Amortized Phylodynamic Inference with Neural Bayes Estimators and Recursive Neural Networks

2026-03-09

AI Summary

This study addresses the computational challenges in likelihood-based inference of dynamic epidemiological parameters—such as the time-varying reproduction number—from phylogenetic trees within complex transmission models. The authors propose a Neural Bayesian Estimator (NBE), which, for the first time, integrates recurrent neural networks with quantile regression to directly and efficiently estimate the posterior median and credible intervals of such parameters from reconstructed phylogenies. By leveraging tree embeddings and a prediction network conditioned on both time and quantile levels, NBE enables low-bias, rapid inference of time-varying reproduction numbers and supports model fine-tuning to substantially reduce computational costs. Experiments demonstrate that NBE achieves excellent predictive performance and conservative uncertainty quantification on simulated data, exhibiting lower bias than BEAST2’s fixed-tree analysis while maintaining high accuracy even after fine-tuning.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Phylodynamics is used to estimate epidemic dynamics from phylogenetic trees or genomic sequences of pathogens, but the likelihood calculations needed can be challenging for complex models. We present a neural Bayes estimator (NBE) for key epidemic quantities: the reproduction number, prevalence, and cumulative infections through time. By performing quantile regression over tree space, the NBE allows us to estimate posterior medians and credible intervals directly from a reconstructed tree. Our approach uses a recursive neural network as a tree embedding network with a prediction network conditioned on time and quantile level to generate the estimates. In simulation studies, the NBE achieves good predictive performance, with conservative uncertainty estimates. Compared with a BEAST2 fixed-tree analysis, the NBE gives less biased estimates of time-varying reproduction numbers in our test setting. Under a misspecified sampling model, the NBE performance degrades (as expected) but remains reasonable, and fine-tuning a pre-trained model yields estimates comparable to those from a model trained from scratch, at substantially lower computational cost.

Problem

• phylodynamics
• epidemic dynamics
• likelihood calculation
• phylogenetic trees
• reproduction number

Innovation

• Neural Bayes Estimator
• Phylodynamic Inference
• Recursive Neural Network
• Quantile Regression
• Amortized Inference