Function Driven Diffusion for Personalized Counterfactual Inference
This work addresses personalized counterfactual inference, particularly for drug trials, by providing a method to estimate individualized treatment effects when long-term outcomes cannot be observed, which is incremental as it builds on diffusion-based approaches.
The paper tackles the problem of constructing diffusion operators for high-dimensional data to address counterfactual functions like individualized treatment effectiveness, proposing a new diffusion metric that captures local geometry and variance directions, and validates it on synthetic and real-world clinical trials to create personalized treatment benefit notions.
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.