(173ah) Discovering Latent Effective Parameters from Heterogeneous Populations

We introduce a data-driven framework that discovers and disentangles latent parameters [1] given trajectories of individuals in heterogeneous populations described by parameter dependent ordinary and stochastic differential equations. In our framework we assume that we have access to trajectories from a black box model that does not provide any information of the effective parameters that describe the dynamics of the individual in the heterogeneous population. Our framework involves (a) using the manifold learning technique Diffusion Maps [2] to discover the effective inputs that characterize the individual’s behavior and (b) using Conformal Autoencoders Neural Networks [1] as well as the Jointly Smooth Function[3] algorithm to disentangle the latent heterogeneity parameters from the remaining degrees of freedom common. We illustrate that the identified latent parameters are one-to-one with the true heterogeneity of the population parameter. We consider synthetic data generated from parameter dependent ordinary and stochastic differential equations as a proof of concept. We also illustrate the ability of our scheme to identify the latent parameter given experimental trajectories of cellular data with applications to aging.

[1] Evangelou, N., Wichrowski, N. J., Kevrekidis, G. A., Dietrich, F., Kooshkbaghi, M., McFann, S., & Kevrekidis, I. G. (2021). On the Parameter Combinations That Matter and on Those That do Not. arXiv preprint arXiv:2110.06717.

[2] Coifman, R. R., & Lafon, S. (2006). Diffusion maps. Applied and computational harmonic analysis, 21(1), 5-30.

[3] Dietrich, F., Yair, O., Mulayoff, R., Talmon, R., & Kevrekidis, I. G. (2022). Spectral discovery of jointly smooth features for multimodal data. SIAM Journal on Mathematics of Data Science, 4(1), 410-430.