Hybrid Square Neural ODE Causal Modeling
Bob Junyi Zou Matthew E. Levine Dessi P. Zaharieva Ramesh Johari Emily B. Fox
Hybrid models combine mechanistic ODE-based dynamics with flexible and
expressive neural network components. Such models have grown rapidly in
popularity, especially in scientific domains where such ODE-based modeling
offers important interpretability and validated causal grounding (e.g., for
counterfactual reasoning). The incorporation of mechanistic models also
provides inductive bias in standard blackbox modeling approaches, critical when
learning from small datasets or partially observed, complex systems.
Unfortunately, as hybrid models become more flexible, the causal grounding
provided by the mechanistic model can quickly be lost. We address this problem
by leveraging another common source of domain knowledge: ranking of treatment
effects for a set of interventions, even if the precise treatment effect is
unknown. We encode this information in a causal loss that we combine with the
standard predictive loss to arrive at a hybrid loss that biases our learning
towards causally valid hybrid models. We demonstrate our ability to achieve a
win-win -- state-of-the-art predictive performance and causal validity -- in
the challenging task of modeling glucose dynamics during exercise.