Network Inference Chris Holmes Oxford Centre for Gene Function, &, Department of Statistics University of Oxford

Overview Statistical Inference Challenges of inferring network topology & the structure of local dependencies Use of “Integrative Genomics” to aid inference Conclusions

Inference Inference is the process of “learning from data” We have two objects to infer: Network structure (topology) Functional form of the dependencies within a given network structure

Probabilistic (Bayesian) Networks Graphical structure used to define interactions which encode a set of conditional independencies Way of simplifying a joint distribution Have become extremely popular in genomics - R. Cowell et al, Springer (1999) - Friedman, http://www.cs.huji.ac.il/~nir/

Probabilistic Networks Advantages: Coherent axiomatic framework Provides a calculus for integrating information from multiple sources that guards against logical inconsistencies Allows precise statements of uncertainty - on global network structure (topologies), and marginals Sequential Experimental design - Calculate optimal follow up experiments to learn most about the network structure given current state of knowledge

Probabilistic Networks Disadvantages: Causal relationships not explicitly handled Dawid AP. Causal inference without counterfactuals (with Discussion). J Am Statist Assoc (2000) Restrictions on valid structures Hammersley-Clifford theorem; Rue & Held, Gaussian Markov Random Fields, Chapman Hall (2005)

Network Inference Prior on network space leads to posterior Computational framework to learn Markov Chain Monte Carlo: Wilks et al, MCMC in practice, Springer, (1999) Stochastic search

Hypothesis-Driven Networks Originally networks were hypothesis driven Well defined small networks Experiments set up to test specific hypothesis Then arrival of high-throughput genomic (disruptive) technologies Treats network structure unknown Data mining (data dredging?)

Bayesian Network Approach Aim is to find graph topology that maximises likelihood given the data

Finding Optimal Network – Hard Problem Need to use heruistics and greedy algorithms

Data Driven Networks Data is extremely sparse, compared with the dimensionality of the network space Great uncertainty in any conclusions High numbers of false positives (false connections) and false negatives (missing connections) This uncertainty is encompassed in a fully Bayesian model, via the posterior distribution on network space, Pr(F | y)

The Learned Network Structure

Data Driven Networks A problem with data mining approaches Often the “data goes in one end and the answer comes out the other end untouched by human thought” – adapted from Doug Altman

Further complicating issues Dynamic networks Imoto (2002); Beal et al, Bioinformatics (2005) Network Dynamics Luscombe et al, Nature, (2004) Interventional analysis Ideker et al, Science, (2002)

Way Forward More refined Prior structures Multiple information sources Literature mining Rajagopalan, Bioinformatics (2005) Comparative genomics Amoutzias, EMBO (2004) Combining other genomic measurement platforms Schadt et al, Nat. Genet. (2005); Zhu et al, Cytogenet Genome Res. (2004); Beer and Tavazoie, Cell. (2004)

Improving Network Inference Perturbations Genetics Biological Context Expression observations Regulatory Signals Comparative Genomics

Integrative Genomics Combine information from multiple sources to improve precision Information is preserved across sources while noise (random variation) is independent across information sources

Germline DNA Somatic DNA RNA Protein Physiology ENVIRONMENT Sequencing SNPs Epigenetics & CGH Microarrays Proteomics Metabonomics

Schadt, Nat. Genet. July 2005. Schadt et al.,

Transcription – cis and trans motifs AND Logic: AND Logic, OR Logic: OR Logic, NOT Logic: Combinatorial patterns help identify groups of transcripts predicted to show similar abundance profiles Beer and Tavazoie, Cell. 2004 Solid: Actual expression Dashed: Predicted

Conclusions Current move back towards more hypothesis driven analysis on smaller networks Conditioning on a well characterised network structures and using multiple data sources to infer and explore local topographic regions

References Bayes nets: Friedman, http://www.cs.huji.ac.il/~nir/