Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression

Compressed computations using wavelets for hidden Markov models with continuous observations

Compression as an accelerant of computation is increasingly recognized as an important component in engineering fast real-world machine learning methods for big data; c.f., its impact on genome-scale approximate string matching. Previous work showed that compression can accelerate algorithms for Hidden Markov Models (HMM) with discrete observations, both for the classical frequentist HMM algorithms-Forward Filtering, Backward Smoothing and Viterbi-and Gibbs sampling for Bayesian HMM. For Bayesian HMM with continuous-valued observations, compression was shown to greatly accelerate computations for specific types of data. For instance, data from large-scale experiments interrogating structural genetic variation can be assumed to be piece-wise constant with noise, or, equivalently, data generated by HMM with dominant self-transition probabilities. Here we extend the compressive computation approach to the classical frequentist HMM algorithms on continuous-valued observations, providing the first compressive approach for this problem. In a large-scale simulation study, we demonstrate empirically that in many settings compressed HMM algorithms very clearly outperform the classical algorithms with no, or only an insignificant effect, on the computed probabilities and infered state paths of maximal likelihood. This provides an efficient approach to big data computations with HMM. An open-source implementation of the method is available from https://github.com/lucabello/wavelet-hmms.

Fuzzy methods for the detection of copy number variations in comparative genomic hybridization arrays

Genomic copy number variations (CNVs) are considered as a significant source of genetic diversity and widely involved in gene expression and regulatory mechanism, genetic disorders and disease risk, susceptibility to certain diseases and conditions, and resistance to medical drugs. Many studies have targeted the identification, profiling, analysis, and associations of genetic CNVs. We propose herein two new fuzzy methods, taht is, one based on the fuzzy inference from the pre-processed input, and another based on fuzzy C-means clustering. Our solutions present a higher true positive rate and a lower false negative with no false positive, efficient performance and consumption of least resources.

Bayesian localization of CNV candidates in WGS data within minutes

BACKGROUND

Full Bayesian inference for detecting copy number variants (CNV) from whole-genome sequencing (WGS) data is still largely infeasible due to computational demands. A recently introduced approach to perform Forward-Backward Gibbs sampling using dynamic Haar wavelet compression has alleviated issues of convergence and, to some extent, speed. Yet, the problem remains challenging in practice.

RESULTS

In this paper, we propose an improved algorithmic framework for this approach. We provide new space-efficient data structures to query sufficient statistics in logarithmic time, based on a linear-time, in-place transform of the data, which also improves on the compression ratio. We also propose a new approach to efficiently store and update marginal state counts obtained from the Gibbs sampler.

CONCLUSIONS

Using this approach, we discover several CNV candidates in two rat populations divergently selected for tame and aggressive behavior, consistent with earlier results concerning the domestication syndrome as well as experimental observations. Computationally, we observe a 29.5-fold decrease in memory, an average 5.8-fold speedup, as well as a 191-fold decrease in minor page faults. We also observe that metrics varied greatly in the old implementation, but not the new one. We conjecture that this is due to the better compression scheme. The fully Bayesian segmentation of the entire WGS data set required 3.5 min and 1.24 GB of memory, and can hence be performed on a commodity laptop.

Embracing heterogeneity: coalescing the Tree of Life and the future of phylogenomics

Building the Tree of Life (ToL) is a major challenge of modern biology, requiring advances in cyberinfrastructure, data collection, theory, and more. Here, we argue that phylogenomics stands to benefit by embracing the many heterogeneous genomic signals emerging from the first decade of large-scale phylogenetic analysis spawned by high-throughput sequencing (HTS). Such signals include those most commonly encountered in phylogenomic datasets, such as incomplete lineage sorting, but also those reticulate processes emerging with greater frequency, such as recombination and introgression. Here we focus specifically on how phylogenetic methods can accommodate the heterogeneity incurred by such population genetic processes; we do not discuss phylogenetic methods that ignore such processes, such as concatenation or supermatrix approaches or supertrees. We suggest that methods of data acquisition and the types of markers used in phylogenomics will remain restricted until a posteriori methods of marker choice are made possible with routine whole-genome sequencing of taxa of interest. We discuss limitations and potential extensions of a model supporting innovation in phylogenomics today, the multispecies coalescent model (MSC). Macroevolutionary models that use phylogenies, such as character mapping, often ignore the heterogeneity on which building phylogenies increasingly rely and suggest that assimilating such heterogeneity is an important goal moving forward. Finally, we argue that an integrative cyberinfrastructure linking all steps of the process of building the ToL, from specimen acquisition in the field to publication and tracking of phylogenomic data, as well as a culture that values contributors at each step, are essential for progress.

Using HaMMLET for Bayesian Segmentation of WGS Read-Depth Data

CNV detection requires a high-quality segmentation of genomic data. In many WGS experiments, sample and control are sequenced together in a multiplexed fashion using DNA barcoding for economic reasons. Using the differential read depth of these two conditions cancels out systematic additive errors. Due to this detrending, the resulting data is appropriate for inference using a hidden Markov model (HMM), arguably one of the principal models for labeled segmentation. However, while the usual frequentist approaches such as Baum-Welch are problematic for several reasons, they are often preferred to Bayesian HMM inference, which normally requires prohibitively long running times and exceeds a typical user's computational resources on a genome scale data. HaMMLET solves this problem using a dynamic wavelet compression scheme, which makes Bayesian segmentation of WGS data feasible on standard consumer hardware.