Score functions

BIC score

Calculate the local score with BIC for the linear Gaussian case.

Parameters

Data: (sample, features).

i: current index.

PAi: parent indexes.

parameters: None.

Returns

score: Local BIC score.

BIC

Schwarz, Gideon. “Estimating the dimension of a model.” The annals of statistics (1978): 461-464.

BDeu score

Calculate the local score with BDeu for the discrete case.

Parameters

Data: (sample, features).

i: current index.

PAi: parent indexes.

parameters:
  • sample_prior: sample prior.

  • structure_prior: structure prior.

  • r_i_map: number of states of the finite random variable ‘X_{i}’.

Returns

score: Local BDeu score.

BDeu

Buntine, Wray. “Theory refinement on Bayesian networks.” Uncertainty proceedings 1991. Morgan Kaufmann, 1991. 52-60.

Generalized score with cross validation

Calculate the local score using negative k-fold cross-validated log likelihood as the score, based on a regression model in RKHS [GeneralizedScore].

Parameters

Data: (sample, features).

i: current index.

PAi: parent indexes.

parameters:
  • kfold: the fold number in cross validation.

  • lambda: regularization parameter.

Returns

score: Local score.

Generalized score with marginal likelihood

Calculate the local score by negative marginal likelihood, based on a regression model in RKHS [GeneralizedScore].

Parameters

Data: (sample, features).

i: current index.

PAi: parent indexes.

parameters: None.

Returns

score: Local score.

Generalized score with cross validation for multi-dimensional variables

Calculate the local score using negative k-fold cross-validated log likelihood as the score, based on a regression model in RKHS for data with multi-dimensional variables [GeneralizedScore].

Parameters

Data: (sample, features).

i: current index.

PAi: parent indexes.

parameters:
  • kfold: the fold number in cross validation.

  • lambda: regularization parameter.

  • dlabel: indicate the data dimensions that belong to each variable. It is only used when the variables have multivariate dimensions.

Returns

score: Local score.

Generalized score with marginal likelihood for multi-dimensional variables

Calculate the local score by negative marginal likelihood, based on a regression model in RKHS for data with multi-dimensional variables [GeneralizedScore].

Parameters

Data: (sample, features).

i: current index.

PAi: parent indexes.

parameters:
  • dlabel: indicate the data dimensions that belong to each variable. It is only used when the variables have multivariate dimensions.

Returns

score: Local score.

GeneralizedScore(1,2,3,4)

Huang, Biwei, et al. “Generalized score functions for causal discovery.” KDD. 2018.