Skeleton of the MMHC algorithm {Rfast2}

The skeleton of a Bayesian network learned with the MMHC algorithm

Description

The skeleton of a Bayesian network learned with the MMHC algorithm.

Usage

mmhc.skel(x, method = "pearson", max_k = 3, alpha = 0.05,
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 from the R package Rfast. 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.

max_k

The maximum conditioning set to use in the conditional indepedence test (see Details). Integer, default value is 3.

alpha

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

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 for parallel computations.

Details

The max_k option: the maximum size of the conditioning set to use in the conditioning independence test. Larger values provide more accurate results, at the cost of higher computational times. When the sample size is small (e.g., <50 observations) the max_k parameter should be 3 for example, otherwise the conditional independence test may not be able to provide reliable results.

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 and Stefanos Fafalios.

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

References

Tsamardinos, I., Aliferis, C. F. and Statnikov, A. (2003). Time and sample efficient discovery of Markov blankets and direct causal relations. In Proceedings of the ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 673-678). ACM.

Brown, L. E., Tsamardinos, I. and Aliferis, C. F. (2004). A novel algorithm for scalable and accurate Bayesian network learning. Medinfo, 711-715.

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.skel, mmpc, mmpc2

Examples

# simulate a dataset with continuous data
x <- matrix( rnorm(300 * 30, 1, 100), nrow = 300 )
a <- mmhc.skel(x)