KBMN Online Appendix

Parameters used in training

Weights are trained using pseudo-likelihood (PL)
We optimize the PL by using conjugate gradient search with line minimization
The PL is considered to have converged if it improves by no more than 0.001% from one iteration to the next. We also stop if it has taken 200 iterations. In our experiments, It usually converged in about 100-200 iterations.
We used a Gaussian prior with mean and standard deviation of 1.0. A uniform prior produced nearly identical results.
For the first iteration, the weights are initialized at the mean of their prior (1.0).
We used exact counting of the number of satisfying assignments to ground clauses.

Parameters used in testing

Testing is done using Gibbs sampling
We take 10000 samples (full passes over all variables) for our probability estimates
The sampling is split in to 10 "chunks". Each chunk is initialized from a random starting point, then optimized using MaxWalkSat to find a mode of the distribution.
Each chunk also has a burnin of 100 samples. That is, we do 100 passes over the variables before starting to collect the 1000 samples for that particular chunk.

Parameters used for Bayesian networks

Data was binned by splitting into 5 bins of equal probability.
Smoothing was done by adding 1 count to each entry in the CPTs.
The class variable was added as a Boolean attribute for the BN, which was then used for class probability estimation.
Structure learning was limited to no more than 4 parents per node.
Vfbn2, part of VFML, was used for training the Bayesian network.

Parameters used for naive Bayes model

Data was binned by splitting into 5 bins of equal probability.
Smoothing was done by adding 1 count to each entry in the P(Xi|class) multinomial.

Parameters used for Claudien

scope(local)
min_accuracy(0.1)
search(breadth)
beam_size(5)
max_real_time(7200) (2 hours)
min_coverage(1)
max_complexity(10)

Claudien Language bias

The language bias is set up to enable arbitrary predicates in the positive and negative sides of the clauses that claudien induces. I limit the number of variables per clause to 3, and allow each predicate to appear up to 2 times as a positive literal and up to 2 times as a negative literal. The bias is aware of predicate typing, which helps it limit the variables. To reduce the search space, I removed the SameXXX predicates.

Here is the exact language bias:

dlab_template('
0-len:[
  pTaughtBy(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pTaughtBy(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pCourseLevel(1-1:[C4_0,C4_1,C4_2],1-1:[C7_0,C7_1,C7_2]),
  pCourseLevel(1-1:[C4_0,C4_1,C4_2],1-1:[C7_0,C7_1,C7_2]),
  pPosition(1-1:[C1_0,C1_1,C1_2],1-1:[C8_0,C8_1,C8_2]),
  pPosition(1-1:[C1_0,C1_1,C1_2],1-1:[C8_0,C8_1,C8_2]),
  pProjectMember(1-1:[C5_0,C5_1,C5_2],1-1:[C1_0,C1_1,C1_2]),
  pProjectMember(1-1:[C5_0,C5_1,C5_2],1-1:[C1_0,C1_1,C1_2]),
  pAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pPhase(1-1:[C1_0,C1_1,C1_2],1-1:[C9_0,C9_1,C9_2]),
  pPhase(1-1:[C1_0,C1_1,C1_2],1-1:[C9_0,C9_1,C9_2]),
  pTempAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pTempAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pYearsInProgram(1-1:[C1_0,C1_1,C1_2],1-1:[C10_0,C10_1,C10_2]),
  pYearsInProgram(1-1:[C1_0,C1_1,C1_2],1-1:[C10_0,C10_1,C10_2]),
  pTA(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pTA(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pProfessor(1-1:[C1_0,C1_1,C1_2]),
  pProfessor(1-1:[C1_0,C1_1,C1_2]),
  pStudent(1-1:[C1_0,C1_1,C1_2]),
  pStudent(1-1:[C1_0,C1_1,C1_2]),
  pPublication(1-1:[C3_0,C3_1,C3_2],1-1:[C1_0,C1_1,C1_2]),
  pPublication(1-1:[C3_0,C3_1,C3_2],1-1:[C1_0,C1_1,C1_2])
  ]

<--

0-len:[
  pTaughtBy(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pTaughtBy(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pCourseLevel(1-1:[C4_0,C4_1,C4_2],1-1:[C7_0,C7_1,C7_2]),
  pCourseLevel(1-1:[C4_0,C4_1,C4_2],1-1:[C7_0,C7_1,C7_2]),
  pPosition(1-1:[C1_0,C1_1,C1_2],1-1:[C8_0,C8_1,C8_2]),
  pPosition(1-1:[C1_0,C1_1,C1_2],1-1:[C8_0,C8_1,C8_2]),
  pProjectMember(1-1:[C5_0,C5_1,C5_2],1-1:[C1_0,C1_1,C1_2]),
  pProjectMember(1-1:[C5_0,C5_1,C5_2],1-1:[C1_0,C1_1,C1_2]),
  pAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pPhase(1-1:[C1_0,C1_1,C1_2],1-1:[C9_0,C9_1,C9_2]),
  pPhase(1-1:[C1_0,C1_1,C1_2],1-1:[C9_0,C9_1,C9_2]),
  pTempAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pTempAdvisedBy(1-1:[C1_0,C1_1,C1_2],1-1:[C1_0,C1_1,C1_2]),
  pYearsInProgram(1-1:[C1_0,C1_1,C1_2],1-1:[C10_0,C10_1,C10_2]),
  pYearsInProgram(1-1:[C1_0,C1_1,C1_2],1-1:[C10_0,C10_1,C10_2]),
  pTA(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pTA(1-1:[C4_0,C4_1,C4_2],1-1:[C1_0,C1_1,C1_2],1-1:[C6_0,C6_1,C6_2]),
  pProfessor(1-1:[C1_0,C1_1,C1_2]),
  pProfessor(1-1:[C1_0,C1_1,C1_2]),
  pStudent(1-1:[C1_0,C1_1,C1_2]),
  pStudent(1-1:[C1_0,C1_1,C1_2]),
  pPublication(1-1:[C3_0,C3_1,C3_2],1-1:[C1_0,C1_1,C1_2]),
  pPublication(1-1:[C3_0,C3_1,C3_2],1-1:[C1_0,C1_1,C1_2])
  ]
').