# Bayesian network learning with cutting planes

This webpage contains supplementary materials for:

• James Cussens. Bayesian network learning with cutting planes In Fabio G. Cozman and Avi Pfeffer, editors, Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011), pages 153-160, Barcelona, 2011. AUAI Press.

The slides of a talk on this work given at the Gatsby Institute on 23 March 2011 are also available.

If anything does not work drop me a line.

## Family scores

This is the data described in Table 1 of the paper and is supplied as a single gzipped tar file. The final 4 datasets are not included since they are not mine to distribute. Note that .tgz file does not create a new directory when unpacked.

These family scores are all you need if you want to try out an alternative approach to BN learning. Each 'family' is a BN variable together with a candidate set of parents. There is a score associated with each family. The score of any given DAG is just the sum of relevant family scores. 'Exact' BN learning from such data therefore consists of nothing more than choosing a parent set for each variable such that: (1) the resulting graph is acylic and (2) the score is maximal.

The format of the data is as follows:

• The first line is the total number of BN variables.
• The rest of the file has a section for each variable. Variables are integers starting from 0. So, for example, if there are 35 variables in total there will be sections for variables 0, 1, ... 34 (in that order).
• The section for a variable starts with a single line with the name of the variable and the number of parent sets recorded for it. So, for example "0 81" states that variable 0 has 81 candidate parent sets.
• The remaining lines in the section for a variable are family scores. Each such line starts with the score itself, the number of parents in the parent set and then the parents themselves, if any. So, for example, "-106.565548505 3 13 15 11" states that parent set {13,15,11} has score -106.565548505 (and contains 3 members).

This format originated with the work done in Learning Bayesian Network Structure using LP Relaxations. Tommi Jaakkola, David Sontag, Amir Globerson, Marina Meila. AISTATS 2010

## Detailed results

The output produced by SCIP is available for the runs reported in Table 2 and Table 3. At the end of each file the BN itself is printed as a list of 'families'. Each family has its family score given. The last line is the time taken to do the SCIP run as measured by UNIX time (not SCIP).

## Source code

GOBNILP, an improved version of the software used for this paper, is now available.