Causal Inference with Noisy and Missing Covariates via Matrix Factorization

TL;DR

This paper introduces a matrix factorization approach to improve causal inference accuracy when confounder measurements are noisy or incomplete, demonstrating theoretical bounds and empirical effectiveness.

Contribution

It proposes a novel matrix factorization method to infer confounders from noisy and missing data, enhancing causal effect estimation.

Findings

The method reduces bias in causal effect estimates.

It provides theoretical error bounds and consistency guarantees.

Empirical results show improved performance on synthetic and clinical data.

Abstract

Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the bias caused by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates, a flexible and principled framework that adapts to missing values, accommodates a wide variety of data types, and can augment many causal inference methods. We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing. We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data.