# Generalized score with marginal likelihood

## Generalized score with marginal likelihood for single dimensional variables

Calculate the local score by negative marginal likelihood, based on a regression model in RKHS 1.

### Usage

    from causal-learn.score.LocalScoreFunction import local_score_marginal_general
    score = local_score_marginal_general(Data, Xi, PAi, parameters)

### Parameters

Data: (sample, features).

Xi: current index.

PAi: parent indexes.

parameters: None.

### 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 1.

### Usage

    from causal-learn.score.LocalScoreFunction import local_score_marginal_multi
    score = local_score_marginal_multi(Data, Xi, PAi, parameters)

### Parameters

Data: (sample, features).

Xi: 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.

1(1,2)

  Huang, B., Zhang, K., Lin, Y., Schölkopf, B., & Glymour, C. (2018, July). Generalized score functions for causal discovery. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (pp. 1551-1560).