End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics. Unfortunately, this flexibility comes at the cost of understanding the dynamical system, for which ODEs are used ubiquitously. Further, experimental data are collected under various conditions (inputs), such as treatments, or grouped in some way, such as part of sub-populations. Understanding the effects of these system inputs on system outputs is crucial to have any meaningful model of a dynamical system. To that end, we propose a structured latent ODE model that explicitly captures system input variations within its latent representation. Building on a static latent variable specification, our model learns (independent) stochastic factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space. This approach provides actionable modeling through the controlled generation of time-series data for novel input combinations (or perturbations). Additionally, we propose a flexible approach for quantifying uncertainties, leveraging a quantile regression formulation. Results on challenging biological datasets show consistent improvements over competitive baselines in the controlled generation of observational data and inference of biologically meaningful system inputs.
|Original language||English (US)|
|Title of host publication||38th Conference on Uncertainty in Artificial Intelligence, UAI 2022|
|Publisher||ML Research Press|
|Number of pages||10|
|State||Published - Jan 1 2022|
Bibliographical noteKAUST Repository Item: Exported on 2023-07-17
Acknowledgements: The authors would like to thank the anonymous reviewers for their insightful comments. This research was supported by NIH/NINDS 1R61NS120246, NIH/NIDDK R01-DK123062, and ONR N00014-18-1-2871-P00002-3.