# A Variational Approach to Bayesian Phylogenetic Inference

arXiv: https://arxiv.org/abs/2204.07747 · HTML: https://mlsanity.com/paper/2204.07747/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 86 references that are in the map.
- First posted on arXiv 16 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows](https://mlsanity.com/paper/2012.00459/) (2020)
- [Systematic Exploration of the High Likelihood Set of Phylogenetic Tree Topologies](https://mlsanity.com/paper/1811.11007/) (2018)

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

- [Learnable Topological Features for Phylogenetic Inference via Graph Neural Networks](https://mlsanity.com/paper/2302.08840/) (2023)
- [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)
- [Efficient Mixture Learning in Black-Box Variational Inference](https://mlsanity.com/paper/2406.07083/) (2024)
- [Variational Bayesian Phylogenetic Inference with Semi-implicit Branch Length Distributions](https://mlsanity.com/paper/2408.05058/) (2024)
- [Prior Density Learning in Variational Bayesian Phylogenetic Parameters Inference](https://mlsanity.com/paper/2302.02522/) (2023)
- [Improving Tree Probability Estimation with Stochastic Optimization and Variance Reduction](https://mlsanity.com/paper/2409.05282/) (2024)
- [Variational phylogenetic inference with products over bipartitions](https://mlsanity.com/paper/2502.15110/) (2025)
- [Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes](https://mlsanity.com/paper/2610.19053/) (2026)

## Abstract (arXiv)

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper, we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We propose combining subsplit Bayesian networks, an expressive graphical model for tree topology distributions, and a structured amortization of the branch lengths over tree topologies for a suitable variational family of distributions. We train the variational approximation via stochastic gradient ascent and adopt gradient estimators for continuous and discrete variational parameters separately to deal with the composite latent space of phylogenetic models. We show that our variational approach provides competitive performance to MCMC, while requiring much fewer (though more costly) iterations due to a more efficient exploration mechanism enabled by variational inference. Experiments on a benchmark of challenging real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods.