# Unscrambling disease progression at scale: fast inference of event permutations with optimal transport

arXiv: https://arxiv.org/abs/2410.14388 · HTML: https://mlsanity.com/paper/2410.14388/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 64 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 11 of 11)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosis](https://mlsanity.com/paper/1705.05267/) (2017)
- [Monge, Bregman and Occam: Interpretable Optimal Transport in High-Dimensions with Feature-Sparse Maps](https://mlsanity.com/paper/2302.04065/) (2023)
- [A Hidden Absorbing Semi-Markov Model for Informatively Censored Temporal Data: Learning and Inference](https://mlsanity.com/paper/1612.06007/) (2016)
- [DIVE: A spatiotemporal progression model of brain pathology in neurodegenerative disorders](https://mlsanity.com/paper/1901.03553/) (2019)
- [A Bayesian Approach to Multi-State Hidden Markov Models: Application to Dementia Progression](https://mlsanity.com/paper/1802.02691/) (2018)

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

- [Joint Progression Modeling (JPM): A Probabilistic Framework for Mixed-Pathology Progression](https://mlsanity.com/paper/2512.03475/) (2025)
- [TEMPO: Transformers for Temporal Disease Progression from Cross-Sectional Data](https://mlsanity.com/paper/2604.23368/) (2026)

## Abstract (arXiv)

Disease progression models infer group-level temporal trajectories of change in patients' features as a chronic degenerative condition plays out. They provide unique insight into disease biology and staging systems with individual-level clinical utility. Discrete models consider disease progression as a latent permutation of events, where each event corresponds to a feature becoming measurably abnormal. However, permutation inference using traditional maximum likelihood approaches becomes prohibitive due to combinatoric explosion, severely limiting model dimensionality and utility. Here we leverage ideas from optimal transport to model disease progression as a latent permutation matrix of events belonging to the Birkhoff polytope, facilitating fast inference via optimisation of the variational lower bound. This enables a factor of 1000 times faster inference than the current state of the art and, correspondingly, supports models with several orders of magnitude more features than the current state of the art can consider. Experiments demonstrate the increase in speed, accuracy and robustness to noise in simulation. Further experiments with real-world imaging data from two separate datasets, one from Alzheimer's disease patients, the other age-related macular degeneration, showcase, for the first time, pixel-level disease progression events in the brain and eye, respectively. Our method is low compute, interpretable and applicable to any progressive condition and data modality, giving it broad potential clinical utility.