable given high-dimensional covariates due to the infamous curse of dimensionality. To overcome this challenge, we propose a simple, fast, yet highly effective approach to matching using Random Hyperplane Tessellations (RHPT). First, we prove that the RHPT representation is an approximate balancing score -- thus maintaining the strong ignorability assumption -- and provide empirical evidence for this claim. Second, we report results of extensive experiments showing that matching using RHPT outperforms traditional matching techniques and is competitive with state-of-the-art deep learning methods for causal effect estimation. In addition, RHPT avoids the need for computationally expensive training of deep neural networks.
Paper Structure (19 sections, 12 equations, 3 figures, 4 tables)

This paper contains 19 sections, 12 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Definition
  4. Locality Sensitive hashing
  5. Random Hyper-Plane Tessellations (RHPT)
  6. Controlling for Confounding Covariates
  7. Causal Effect Estimation Using Random Hyperplane Tessellations
  8. Approximate Balancing Scores using RHPT
  9. Empirical evidence that RHPT yields approximate balancing scores
  10. Uncertainty in causal estimates using RHPT matching
  11. Experiments
  12. Evaluation Metrics
  13. Data sets
  14. News
  15. HC-MNIST
  16. ...and 4 more sections

Figures (3)

  • Figure 1: An example of a Random Hyperplane Tessellation (RHPT) for a set of points in a two-dimensional space from RHPT_figure_cite. Three hyperplanes -- indicated by dashed lines -- are used to construct a three-dimensional binary hash code for each point. The color of each point represents its binary hash code: red represents $101$, black represents $100$, etc.
  • Figure 2: Error of propensity score predictions $\psi$ across various RHPT embedding dimensionalities. Means and confidence intervals are computed over 100 instantiations of RHPT on a single draw of the synthetic data. Lower $\psi$ favors ignorability.
  • Figure 3: Estimated ATE using RHPT on one instantiation of the synthetic dataset with various hash dimensions, each over 100 randomized runs. Higher dimensionality embeddings result in more reliable estimates.