4. Learning Bayesian Networks from data
BNnder
Wilczy«ski
We can score dierent networks for the same data using
Bayesian Maximum Likelihood (ML)
Networks
Network
Finding the best (ML) probability distributions parameters
recontruction for a given network topology is easy
Application
examples Finding the best (ML) topology is NP-hard in a general
Wrap-up case (Chickering, 1995)
Many heuristic (mostly MCMC) approaches are in use for
learning BN topology (Friedman et al. '00, Husmeier '03,
Beer et al. 2003, Segal et al. 2003)
Software available: BN-toolbox for matlab (Murphy,
extended by Husmeier for DBNs), and Banjo (java,
Hartemink et al.)
5. But it doesn't have to be so hard
BNnder
Wilczy«ski
The space of possible graph topologies for N nodes is
N
Bayesian super-exponential (22 ), the fact that BNs need to be
Networks
acyclic does not help.
Network
recontruction This makes it extremely hard for MCMC methods to nd
Application
examples the right solution, so people settle for the average of
Wrap-up locally optimal results
If you know that your dataset is of limited size (which is
usually the case in bioinformatics) you can actually nd
your solution relatively fast (Dojer, 2006)
There is a price: you need to know something about the
ordering of your nodes, because we can't control the
acyclicity when using the fast algorithm
6. Enter BNnder
BNnder
Wilczy«ski
Bayesian
Networks
BNnder: python implementation of the fast and exact (!)
Network
algorithm for BN and DBN reconstruction (BW and
recontruction Norbert Dojer, Bioinformatics, 2009)
Application
examples Supports two dierent scoring functions (MDL and BDe)
Wrap-up Works with discretized and continuous data
Accepts datasets with perturbations (like gene KOs)
Free software (GPL), project hosted on
http://launchpad.net/bnfinder
7. Enter BNnder
BNnder
Wilczy«ski
Bayesian
Networks
BNnder: python implementation of the fast and exact (!)
Network
algorithm for BN and DBN reconstruction (BW and
recontruction Norbert Dojer, Bioinformatics, 2009)
Application
examples Supports two dierent scoring functions (MDL and BDe)
Wrap-up Works with discretized and continuous data
Accepts datasets with perturbations (like gene KOs)
Free software (GPL), project hosted on
http://launchpad.net/bnfinder
Runs fast!
8. How fast is fast?
BNnder
Wilczy«ski
Bayesian
Networks DBN example (Smith et al 2006) 2000 observations of
Network
recontruction
signal from 20 electrodes in a bird brain.
Application 6.4 · 1084 possible network topologies with not more than 5
examples
inputs per node
Wrap-up
Even when evaluating 1 million networks per minute we
need 1070 years to search through all of them
It takes 2 hours on my laptop to nd the optimal network
with BNFinder
9. (Almost) real world example
BNnder Reconstructing genetic network from simulated data (Dojer
Wilczy«ski
et al. 2006)
Husmeier (2003) analyzed performance of DBN
Bayesian
Networks reconstruction on the data simulated from an articial gene
Network network (Zak et al., 2001) showing that it does not
recontruction
Application
perform well
examples We showed (using BNnder prototype) that DBNs can
Wrap-up
recover the network structure if provided with data with
gene KOs
10. Predicting gene expression from sequence features
BNnder
Wilczy«ski
We know that sequence features (motifs, CRMs, chromatin
Bayesian
Networks
marks etc.) can be predictive of the target gene expression
Network
pattern (Segal et al 2003, Beer et al 2004, Dabrowski et al.
recontruction submitted)
Application
examples BNs are a very convenient framework for describing and
Wrap-up discovering such dependencies in a probabilistic model
11. Yet another regulatory genomics example
BNnder
Wilczy«ski Given a number of known examples of CRMs with their binding
Bayesian patterns and activity (expression pattern), can understand the
Networks rules of gene expression in Drosophila Development?
Network
recontruction
Application
examples
Wrap-up
(with Zhen Xuan Yeo)
12. Summary and Future plans
BNnder
Wilczy«ski Fast, exact, method to nd BN DBN topology
Bayesian Free software, Open source, python implementation
Networks
Network
recontruction
Application
examples
Wrap-up
http://launchpad.net/bnfinder
bartek@mimuw.edu.pl
13. Summary and Future plans
BNnder
Wilczy«ski Fast, exact, method to nd BN DBN topology
Bayesian Free software, Open source, python implementation
Networks
Network
recontruction Create a parallel version which would be easy to use on a
Application typical cluster.
examples
Wrap-up
Rewrite some crucial number crunching code in c
Improve models for continuous variables
Make the use of BN classication with BNFinder easier
Get more people invloved
http://launchpad.net/bnfinder
bartek@mimuw.edu.pl
14. Acknowledgments
BNnder
Wilczy«ski
Norbert Dojer
Bayesian
Networks Jerzy Tiuryn, Ania Gambin
Network
recontruction Michaª D¡browski
Application
examples
Zhen Xuan Yeo
Wrap-up Eileen Furlong
Funding: Polish ministry of Science grants No PBZ-MNiI-2/1/2005
and 3 T11F 021 28
