In this project, we develop new methods for recovering latent tree models. In such models, one observes only the terminal nodes of a tree, while the tree structure and its non-terminal nodes are unobserved. The task is to recover the structure of the tree and its parameters.
An important application is phylogenetics, where one observes only current species, while their extinct ancestors are unobserved. The task is then to recover the evolutionary history of the set of observed organisms.
In our work we develop new results in spectral graph theory that are relevant for the task of tree models. We show how the spectrum of the graph relates to the hidden tree structure and can thus be used to recover it.
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Link to papers:
https://epubs.siam.org/doi/abs/10.1137/20M1365715
https://arxiv.org/abs/2102.13276
Link to code: