# 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 causallearn.search.ScoreBased.GES import ges
Record = ges(X, score_func, maxP, parameters)
```

## Parameters

**X**: numpy.ndarray, shape (n_samples, n_features). Data, where n_samples is the number of samples
and n_features is the number of features.

**score_func**: The score function you would like to use, including (see score_functions.).“local_score_BIC”: BIC score 3.

“local_score_BDeu”: BDeu score 4.

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

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

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

“local_score_marginal_multi”: 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.