Function Driven Diffusion for Personalized Counterfactual Inference

TL;DR

This paper introduces a new diffusion metric that combines data geometry and function variance to improve counterfactual inference, especially in personalized medicine scenarios like drug trials.

Contribution

It proposes a novel diffusion metric $K_F$ that captures local geometry and function variance for personalized counterfactual analysis.

Findings

Validated on synthetic and real clinical trial data.

Enabled individualized benefit assessment from treatments.

Improved counterfactual inference accuracy.

Abstract

We consider the problem of constructing diffusion operators high dimensional data $X$ to address counterfactual functions $F$, such as individualized treatment effectiveness. We propose and construct a new diffusion metric $K_F$ that captures both the local geometry of $X$ and the directions of variance of $F$. The resulting diffusion metric is then used to define a localized filtration of $F$ and answer counterfactual questions pointwise, particularly in situations such as drug trials where an individual patient's outcomes cannot be studied long term both taking and not taking a medication. We validate the model on synthetic and real world clinical trials, and create individualized notions of benefit from treatment.