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

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

3. 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

4. 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,

5. 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

6. 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)

7. 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

8. 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?)

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

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

12. 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)

13. The Learned Network Structure

14. 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

15. 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)

16. 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)

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

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

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

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

21. 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

22. 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

23. References
Bayes nets: Friedman,