Hence, during the training of VaiPhy, we used a maximum likelihood heuristic toupdate thebranch lengths givenatree topology. The branch lengths of the NJ tree are optimized with the same software. The optimized branch lengths are used as the initial set of lengths fore E(τ). In all of the figures, the left column is the current state ofτ, the middle column is two trees that are compared, and the right column is the selected tree. Solid lines indicate the edges inτ, and bold green lines are accepted edges (edges inM).

Phylogenetics is a classical methodology in computational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of development of cancer. The exponential size of the tree space is unfortunately a formidable obstacle for current Bayesian phylogenetic inference using Markov chain Monte Carlo based methods since these rely on local operations. And although more recent variational inference (VI) based methods offer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy, a remarkably fast VI based algorithm for approximate posterior inference in an \textit{augmented tree space}. VaiPhy produces marginal log-likelihood estimates on par with the state-of-the-art methods on real data, and is considerably faster since it does not require auto-differentiation. Instead, VaiPhy combines coordinate ascent update equations with two novel sampling schemes: (i) \textit{SLANTIS}, a proposal distribution for tree topologies in the augmented tree space, and (ii) the \textit{JC sampler}, the, to the best of our knowledge, first ever scheme for sampling branch lengths directly from the popular Jukes-Cantor model. We compare VaiPhy in terms of density estimation and runtime. Additionally, we evaluate the reproducibility of the baselines.

Phylogenetics is a classical methodology in computational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of development of cancer. The exponential size of the tree space is unfortunately a formidable obstacle for current Bayesian phylogenetic inference using Markov chain Monte Carlo based methods since these rely on local operations. And although more recent variational inference (VI) based methods offer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy, a remarkably fast VI based algorithm for approximate posterior inference in an \textit{augmented tree space}. VaiPhy produces marginal log-likelihood estimates on par with the state-of-the-art methods on real data, and is considerably faster since it does not require auto-differentiation. Instead, VaiPhy combines coordinate ascent update equations with two novel sampling schemes: (i) \textit{SLANTIS}, a proposal distribution for tree topologies in the augmented tree space, and (ii) the \textit{JC sampler}, the, to the best of our knowledge, first ever scheme for sampling branch lengths directly from the popular Jukes-Cantor model.

Phylogenetics is a classical methodology in computational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of cancer development. The exponential size of the tree space is, unfortunately, a substantial obstacle for Bayesian phylogenetic inference using Markov chain Monte Carlo based methods since these rely on local operations. And although more recent variational inference (VI) based methods offer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy, a remarkably fast VI based algorithm for approximate posterior inference in an augmented tree space. VaiPhy produces marginal log-likelihood estimates on par with the state-of-the-art methods on real data and is considerably faster since it does not require auto-differentiation. Instead, VaiPhy combines coordinate ascent update equations with two novel sampling schemes: (i) SLANTIS, a proposal distribution for tree topologies in the augmented tree space, and (ii) the JC sampler, to the best of our knowledge, the first-ever scheme for sampling branch lengths directly from the popular Jukes-Cantor model. We compare VaiPhy in terms of density estimation and runtime. Additionally, we evaluate the reproducibility of the baselines.