Network Inference

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Network Inference

• Chris Holmes
• Oxford Centre for Gene Function, ,
• Department of Statistics
• University of Oxford

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Overview

• Statistical Inference
• Challenges of inferring network topology the
  structure of local dependencies
• Use of Integrative Genomics to aid inference
• Conclusions

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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

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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/

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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

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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)

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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

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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?)

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Bayesian Network Approach
Aim is to find graph topology that maximises
likelihood given the data
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Finding Optimal Network Hard Problem
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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)

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The Learned Network Structure
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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

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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)

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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)

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

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

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Germline DNA
ENVIRONMENT
Somatic DNA
RNA
Protein
Physiology
Sequencing SNPs
Epigenetics CGH
Microarrays
Proteomics
Metabonomics
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Schadt et al.,
Schadt, Nat. Genet. July 2005.
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Transcription cis and trans motifs
AND Logic, OR Logic
AND 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
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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

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References

• Bayes nets Friedman, http//www.cs.huji.ac.il/ni
  r/