Skeleton of the FEDHC algorithm {pchc}

The skeleton of a Bayesian network produced by the FEDHC algorithm

Description

The skeleton of a Bayesian network produced by the FEDHC algorithm.

Usage

fedhc.skel(x, method = "pearson", alpha = 0.05, robust = FALSE,
ini.stat = NULL, R = NULL, parallel = FALSE)

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, this "pearson". If you have categorical data though, this must be "cat". In this case, make sure the minimum value of each variable is zero. The function "g2Test" in the R package Rfast and the relevant functions work that way.

alpha

The significance level (suitable values in (0, 1)) for assessing the p-values. Default value is 0.05.

robust

Do you want outliers to be removed prior to applying the PCHC algorithm? If yes, set this to TRUE to utilise the MCD.

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.

parallel

Set this to TRUE if you have millions of observations. In that instance it can reduce the computaitonal time by 1/3.

Details

Similar to MMHC and PCHC the first phase consists of a variable selection procedure, the FBED algortihm (Borboudakis and Tsamardinos, 2019).

Value

A list including:

ini.stat

The test statistics of the univariate associations.

ini.pvalue

The initial p-values univariate associations.

pvalue

A matrix with the logarithm of the p-values of the updated associations. This final p-value is the maximum p-value among the two p-values in the end.

runtime

The duration of the algorithm.

ntests

The number of tests conducted during each k.

G

The adjancency matrix. A value of 1 in G[i, j] appears in G[j, i] also, indicating that i and j have an edge between them.

Author(s)

Michail Tsagris.

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

References

Tsagris M. (2022). The FEDHC Bayesian Network Learning Algorithm. Mathematics, 10(25): 2604.

Borboudakis G. and Tsamardinos I. (2019). Forward-backward selection with early dropping. Journal of Machine Learning Research, 20(8): 1-39.

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

pchc.skel, mmhc.skel, fedhc, fedhc.skel.boot, dcor.fedhc.skel

Examples

# simulate a dataset with continuous data
x <- matrix( rnorm(200 * 50, 1, 10), nrow = 200 )
a <- fedhc.skel(x)