# GES with the BIC score or generalized score

## Algorithm Introduction

Greedy Equivalence Search (GES) algorithm with BIC score 1 and generalized score 2.

## Usage

    from causal-learn.search.ScoreBased.GES import ges
    Record = ges(X, score_func, maxP, parameters)

## Parameters

X: Data with T*D dimensions.

score_func: The score function you would like to use, including (see Score functions.).

  - “local_score_BIC”: BIC score 3.

  - “:ref:`local_score_BDeu <BDeu score>”: BDeu score 4.

  - “:ref:`local_score_CV_general <Generalized score with cross validation>”: Generalized score with cross validation for data with single-dimensional variates 2.

  - “:ref:`local_score_marginal_general <Generalized score with marginal likelihood>”: Generalized score with marginal likelihood for data with single-dimensional variates 2.

  - “:ref:`local_score_CV_multi <Generalized score with cross validation>”: Generalized score with cross validation for data with multi-dimensional variables 2.

  - “:ref:`local_score_marginal_multi <Generalized score with marginal likelihood>”: Generalized score with marginal likelihood for data with multi-dimensional variates 2.

maxP: Allowed maximum number of parents when searching the graph.

parameters: when using CV likelihood,

  - parameters[‘kfold’]: k-fold cross validation.

  - parameters[‘lambda’]: regularization parameter.

  - parameters[‘dlabel’]: for variables with multi-dimensions, indicate which dimensions belong to the i-th variable.

## Returns

- Record[‘G’]: learned causal graph.

- Record[‘update1’]: each update (Insert operator) in the forward step.

- Record[‘update2’]: each update (Delete operator) in the backward step.

- Record[‘G_step1’]: learned graph at each step in the forward step.

- Record[‘G_step2’]: learned graph at each step in the backward step.

- Record[‘score’]: the score of the learned graph.

1

  Chickering, D. M. (2002). Optimal structure identification with greedy search. Journal of machine learning research, 3(Nov), 507-554.

2(1,2,3,4,5)

  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).

3

  Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, 461-464.

4

  Buntine, W. (1991). Theory refinement on Bayesian networks. In Uncertainty proceedings 1991 (pp. 52-60). Morgan Kaufmann.