[Paper Review] A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks

Jeffrey Chan, Valerio Perrone+4 more|arXiv (Cornell University)|Feb 16, 2018

Bayesian Methods and Mixture Models45 references40 citations

TL;DR

The paper introduces an exchangeable neural network with a simulation-on-the-fly training paradigm to perform likelihood-free, summary-statistic-free Bayesian inference on exchangeable population genetic data, demonstrated on recombination hotspot testing.

ABSTRACT

An explosion of high-throughput DNA sequencing in the past decade has led to a surge of interest in population-scale inference with whole-genome data. Recent work in population genetics has centered on designing inference methods for relatively simple model classes, and few scalable general-purpose inference techniques exist for more realistic, complex models. To achieve this, two inferential challenges need to be addressed: (1) population data are exchangeable, calling for methods that efficiently exploit the symmetries of the data, and (2) computing likelihoods is intractable as it requires integrating over a set of correlated, extremely high-dimensional latent variables. These challenges are traditionally tackled by likelihood-free methods that use scientific simulators to generate datasets and reduce them to hand-designed, permutation-invariant summary statistics, often leading to inaccurate inference. In this work, we develop an exchangeable neural network that performs summary statistic-free, likelihood-free inference. Our framework can be applied in a black-box fashion across a variety of simulation-based tasks, both within and outside biology. We demonstrate the power of our approach on the recombination hotspot testing problem, outperforming the state-of-the-art.

Motivation & Objective

• Develop a general-purpose likelihood-free inference framework that works directly on raw, exchangeable population genetic data without hand-crafted summaries.
• Leverage exchangeable neural networks to respect permutation invariance in data and learn posterior mappings.
• Introduce a simulation-on-the-fly training paradigm to calibrate posteriors and improve generalization.
• Demonstrate the method on recombination hotspot testing and estimation and compare to state-of-the-art methods.
• Provide theoretical properties and diagnostics under an ABC-equivalent likelihood-free setting.

Proposed method

• Design an exchangeable neural network that applies the same function to each row of the binary data matrix, aggregates with a symmetric function, and maps to a posterior.
• Use a convolutional subnetwork Phi to process row inputs, a symmetric function g to combine row outputs, and a final network h to output the posterior over theta.
• Adopt a simulation-on-the-fly training regime where each training point is drawn fresh from the prior and simulator, ensuring calibrated posteriors.
• Argue that the approach yields amortized, statistic-free inference with calibration comparable to or better than ABC.
• Provide theoretical justification linking calibration and asymptotics to the simulation-on-the-fly paradigm.
• Apply the framework to recombination hotspot testing with binary population-genetic data and continuous hotspot intensity estimation.

Experimental results

Research questions

• RQ1 Can a likelihood-free Bayesian inference method be built directly on raw exchangeable population genetic data without summary statistics?
• RQ2 How does an exchangeable neural network compare to non-exchangeable architectures in learning posteriors from population-genetic data?
• RQ3 Does a simulation-on-the-fly training regime yield calibrated posteriors and improved generalization over fixed training sets?
• RQ4 How does the proposed method perform on recombination hotspot testing and intensity estimation compared with LDhot and other baselines?
• RQ5 To what extent can this framework be extended to other population-genetic settings beyond hotspot testing?

Key findings

• The exchangeable neural network respects permutation invariance and maps data to posterior distributions.
• Simulation-on-the-fly training yields calibrated posteriors and reduces bias and variance compared to fixed training sets.
• The method outperforms LDhot on recombination hotspot testing under realistic recombination maps and scales linearly with sequence count.
• For hotspot intensity estimation, the posterior calibration is close to nominal and posterior means show strong correlation with true values.
• The approach achieves 90% accuracy in hotspot detection with relatively low computational cost compared to LDhot.
• The method scales to large local regions and can be extended to various population-genetic tasks without hand-crafted summaries.