🤖 AI Summary
This work addresses the challenge that existing proximal causal inference methods cannot identify the interventional joint distribution involving all proxy variables. To overcome this limitation, we propose, for the first time, an extended bridge function and establish a theoretical identifiability result for this distribution, integrating it into a kernel-based proximal causal inference framework. By introducing a synergistic mechanism between the interventional kernel and the extended bridge function, we derive novel identification conditions for the interventional joint distribution and develop a general, computable kernelized proximal identification algorithm. This contribution not only broadens the theoretical foundations of proximal causal inference but also provides a practical tool for estimating causal effects in settings with high-dimensional proxy variables.
📝 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.