# Improved Variational Bayesian Phylogenetic Inference using Mixtures

arXiv: https://arxiv.org/abs/2310.00941 · HTML: https://mlsanity.com/paper/2310.00941/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Models](https://mlsanity.com/paper/1911.03393/) (2019)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [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)
- [Learnable Topological Features for Phylogenetic Inference via Graph Neural Networks](https://mlsanity.com/paper/2302.08840/) (2023)
- [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)
- [VaiPhy: a Variational Inference Based Algorithm for Phylogeny](https://mlsanity.com/paper/2203.01121/) (2022)
- [A Variational Approach to Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2204.07747/) (2022)
- [Overdispersed Black-Box Variational Inference](https://mlsanity.com/paper/1603.01140/) (2016)
- [Cooperation in the Latent Space: The Benefits of Adding Mixture Components in Variational Autoencoders](https://mlsanity.com/paper/2209.15514/) (2022)

## Built on by (most cited first, 4 of 4)

- [Streaming Bayes GFlowNets](https://mlsanity.com/paper/2411.05899/) (2024)
- [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)
- [Variational phylogenetic inference with products over bipartitions](https://mlsanity.com/paper/2502.15110/) (2025)

## Abstract (arXiv)

We present VBPI-Mixtures, an algorithm designed to enhance the accuracy of phylogenetic posterior distributions, particularly for tree-topology and branch-length approximations. Despite the Variational Bayesian Phylogenetic Inference (VBPI), a leading-edge black-box variational inference (BBVI) framework, achieving remarkable approximations of these distributions, the multimodality of the tree-topology posterior presents a formidable challenge to sampling-based learning techniques such as BBVI. Advanced deep learning methodologies such as normalizing flows and graph neural networks have been explored to refine the branch-length posterior approximation, yet efforts to ameliorate the posterior approximation over tree topologies have been lacking. Our novel VBPI-Mixtures algorithm bridges this gap by harnessing the latest breakthroughs in mixture learning within the BBVI domain. As a result, VBPI-Mixtures is capable of capturing distributions over tree-topologies that VBPI fails to model. We deliver state-of-the-art performance on difficult density estimation tasks across numerous real phylogenetic datasets.