# Deep learning and differential equations for modeling changes in individual-level latent dynamics between observation periods

arXiv: https://arxiv.org/abs/2202.07403 · HTML: https://mlsanity.com/paper/2202.07403/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 71 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)
- [Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder](https://mlsanity.com/paper/2102.01331/) (2021)
- [DiffEqFlux.jl - A Julia Library for Neural Differential Equations](https://mlsanity.com/paper/1902.02376/) (2019)
- [Deep dynamic modeling with just two time points: Can we still allow for individual trajectories?](https://mlsanity.com/paper/2012.00634/) (2020)
- [Using Differentiable Programming for Flexible Statistical Modeling](https://mlsanity.com/paper/2012.05722/) (2020)

## Built on by (most cited first, 1 of 1)

- [A statistical approach to latent dynamic modeling with differential equations](https://mlsanity.com/paper/2311.16286/) (2023)

## Abstract (arXiv)

When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction, and differential equations for dynamic modeling of individual-level trajectories. However, such approaches so far assume that parameters of individual-level dynamics are constant throughout the observation period. Motivated by an application from psychological resilience research, we propose an extension where different sets of differential equation parameters are allowed for observation sub-periods. Still, estimation for intra-individual sub-periods is coupled for being able to fit the model also with a relatively small dataset. We subsequently derive prediction targets from individual dynamic models of resilience in the application. These serve as interpretable resilience-related outcomes, to be predicted from characteristics of individuals, measured at baseline and a follow-up time point, and selecting a small set of important predictors. Our approach is seen to successfully identify individual-level parameters of dynamic models that allows us to stably select predictors, i.e., resilience factors. Furthermore, we can identify those characteristics of individuals that are the most promising for updates at follow-up, which might inform future study design. This underlines the usefulness of our proposed deep dynamic modeling approach with changes in parameters between observation sub-periods.