# Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference

arXiv: https://arxiv.org/abs/2106.00075 · HTML: https://mlsanity.com/paper/2106.00075/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 55 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 11 of 11)

- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Nested Sequential Monte Carlo Methods](https://mlsanity.com/paper/1502.02536/) (2015)
- [Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows](https://mlsanity.com/paper/2012.00459/) (2020)
- [High-dimensional Filtering using Nested Sequential Monte Carlo](https://mlsanity.com/paper/1612.09162/) (2016)
- [Particle Smoothing Variational Objectives](https://mlsanity.com/paper/1909.09734/) (2019)
- [Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data](https://mlsanity.com/paper/1811.02459/) (2018)
- [A Bayesian Phylogenetic Hidden Markov Model for B Cell Receptor Sequence Analysis](https://mlsanity.com/paper/1906.11982/) (2019)

## Built on by (most cited first, 11 of 11)

- [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)
- [VaiPhy: a Variational Inference Based Algorithm for Phylogeny](https://mlsanity.com/paper/2203.01121/) (2022)
- [Sequential Monte Carlo Learning for Time Series Structure Discovery](https://mlsanity.com/paper/2307.09607/) (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 Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space](https://mlsanity.com/paper/2501.17965/) (2025)
- [Variational Pseudo Marginal Methods for Jet Reconstruction in Particle Physics](https://mlsanity.com/paper/2406.03242/) (2024)
- [Orchard: building large cancer phylogenies using stochastic combinatorial search](https://mlsanity.com/paper/2311.12917/) (2023)
- [Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes](https://mlsanity.com/paper/2610.19053/) (2026)

## Abstract (arXiv)

Bayesian phylogenetic inference is often conducted via local or sequential search over topologies and branch lengths using algorithms such as random-walk Markov chain Monte Carlo (MCMC) or Combinatorial Sequential Monte Carlo (CSMC). However, when MCMC is used for evolutionary parameter learning, convergence requires long runs with inefficient exploration of the state space. We introduce Variational Combinatorial Sequential Monte Carlo (VCSMC), a powerful framework that establishes variational sequential search to learn distributions over intricate combinatorial structures. We then develop nested CSMC, an efficient proposal distribution for CSMC and prove that nested CSMC is an exact approximation to the (intractable) locally optimal proposal. We use nested CSMC to define a second objective, VNCSMC which yields tighter lower bounds than VCSMC. We show that VCSMC and VNCSMC are computationally efficient and explore higher probability spaces than existing methods on a range of tasks.