Granular Forum — Dr Matthew MacAulay

Hyperbolic tree embeddings for Bayesian inference of evolutionary trees.

Viruses, like COVID-19, evolve over time as mutations in the DNA sequence constantly produce different lineages on the tree of evolution. Finding this evolutionary tree allows scientists to better understand the similarity of strains, regional outbreaks, and aids in developing vaccines. Unfortunately, there are a super-exponential number of trees, resulting in many more candidate trees than there are atoms in the universe for COVID-19. Furthermore, these trees are not always robust and may change wildly as new DNA sequences are analysed.

To better navigate through the high dimensional space of trees, we embed them into hyperbolic space. This enables many powerful statistical and machine learning tools that only work on continuous parameters to work on discrete tree structures. For robustness, we developed several Bayesian inference tools based on hyperbolic tree embeddings: maximum a priori, Markov Chain Monte Carlo and variational inference. The last of which uses automatic differentiation, a tool widely used in the deep learning community.

Whilst this talk is on a problem from biology, fear not. It is aimed at engineers interested in broader mathematical and statistical techniques for scientific problems.