Identifying Interventional Joint Distributions via Extended Bridge Functions

TL;DR

This paper introduces extended bridge functions to identify joint interventional distributions in proximal causal inference, enabling retention of all relevant proxy variables and generalizing existing methods through kernel operations.

Contribution

It proposes a novel framework for identifying joint interventional distributions using extended bridge functions and kernel-based algorithms, expanding the scope of proximal causal inference.

Findings

Derived new identification results for joint interventional distributions.

Developed a generalized kernel-based framework for proximal identification.

Enhanced the ability to retain all relevant proxy variables in causal analysis.

Abstract

Existing identification results in proximal causal inference often focus on marginal interventional distributions using standard outcome or treatment bridge functions. These methods do not generally identify joint interventional distributions that contain all proxy variables that were used to define the corresponding bridge functions. In many applications, however, these joint interventional distributions are a natural target of interest. We introduce extended bridge functions and derive new identification results for joint interventional distributions that may retain all relevant proxy variables. We then apply these results to proximal identification algorithms, where interventional kernels naturally arise as intermediate objects, yielding a generalized framework based on kernel operations.