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The course offers an introduction to graphical models and their application to complex biological systems. Graphical models combine a statistical methodology with efficient algorithms for inference in settings of high dimension and uncertainty. The unifying graphical model framework is developed and used to examine several classical and topical computational biology methods.
The goal of this course is to establish the common language of graphical models for applications in computational biology and to see this methodology at work for several real-world data sets.
Graphical models are a marriage between probability theory and graph theory. They combine the notion of probabilities with efficient algorithms for inference among many random variables. Graphical models play an important role in computational biology, because they explicitly address two features that are inherent to biological systems: complexity and uncertainty. We will develop the basic theory and the common underlying formalism of graphical models and discuss several computational biology applications. Topics covered include conditional independence, Bayesian networks, Markov random fields, Gaussian graphical models, EM algorithm, junction tree algorithm, model selection, Dirichlet process mixture, causality, the pair hidden Markov model for sequence alignment, probabilistic phylogenetic models, phylo-HMMs, microarray experiments and gene regulatory networks, protein interaction networks, learning from perturbation experiments, time series data and dynamic Bayesian networks. Some of the biological applications will be explored in small data analysis problems as part of the exercises.
Course number: 262-0002-00L
|Lecture||Thursday, 10am – 12pm||CAB G 56|
|Tutorial||Thursday, 12pm – 1:30pm||
CAB G 59
All lectures will be given in English and are accompanied by a 2h tutorial every second week. For each tutorial, there will be assignments that need to be handed in (schedule to be announced). To be admitted to the final exam, 50% of the points for exercises (involving both theory and practical data analysis in R) during the semester are required. The final grade is based on the oral exam.
||Bayesian networks and gene regulation||
||EM algorithm and motif finding||
||Markov chains and hidden Markov models||Lecture 3||
Hidden Markov models for sequence alignment
||Statistical phylogenetics||Lecture 5||
||Exact inference in graphical models: sum-product algorithm||Lecture 6|
||Sampling and variational inference||Lecture 7||
|Apr 12||--- Easter break ---|
||Model selection||Lecture 8|
||Dynamic Bayesian networks and gene expression time series||Lecture 9||Exercise 5||
||Nested effects models and RNA interference||
||May 10||Conjunctive Bayesian networks and cancer progression||
||--- Ascension Day ---|
Single-nucleotide variant calling in tumor cell populations
Estimating the genetic diversity of virus populations
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