17w5131: Statistical & Computational Challenges in Large Scale Molecular Biology Workshop @BIRS_Math 3/2017 #ITBio

Arriving in Banff, Alberta Sunday, March 26 and departing Friday March 31, 2017

Organizers

• Barbara Engelhardt (Princeton University)
• Anna Goldenberg (University of Toronto)
• Manolis Kellis (Massachusetts Institute of Technology)
• Jacob Laurent (Centre national de la recherche scientifique)
• Jeff Leek (John Hopkins University)
• Stephen Montgomery (Stanford University)

Objectives

Over the past few years, an increasing number of large scale data sets have been made available in molecular biology. GTEx, for example, produced more than 18,000 RNA-Seq assays for multiple tissues in 900 individuals, Mindact generated gene expression data from about 7000 breast tumors in a single study, and 23andMe claims to have sequenced about 900,000 genomes. This growth in the available genomic data is expected to increase our capacity to identify cancer subtypes, regulatory genes, SNPs associated with phenotypes of interest, and biomarkers for many human traits. It also suggests exploring more complex feature representations when analyzing these datasets.

However, increasing the number of samples and features leads to a set of \textbf{interrelated statistical and computational problems}. Accordingly, the objectives of our workshop will be to:

Systematically identify the statistical and computational

problems arising during the analysis of large scale data in molecular biology;

Bring together experts in computational biology, molecular

biology, computer science, and statistics to propose innovative solutions to these problems, by leveraging recent advances in each of these fields.

Relevance, importance and timeliness

A number of studies generating high throughput molecular data for a large number of biological samples have been completed over the past five years. \textbf{Our workshop is important because the availability of these datasets holds great promises in terms of health improvement and understanding of molecular biology}. First of all, if exploited correctly, larger sample sizes should improve our ability to predict phenotypes of interest from molecular data. This entails very important applications such as improving the survival of cancer patients by better predicting which treatment they should receive, or decreasing bacterial resistances by predicting which antibiotic is efficient against a new strain. Correctly exploiting large scale datasets should also allow us to \textbf{better identify genetic and epigenetic determinants of these phenotypes, yielding a better understanding of human diseases and potentially guiding the development of new treatments and prevention policies}. In particular, more samples should allow the detection of less frequent variants in the human genome, or more complex features involving several modalities (copy number, expression, methylation, etc) associated with diseases. Finally, larger sample sizes should help with essential unsupervised tasks such as the \textbf{inference of regulation networks, or the identification of cancer subtypes}.

Our workshop is relevant because \textbf{all of these promises are conditioned on our solving of new statistical and computational challenges}. First (Challenge 1), we need to build new feature spaces and estimators whose complexity is adapted to these larger sample sizes, which involves designing novel, potentially more complex descriptors of the samples but still controlling the bias/variance trade-off. Second (Challenge 2), we need to build models which correctly integrate different modalities, such as copy number variation and gene expression. Third (Challenge 3), larger scale studies are more prone to unwanted variations, because they typically involve different labs and technical changes which can affect the measurements and become confounders in retrospective analyses. Similar or worse problems arise when trying to combine several existing datasets. We need methods which take this unwanted variation into account. Finally, (Challenge 4), we need new algorithms that make existing statistical tools scalable to the new sample sizes, and make estimation over the larger and more complex features of Challenge 1 tractable.

We also believe our workshop is very timely because \textbf{some of these statistical and computational challenges are starting to be addressed in other application fields} of statistics. It is crucial to recognize that the orders of magnitude are still very different in molecular biology and other data science application fields because of the cost and complexity of the data generation process: current large scale high throughput sequencing data sets typically contain a few thousand of samples but millions of features while computer vision, web, or astronomy datasets can involve billions or trillions of samples and relatively fewer features. A first consequence is that not all recent developments in machine learning are immediately transferable to computational biology. For example, so called deep learning methods have gained a lot of popularity and now represent the state of the art in computer vision but may not be the most appropriate tool for prediction of cancer outcome from molecular data. However, the fact that other fields already have much larger sample sizes also means that they had to develop efficient and scalable algorithms for basic tasks like feature selection, classification or clustering. \textbf{These recent developments are a great source of inspiration for computational biology, where large scale computation is still an emerging challenge}.

We believe \textbf{having a small scale workshop involving international experts in machine learning, statistics, computational biology and molecular biology is of utmost importance} for three main reasons. The first reason is that the technical advances we are referring to are very recent, often unknown to computational biologists and involve paradigms such as online optimization, accelerated gradient methods and network flow optimization, with which they are sometimes unfamiliar. The second reason is that it is not always obvious to non-statisticians which novel methods are appropriate given the current n/p regime. Conversely, the third reason is that statisticians do not know what the recent challenges are in molecular biology. Having them work on abstract versions of the problems is often not satisfactory as it is necessary to be aware of technical realities and of the underlying biology of the problem to come up with useful solutions.

17w5104: Mathematical Approaches to Evolutionary Trees and Networks Workshop @BIRS_math 2/12/17 #ITBio

Arriving in Banff, Alberta Sunday, February 12 and departing Friday February 17, 2017

Organizers

• Leonid Chindelevitch (Simon Fraser University)
• Caroline Colijn (Imperial College London)
• Amaury Lambert (University Pierre and Marie Curie, Paris)
• Marta Luksza (Institute of Advanced Study, Princeton University)
• Vincent Moulton (University of East Anglia)
• Tandy Warnow (University of Illinois)

Objectives

The objectives of the workshop are to bring mathematicians working in three key areas together to make progress in these problems. We will also invite several biologists who are keen to engage with mathematicians on the challenges posed by new data on evolutionary processes. Key challenges in the field at the moment are focused around the following emerging inter-related areas, each of which is raising mathematically interesting problems:

1. Inference with evolutionary trees and networks: Ultimately it is necessary not just to obtain evolutionary trees from data using standard methods, but to infer aspects of an underlying biological process. This requires understanding the likelihood of an evolutionary tree or network, or at least some of its informative features, using some stochastic process as the underlying ecological model. In principle, this approach allows simultaneous inference of both evolutionary trees and parameters of the ecological model. Coalescent theory has made considerable progress, for example, in obtaining tree likelihoods for sparsely sampled populations with geographical structure or with known past demographics (see for just one example [5]). In some simplified cases, epidemiological inference methods can estimate transmission trees [2], branching rates through time [5] and other aspects of epidemic spread [7]. However, none of these approaches is currently applicable if there is non-tree-like evolution, or where datasets are large. Furthermore, the range of models for which we can write down a tree likelihood is very limited. This raising nice new problems in probability, statistical inference and ecological modelling. Recently, more general processes (e.g. Lambda-coalescents, which allow multiple rather than strictly pairwise coalescent events) are beginning to be used to model populations with large offspring variance, or even to model selection in a non-parametric fashion [3]. This is potentially a powerful tool particularly for bacteria, which may acquire resistance to antibiotics and spread rapidly as a consequence, yielding both highly variable effective offspring numbers and a need to model selection carefully.

2. Understanding spaces of evolutionary trees: There are a large number of possible labelled, rooted binary trees for a given set of nn tips (ie for a given set of sequence data): (2n−3)!!=(2n−3)(2n−5)...(3)(1)(2n−3)!!=(2n−3)(2n−5)...(3)(1). This works out to 1018410184 trees on 100 tips; in contrast, current datasets for evolving bacteria contain thousands of tips. Not even the tools of Bayesian inference, the natural approach in such situations, can systematically explore spaces this big. This motivates the development of mathematical approaches for the exploration of tree space. These include new approaches to continuous tree spaces, including those from tropical geometry [8], and the use of tree metrics [1]. These in turn can lead to tools for averaging trees , and for navigating tree space in efficient ways [6] -- with profound applications in statistical inference from sequence data. Generalizing metrics to the case of evolutionary networks (for example tree-based networks) is another natural and important question. 

3. Summarising trees and networks using combinatorial tools: Uncovering shape features, spectral features and other ways to describe trees using quantities that are mathematically tractable will be of considerable interest [4]. As one example, where likelihoods are truly intractable, rapid tools for likelihood-free inference can be used to infer evolutionary processes from sequence data, but only where there are informative ways to summarize key features of the data. Trees are natural combinatorial structures with connections to data; for example, a binary tree is a sequence of partitions of the set of tips (sequences in a dataset), where each partition is one block smaller than the previous one, moving back through time from the partition with each tip on its own to the partition with all tips in one block as we move from the tips of the tree to the root. If the tree is not binary (ie it allows multifurcations), more than two blocks can combine at a branching event. Because of the natural link to partitions, the study of tree shapes links to the enumeration of partitions and to lattice path combinatorics. These in turn allow the characterization and enumeration of possible tree shapes. Meanwhile the study of motifs in other biological networks has been fruitful, and could be extended to tree and evolutionary network shapes. Trees and evolutionary networks are of course also graphs (with an added time dimension); the tools of algebraic graph theory are now finding application in this area of mathematical biology.

The community's response to the idea for this workshop has been very positive. A * beside a participant's name indicates that they have expressed enthusiasm for the workshop, and plan to attend. 

References [1] Louis J Billera, Susan P Holmes, and Karen Vogtmann. Geometry of the space of phylogenetic trees. Adv. Appl. Math., 27(4):733–767, November 2001. [2] Xavier Didelot, Jennifer Gardy, and Caroline Colijn. Bayesian inference of infectious disease transmission from whole-genome sequence data. Mol. Biol. Evol., 31(7):1869–1879, July 2014. [3] Alison M Etheridge, Robert C Griffiths, and Jesse E Taylor. A coalescent dual process in a moran model with genic selection, and the lambda coalescent limit. Theor. Popul. Biol., 78(2):77–92, September 2010. [4] Fanny Gascuel, Regis Ferriere, Robin Aguilee, and Amaury Lambert. How ecology and landscape dynamics shape phylogenetic trees. Syst. Biol., 64(4):590–607, July 2015. [5] Amaury Lambert and Tanja Stadler. Birth–death models and coalescent point processes: The shape and probability of reconstructed phylogenies. Theor. Popul. Biol., 90(0):113–128, December 2013. [6] Tom M W Nye. An algorithm for constructing principal geodesics in phylogenetic treespace. IEEE/ACM Trans. Comput. Biol. Bioinform., 11(2):304–315, March 2014. [7] David A Rasmussen, Erik M Volz, and Katia Koelle. Phylodynamic inference for structured epidemiological models. PLoS Comput. Biol., 10(4):e1003570, April 2014. 2 [8] David Speyer and Bernd Sturmfels. The tropical grassmannian. Adv. Geom., 4(3):389–411, 2004.

.@JohnsHopkins has an @Coursera sequence of 7 courses on Genomic Data Science starting soon.

Introduction to Genomic Technologies
Genomic Data Science with Galaxy
Python for Genomic Data Science
Command Line Tools for Genomic Data Science
Algorithms for DNA Sequencing
Bioconductor for Genomic Data Science
Statistics for Genomic Data Science
Genomic Data Science Capstone