aron0093 / cy2path

Factorial latent dynamic models trained on Markovian simulations of biological processes using single cell RNA sequencing data.

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) 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), $P(o \mid i) = \sum\limits_{s_{i} \in S} P(o \mid s_{i}) \sum\limits_{l \in L} P(l) \sum\limits_{s_{i-1} \in S} P(s_{i} \mid s_{i-1}, l)$

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.