A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks

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.Comment: 9 pages, 8 figure

Simultaneous identification of models and parameters of scientific simulators

Many scientific models are composed of multiple discrete components, and scien tists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in an amortized simulation-based inference framework: We define implicit model priors over a fixed set of candidate components and train neural networks to infer joint probability distributions over both, model components and associated parameters from simulations. To represent distributions over model components, we introduce a conditional mixture of multivariate binary distributions in the Grassmann formalism. Our approach can be applied to any compositional stochastic simulator without requiring access to likelihood evaluations. We first illustrate our method on a simple time series model with redundant components and show that it can retrieve joint posterior distribution over a set of symbolic expressions and their parameters while accurately capturing redundancy with strongly correlated posteriors. We then apply our approach to drift-diffusion models, a commonly used model class in cognitive neuroscience. After validating the method on synthetic data, we show that our approach explains experimental data as well as previous methods, but that our fully probabilistic approach can help to discover multiple data-consistent model configurations, as well as reveal non-identifiable model components and parameters. Our method provides a powerful tool for data-driven scientific inquiry which will allow scientists to systematically identify essential model components and make uncertainty-informed modelling decisions

Using deep learning to identify recent positive selection in malaria parasite sequence data.

BACKGROUND: Malaria, caused by Plasmodium parasites, is a major global public health problem. To assist an understanding of malaria pathogenesis, including drug resistance, there is a need for the timely detection of underlying genetic mutations and their spread. With the increasing use of whole-genome sequencing (WGS) of Plasmodium DNA, the potential of deep learning models to detect loci under recent positive selection, historically signals of drug resistance, was evaluated. METHODS: A deep learning-based approach (called "DeepSweep") was developed, which can be trained on haplotypic images from genetic regions with known sweeps, to identify loci under positive selection. DeepSweep software is available from https://github.com/WDee/Deepsweep . RESULTS: Using simulated genomic data, DeepSweep could detect recent sweeps with high predictive accuracy (areas under ROC curve > 0.95). DeepSweep was applied to Plasmodium falciparum (n = 1125; genome size 23 Mbp) and Plasmodium vivax (n = 368; genome size 29 Mbp) WGS data, and the genes identified overlapped with two established extended haplotype homozygosity methods (within-population iHS, across-population Rsb) (~ 60-75% overlap of hits at P < 0.0001). DeepSweep hits included regions proximal to known drug resistance loci for both P. falciparum (e.g. pfcrt, pfdhps and pfmdr1) and P. vivax (e.g. pvmrp1). CONCLUSION: The deep learning approach can detect positive selection signatures in malaria parasite WGS data. Further, as the approach is generalizable, it may be trained to detect other types of selection. With the ability to rapidly generate WGS data at low cost, machine learning approaches (e.g. DeepSweep) have the potential to assist parasite genome-based surveillance and inform malaria control decision-making

Neural Point Estimation for Fast Optimal Likelihood-Free Inference

Neural point estimators are neural networks that map data to parameter point estimates. They are fast, likelihood free and, due to their amortised nature, amenable to fast bootstrap-based uncertainty quantification. In this paper, we aim to increase the awareness of statisticians to this relatively new inferential tool, and to facilitate its adoption by providing user-friendly open-source software. We also give attention to the ubiquitous problem of making inference from replicated data, which we address in the neural setting using permutation-invariant neural networks. Through extensive simulation studies we show that these neural point estimators can quickly and optimally (in a Bayes sense) estimate parameters in weakly-identified and highly-parameterised models with relative ease. We demonstrate their applicability through an analysis of extreme sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates and bootstrap-based confidence intervals from hundreds of spatial fields in a fraction of a second

A likelihood-free inference framework for population genetic data using exchangeable neural networks

Inference for population genetics models is hindered by computationally intractable likelihoods. While this issue is tackled by likelihood-free methods, these approaches typically rely on hand-crafted summary statistics of the data. In complex settings, designing and selecting suitable summary statistics is problematic and results are very sensitive to such choices. In this paper, we learn the first exchangeable feature representation for population genetic data to work directly with genotype data. This is achieved by means of a novel Bayesian likelihood-free inference framework, where a permutation-invariant convolutional neural network learns the inverse functional relationship from the data to the posterior. We leverage access to scientific simulators to learn such likelihood-free function mappings, and establish a general framework for inference in a variety of simulation-based tasks. We demonstrate the power of our method on the recombination hotspot testing problem, outperforming the state-of-the-art

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Probabilistic symmetries and invariant neural networks

Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has been devoted to encoding invariance under symmetry transformations into neural network architectures, in an effort to improve the performance of deep neural networks in data-scarce, non-i.i.d., or unsupervised settings. By considering group invariance from the perspective of probabilistic symmetry, we establish a link between functional and probabilistic symmetry, and obtain generative functional representations of probability distributions that are invariant or equivariant under the action of a compact group. Our representations completely characterize the structure of neural networks that can be used to model such distributions and yield a general program for constructing invariant stochastic or deterministic neural networks. We demonstrate that examples from the recent literature are special cases, and develop the details of the general program for exchangeable sequences and arrays.Comment: Revised structure for clarity; fixed minor mistakes; incorporated reviewer feedback for publicatio