Backward selection algorithms using the distance correlation {dcorVS}

Backward selection algorithms using the distance correlation

Description

Backward selection algorithms using the distance correlation.

Usage

dcor.bsmmpc(y, x, max_k = 3, alpha = 0.05, B = 999)
dcor.bs(y, x, alpha = 0.05)

Arguments

y

A numerical vector with the response variable.

x

A numerical matrix with the predictor variables.

max_k

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

alpha

The significance level for assessing the p-values. Default value is 0.05.

B

The number of permutations to execute to compute the p-value of the distance correlation.

Details

The max_k option in the mmpc algorithm: 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.

The dcor.bs() performs the classical backward selection.

Value

A list including:

runtime

The duration of the algorithm.

res

A matrix with all variables and their corresponding (logarithm) of the p-values of the updated associations. For the mmpc algorithm, the final p-value is the maximum p-value among the two p-values in the end.

Author(s)

Michail Tsagris.

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

References

Szekely G.J., Rizzo M.L. and Bakirov N.K. (2007). Measuring and Testing Independence by Correlation of Distances. Annals of Statistics, 35(6): 2769–2794.

Szekely G.J. and Rizzo M. L. (2014). Partial distance correlation with methods for dissimilarities. Annals of Statistics, 42(6): 2382–2412.

Huo X. and Szekely G.J. (2016). Fast computing for distance covariance. Technometrics, 58(4): 435–447.

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.

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

See Also

dcor.fbed

Examples

y <- rnorm(100)
x <- matrix( rnorm(100 * 10), ncol = 10 )
a <- dcor.bs(y, x)