https://github.com/aron0093/cy2path
Factorial latent dynamic models trained on Markovian simulations of biological processes using single cell RNA sequencing data.
https://github.com/aron0093/cy2path
hidden-markov-model markov-chain simulation single-cell-omics state-space-model
Last synced: 9 days ago
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Factorial latent dynamic models trained on Markovian simulations of biological processes using single cell RNA sequencing data.
- Host: GitHub
- URL: https://github.com/aron0093/cy2path
- Owner: aron0093
- License: gpl-3.0
- Created: 2022-12-19T18:32:29.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2025-05-07T08:20:01.000Z (9 months ago)
- Last Synced: 2025-05-07T08:36:56.995Z (9 months ago)
- Topics: hidden-markov-model, markov-chain, simulation, single-cell-omics, state-space-model
- Language: Python
- Homepage:
- Size: 224 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
### Factorial latent dynamic models trained on Markovian simulations of biological processes using scRNAseq. data.
With a transition probability matrix $T$ over observed states $O$ and assuming Markovian dynamics,
$P(o \mid i) = P(o \mid o_{i-1})$
For iteration $i$,
$P(o \mid i) = P(o \mid i=0) \cdot T^i$
The animation overlays $P(i \mid o)$ on a 2D UMAP embedding of the data ([Cerletti et. al. 2020](https://doi.org/10.1101/2020.12.22.423929)) Since we are interested in modelling the dynamics in a smaller latent state space, we factorise the MSM simulation,
$P(o \mid i) = \sum\limits_{s \in S} P(o \mid s,i) P(s \mid i)$
Assuming Markovian dynamics in the latent space aswell,
$P(o \mid i) = \sum\limits_{s_{i} \in S} P(o \mid s_{i}) \sum\limits_{s_{i-1} \in S} P(s_{i} \mid s_{i-1})$
Multiple independent chains in a common latent space can be modelled using conditional latent TPMs ([Ghahramani & Jordan 1997](https://doi.org/10.1023/A:1007425814087)),
$P(o \mid i) = \sum\limits_{s_{i} \in S} P(o \mid s_{i}) \sum\limits_{l \in L} P(l) \sum\limits_{s_{i-1} \in S} P(s_{i} \mid s_{i-1}, l)$
### Citation
Claassen, M., & Gupta, R. (2023). Factorial state-space modelling for kinetic clustering and lineage inference. https://doi.org/10.1101/2023.08.21.554135
### Notebooks
Demonstration notebooks can be found [here](https://github.com/aron0093/cy2path_notebooks).