# Improving Tree Probability Estimation with Stochastic Optimization and Variance Reduction

arXiv: https://arxiv.org/abs/2409.05282 · HTML: https://mlsanity.com/paper/2409.05282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows](https://mlsanity.com/paper/2012.00459/) (2020)
- [A Variational Approach to Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2204.07747/) (2022)

## Abstract (arXiv)

Probability estimation of tree topologies is one of the fundamental tasks in phylogenetic inference. The recently proposed subsplit Bayesian networks (SBNs) provide a powerful probabilistic graphical model for tree topology probability estimation by properly leveraging the hierarchical structure of phylogenetic trees. However, the expectation maximization (EM) method currently used for learning SBN parameters does not scale up to large data sets. In this paper, we introduce several computationally efficient methods for training SBNs and show that variance reduction could be the key for better performance. Furthermore, we also introduce the variance reduction technique to improve the optimization of SBN parameters for variational Bayesian phylogenetic inference (VBPI). Extensive synthetic and real data experiments demonstrate that our methods outperform previous baseline methods on the tasks of tree topology probability estimation as well as Bayesian phylogenetic inference using SBNs.