Bootstrapping the PCHC and PCTABU Bayesian network learning algorithms {pchc}

Bootstrapping the PCHC and PCTABU Bayesian network learning algorithms

Description

Bootstrapping the PCHC and PCTABU Bayesian network learning algorithms.

Usage

pchc.boot(x, method = "pearson", alpha = 0.05, ini.stat = NULL,
R = NULL, restart = 10, score = "bic-g", blacklist = NULL, whitelist = NULL,
B = 200, ncores = 1)

pctabu.boot(x, method = "pearson", alpha = 0.05, ini.stat = NULL,
R = NULL, tabu = 10, score = "bic-g", blacklist = NULL, whitelist = NULL,
B = 200, ncores = 1)

Arguments

x

A numerical matrix with the variables. If you have a data.frame (i.e. categorical data) turn them into a matrix using data.frame.to_matrix. Note, that for the categorical case data, the numbers must start from 0. No missing data are allowed.

method

If you have continuous data, you can choose either "pearson" or "spearman". If you have categorical data though, this must be "cat". In this case, make sure the minimum value of each variable is zero. The g2test and the relevant functions work that way.

alpha

The significance level for assessing the p-values.

ini.stat

If the initial test statistics (univariate associations) are available, pass them through this parameter.

R

If the correlation matrix is available, pass it here.

restart

An integer, the number of random restarts.

tabu

An integer, the length of the tabu list used in the tabu function.

score

A character string, the label of the network score to be used in the algorithm. If none is specified, the default score is the Bayesian Information Criterion for both discrete and continuous data sets. The available score for continuous variables are: "bic-g" (default), "loglik-g", "aic-g", "bic-g" or "bge". The available score categorical variables are: "bde", "loglik" or "bic".

blacklist

A data frame with two columns (optionally labeled "from" and "to"), containing a set of arcs not to be included in the graph.

whitelist

A data frame with two columns (optionally labeled "from" and "to"), containing a set of arcs to be included in the graph.

B

The number of bootstrap resamples to draw. The algorithm is performed in each bootstrap sample. In the end, the adjacency matrix on the observed data is returned, along with another adjacency matrix produced by the bootstrap. The latter one contains values from 0 to 1 indicating the proportion of times an edge between two nodes was present.

ncores

The number of cores to use, in case of parallel computing.

Details

The PC algorithm as proposed by Spirtes et al. (2001) is first implemented followed by a scoring phase, such as hill climbing or tabu search. The PCHC was proposed by Tsagris (2021), while the PCTABU algorithm is the same but instead of the hill climbing scoring phase, the tabu search is employed.

Value

A list including:

mod

A list including the output of the pchc or the pctabu function.

Gboot

The bootstrapped adjancency matrix of the Bayesian network.

runtime

The duration of the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Tsagris M. (2021). A new scalable Bayesian network learning algorithm with applications to economics. Computational Economics, 57(1):341-367.

Spirtes P., Glymour C. and Scheines R. (2001). Causation, Prediction, and Search. The MIT Press, Cambridge, MA, USA, 3nd edition.

Tsamardinos I. and Borboudakis G. (2010) Permutation Testing Improves Bayesian Network Learning. In Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2010, 322-337.

Tsamardinos I., Brown E.L. and Aliferis F.C. (2006). The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning, 65(1): 31-78.

See Also

fedhc, mmhc, pchc, pchc.skel

Examples

# simulate a dataset with continuous data
x <- matrix( rnorm(200 * 20, 1, 10), nrow = 200 )
a <- pchc.boot(x, B = 50)