ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference
Krzysztof Kacprzyk Samuel Holt Jeroen Berrevoets Zhaozhi Qian Mihaela van der Schaar
Inferring unbiased treatment effects has received widespread attention in the
machine learning community. In recent years, our community has proposed
numerous solutions in standard settings, high-dimensional treatment settings,
and even longitudinal settings. While very diverse, the solution has mostly
relied on neural networks for inference and simultaneous correction of
assignment bias. New approaches typically build on top of previous approaches
by proposing new (or refined) architectures and learning algorithms. However,
the end result -- a neural-network-based inference machine -- remains
unchallenged. In this paper, we introduce a different type of solution in the
longitudinal setting: a closed-form ordinary differential equation (ODE). While
we still rely on continuous optimization to learn an ODE, the resulting
inference machine is no longer a neural network. Doing so yields several
advantages such as interpretability, irregular sampling, and a different set of
identification assumptions. Above all, we consider the introduction of a
completely new type of solution to be our most important contribution as it may
spark entirely new innovations in treatment effects in general. We facilitate
this by formulating our contribution as a framework that can transform any ODE
discovery method into a treatment effects method.