# 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.