Modeling how individuals evolve over time is a fundamental problem in the
natural and social sciences. However, existing datasets are often
cross-sectional with each individual observed only once, making it impossible
to apply traditional time-series methods...
Motivated by the study of human
aging, we present an interpretable latent-variable model that learns temporal
dynamics from cross-sectional data. Our model represents each individual's
features over time as a nonlinear function of a low-dimensional,
linearly-evolving latent state. We prove that when this nonlinear function is
constrained to be order-isomorphic, the model family is identifiable solely
from cross-sectional data provided the distribution of time-independent
variation is known. On the UK Biobank human health dataset, our model
reconstructs the observed data while learning interpretable rates of aging
associated with diseases, mortality, and aging risk factors.