{"id":37615289,"url":"https://github.com/aron0093/cy2path","last_synced_at":"2026-01-16T10:30:03.610Z","repository":{"id":116401065,"uuid":"580107705","full_name":"aron0093/cy2path","owner":"aron0093","description":"Factorial latent dynamic models trained on Markovian simulations of biological processes using single cell RNA sequencing 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unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["hidden-markov-model","markov-chain","simulation","single-cell-omics","state-space-model"],"created_at":"2026-01-16T10:30:03.470Z","updated_at":"2026-01-16T10:30:03.597Z","avatar_url":"https://github.com/aron0093.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"### Factorial latent dynamic models trained on Markovian simulations of biological processes using scRNAseq. data.\n\n\u003ctable border=\"0\"\u003e\n\u003ctr \u003e\n\u003ctd\u003e\u003cimg align=\"left\" src=\"https://user-images.githubusercontent.com/25486108/208702939-0f2e9339-0d1f-467a-934c-56d5db388f22.gif\" width=\"350\" height=\"300\"\u003e\u003c/td\u003e\n \n\u003ctd\u003eWith a transition probability matrix $T$ over observed states $O$ and assuming Markovian dynamics, \u003cbr /\u003e\u003cbr /\u003e\n\n\u003cp align=center\u003e $P(o \\mid i) = P(o \\mid o_{i-1})$ \u003c/p\u003e\n\nFor iteration $i$,\n\n\u003cp align=center\u003e $P(o \\mid i) = P(o \\mid i=0) \\cdot T^i$ \u003c/p\u003e\n\nThe 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,\n\n\u003cp align=center\u003e $P(o \\mid i) = \\sum\\limits_{s \\in S} P(o \\mid s,i) P(s \\mid i)$ \u003c/p\u003e\n\nAssuming Markovian dynamics in the latent space aswell,\n\n\u003cp align=center\u003e $P(o \\mid i) = \\sum\\limits_{s_{i} \\in S} P(o \\mid s_{i}) \\sum\\limits_{s_{i-1} \\in S} P(s_{i} \\mid s_{i-1})$ \u003c/p\u003e\n\nMultiple independent chains in a common latent space can be modelled using conditional latent TPMs ([Ghahramani \u0026 Jordan 1997](https://doi.org/10.1023/A:1007425814087)),\n\n\u003cp align=center\u003e $P(o \\mid i) = \\sum\\limits_{s_{i} \\in S} P(o \\mid s_{i}) \\sum\\limits_{l \\in L} P(l) \\sum\\limits_{s_{i-1} \\in S} P(s_{i} \\mid s_{i-1}, l)$ \u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/table\u003e\n\n### Citation\n\nClaassen, M., \u0026 Gupta, R. (2023). Factorial state-space modelling for kinetic clustering and lineage inference. https://doi.org/10.1101/2023.08.21.554135\n\n### Notebooks\n\nDemonstration notebooks can be found [here](https://github.com/aron0093/cy2path_notebooks). \n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Faron0093%2Fcy2path","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Faron0093%2Fcy2path","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Faron0093%2Fcy2path/lists"}