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Variational Phylogenetic Inference with Products over Bipartitions

ICML 2025 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Sequential Monte Carlo for inference

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Proposes VIPR, a variational family for ultrametric phylogenetic trees built by running single-linkage clustering on a random log-normal distance matrix, with a closed-form tree density enabling gradient-based VI without MCMC subroutines.

Problem

Variational Bayesian inference over rooted ultrametric phylogenetic trees (topology plus coalescent times) is hard because existing tractable methods either rely on MCMC to restrict tree support or cannot express the full tree space.

Approach

Place independent variational distributions (log-normal) on the pairwise coalescent times of a distance matrix, push them through single-linkage clustering, and derive a closed-form density over trees via survival functions, giving a differentiable variational family over all of tree space.

Key results

• VBPI10 attains higher MLL than VIPR on most datasets (e.g., DS1 gap -0.53 vs -0.95 for VIMCO), while VIPR beats VBPI10 on ELBO for exactly half of the datasets.
• On the COVID-19 dataset VBPI10 gap is -39.1 nats vs. -214 to -611 for VIPR variants, so VIPR underperforms there.
• VIPR's empirical runtime scales roughly as O(N) and it outperforms VBPI per iteration at 512 taxa, though it is about twice as slow at 8 taxa.

Measured effects reported in the paper

Surprising findings

• VIPR's ELBO is competitive with or better than VBPI10 on half the datasets even though VBPI attains higher marginal log-likelihood.
• On COVID-19, VIPR's ELBO is substantially below VBPI10 (e.g., -8489.82 LOOR vs -8100.96 VBPI10 at COV), suggesting optimization trouble from poor initialization.

Limitations

• Log-normal pairwise coalescent distributions are a restrictive choice and VIPR underestimates tree length variance compared to BEAST.
• Optimization converges slowly and is sensitive to initialization; COVID-19 results are substantially worse than VBPI.
• Parameter count is O(N^2) and the reparameterized gradient estimator is biased.

Experimental setup

Datasets: DS1-DS11 (Lakner et al. 2008) COVID-19 JN.1 genomes from GISAID (72 taxa) MS simulated datasets (ms software)

Benchmarks: DS1-DS11 COVID-19 GISAID dataset MS simulated datasets

Metrics: marginal log-likelihood gap to BEAST gold standard (nats) ELBO (nats) wall-clock time per 1000 iterations number of tree structure parameters

Baselines: VBPI BEAST stepping-stone gold standard

Builds on: variational Bayesian phylogenetic inference (VBPI) cubeVB Kingman coalescent VIMCO Jukes-Cantor model

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