Bayesian network learning with the Gurobi MIP solver

## Project description

# Python implementation of GOBNILP

The Python implementation of GOBNILP is a program that uses Gurobi to learn Bayesian network structure from either complete discrete data or complete continuous data or precomputed local scores.

The Python implementation has benefited from work done by Josh Neil on computing BDeu local scores from discrete data and from work done by Matt Horder on BGe scoring. In both cases this work was done as a final-year BEng project at the University of York.

For full details on GOBNILP (including the C version), please consult the GOBNILP page:

https://www.cs.york.ac.uk/aig/sw/gobnilp/

# Running GOBNILP

To use the Python implementation of GOBNILP it is assumed that you have Anaconda Python installed as well as Gurobi. One easy way to achieve this is to install both using these instructions provided by Gurobi. You also need to install the numba and pygraphviz Python packages (this be done easily using Conda). pygraphviz requires GraphViz to be installed. Once you have done all this you just need to grab the Python files in this git repo and you are good to go.

Here are some example of running the Python implementation using the command line script rungobnilp.py and data files in the data directory. The discrete data files have the following format: the first line gives the names of the variables, the second line gives the arity of each variable (i.e. how many values each can take) and the remaining lines are the data values. Values are separated by spaces.

Running with default settings:

`python rungobnilp.py data/asia_10000.dat`

Finding the 4 best BNs (with the default limit, 3, on the size of parent sets):

`python rungobnilp.py --nopruning --kbest --nsols 4 data/asia_10000.dat`

Finding the 4 best BNs (with the default limit, 3, on the size of parent sets) and where only one BN for each Markov equivalence class is allowed:

`python rungobnilp.py --nopruning --mec --kbest --nsols 4 data/asia_10000.dat`

Finding the 4 best BNs with no limit on parent set size and where only one BN for each Markov equivalence class is allowed:

`python rungobnilp.py --nopruning --mec --kbest --nsols 4 --palim 999 data/asia_10000.dat`

In the examples above where the goal was to find the 'k best' BNs (subject to various constraints), it was necessary to use '--nopruning', to turn off pruning. When pruning is used (which is the default behaviour) then parent sets for BN variables which cannot occur in an optimal BN are removed, which typically greatly reduces the size of the problem and speeds up learning. However, when we seek not just an optimal BN but also sub-optimal ones then pruning must be turned off to ensure correct results.

The limit on parent set size is an important parameter. Note that its
default value is 3. Raising this value will slow down learning but may
lead to a higher scoring BN. For example, doing `python rungobnilp.py --palim 4 data/alarm_100.dat`

finds
a higher scoring network than using '--palim 3', and does not take too
long. Raising to '--palim 5' finds a better (well, higher scoring)
network, but takes just under 100 seconds on my desktop.

The Python implementation of GOBNILP also learns Gaussian networks from continuous data using BGe scoring. To do this use '--score BGe' on the command line. (The format for continuous data is similar to that for discrete data except there is no line for arity.) For example

`python rungobnilp.py --score BGe data/gaussian.dat`

or, to find a higher scoring Gaussian network (with BGe score -53258.9402):

`python rungobnilp.py --score BGe -p 4 data/gaussian.dat`

The file `gaussian.dat`

is from bnlearn where it is called
`guassian.test`

. See the bnlearn
page for
more information. bnlearn's hillclimbing algorithm `hc`

also finds an
optimal network (i.e. with score -53258.9402) using this data. Good
work Marco!

For more details run:
`python rungobnilp.py -h`

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