# Variational Mixtures of ODEs for Inferring Cellular Gene Expression Dynamics

arXiv: https://arxiv.org/abs/2207.04166 · HTML: https://mlsanity.com/paper/2207.04166/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 9 Jul 2022.

## Builds on (most cited first, 6 of 6)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ODE2VAE: Deep generative second order ODEs with Bayesian neural networks](https://mlsanity.com/paper/1905.10994/) (2019)
- [Scalable Variational Inference for Dynamical Systems](https://mlsanity.com/paper/1705.07079/) (2017)
- [STRODE: Stochastic Boundary Ordinary Differential Equation](https://mlsanity.com/paper/2107.08273/) (2021)

## Built on by (most cited first, 2 of 2)

- [Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis](https://mlsanity.com/paper/2503.11347/) (2025)
- [MoCLIM: Towards Accurate Cancer Subtyping via Multi-Omics Contrastive Learning with Omics-Inference Modeling](https://mlsanity.com/paper/2308.09725/) (2023)

## Abstract (arXiv)

A key problem in computational biology is discovering the gene expression changes that regulate cell fate transitions, in which one cell type turns into another. However, each individual cell cannot be tracked longitudinally, and cells at the same point in real time may be at different stages of the transition process. This can be viewed as a problem of learning the behavior of a dynamical system from observations whose times are unknown. Additionally, a single progenitor cell type often bifurcates into multiple child cell types, further complicating the problem of modeling the dynamics. To address this problem, we developed an approach called variational mixtures of ordinary differential equations. By using a simple family of ODEs informed by the biochemistry of gene expression to constrain the likelihood of a deep generative model, we can simultaneously infer the latent time and latent state of each cell and predict its future gene expression state. The model can be interpreted as a mixture of ODEs whose parameters vary continuously across a latent space of cell states. Our approach dramatically improves data fit, latent time inference, and future cell state estimation of single-cell gene expression data compared to previous approaches.