# Inferring Multidimensional Rates of Aging from Cross-Sectional Data

arXiv: https://arxiv.org/abs/1807.04709 · HTML: https://mlsanity.com/paper/1807.04709/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

## Built on by (most cited first, 9 of 9)

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- [Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data](https://mlsanity.com/paper/2202.09463/) (2022)
- [Learning Disease Progression Models That Capture Health Disparities](https://mlsanity.com/paper/2412.16406/) (2024)
- [Modeling differential rates of aging using routine laboratory data; Implications for morbidity and health care expenditure](https://mlsanity.com/paper/2103.09574/) (2021)
- [Interpretable machine learning for high-dimensional trajectories of aging health](https://mlsanity.com/paper/2105.03410/) (2021)
- [Variational Sampling of Temporal Trajectories](https://mlsanity.com/paper/2403.11418/) (2024)

## Abstract (arXiv)

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.