# VaiPhy: a Variational Inference Based Algorithm for Phylogeny

arXiv: https://arxiv.org/abs/2203.01121 · HTML: https://mlsanity.com/paper/2203.01121/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Automatic Differentiation Variational Inference with Mixtures](https://mlsanity.com/paper/2003.01687/) (2020)
- [Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows](https://mlsanity.com/paper/2012.00459/) (2020)
- [Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximations](https://mlsanity.com/paper/2202.10951/) (2022)
- [Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2106.00075/) (2021)

## Built on by (most cited first, 9 of 9)

- [PhyloGFN: Phylogenetic inference with generative flow networks](https://mlsanity.com/paper/2310.08774/) (2023)
- [GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologies](https://mlsanity.com/paper/2307.03675/) (2023)
- [Cooperation in the Latent Space: The Benefits of Adding Mixture Components in Variational Autoencoders](https://mlsanity.com/paper/2209.15514/) (2022)
- [ARTree: A Deep Autoregressive Model for Phylogenetic Inference](https://mlsanity.com/paper/2310.09553/) (2023)
- [Improved Variational Bayesian Phylogenetic Inference using Mixtures](https://mlsanity.com/paper/2310.00941/) (2023)
- [Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space](https://mlsanity.com/paper/2501.17965/) (2025)
- [PhyloGen: Language Model-Enhanced Phylogenetic Inference via Graph Structure Generation](https://mlsanity.com/paper/2412.18827/) (2024)
- [Variational Bayesian Phylogenetic Inference with Semi-implicit Branch Length Distributions](https://mlsanity.com/paper/2408.05058/) (2024)
- [Variational phylogenetic inference with products over bipartitions](https://mlsanity.com/paper/2502.15110/) (2025)

## Abstract (arXiv)

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. We provide our code on GitHub: urlhttps://github.com/Lagergren-Lab/VaiPhy.