Orthogonal matching pursuit variable selection {Rfast}

Orthogonal matching pursuit variable selection

Description

Orthogonal matching pursuit variable selection.

Usage

ompr(y, x, ystand = TRUE, xstand = TRUE, method = "BIC", tol = 2 )
omp(y, x, xstand = TRUE, tol = qchisq(0.95, 1) + log( length(y) ), type = "logistic" ) 

Arguments

y

The response variable, a numeric vector. For "ompr" this is a continuous variable. For "omp" this can be either a vector with discrete (count) data, 0 and 1, non negative values, strictly positive or proportions including 0 and 1.

x

A matrix with the data, where the rows denote the observations and the columns are the variables.

ystand

If this is TRUE the response variable is centered. The mean is subtracted from every value.

xstand

If this is TRUE the independent variables are standardised.

method

You can choose between the change in the BIC ("BIC"), the adjusted R^2 ("ar2"), the SSE ("SSE") or the classical p-value based ("pvalue").

tol

The tolerance value to terminate the algorithm. This is the change in the criterion value between two successive steps. For "ompr" the default value is 2 because the default method is "BIC". For "omp" the default value is the 95% quantile of the \chi^2 distribution with 1 degree of freedom plus the logarithm of the sample size.

type

This denotes the parametric model to be used each time. It depends upon the nature of y. The possible values are "logistic", "poisson", "quasipoisson", "quasibinomial", "normlog", "gamma", "weibull", "mv" (for multivariate response variable) or "multinomial".

Value

For "ompr" a list including:

runtime

The runtime of the algorithm.

info

A matrix with two columns. The selected variable(s) and the criterion value at every step.

For "omp" a list including:

runtime

The runtime of the algorithm.

phi

The \phi parameter. In the cases of "quasipoisson", "quasibinomial" and "normlog" this is useful. For all other cases this is NULL.

info

A matrix with two columns. The selected variable(s) and the criterion value at every step.

Author(s)

Michail Tsagris

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

References

Pati Y. C., Rezaiifar R. & Krishnaprasad P. S. (1993). Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In Signals, Systems and Computers. 1993 Conference Record of The Twenty-Seventh Asilomar Conference on. IEEE.

Mazin Abdulrasool Hameed (2012). Comparative analysis of orthogonal matching pursuit and least angle regression. MSc thesis, Michigan State University. https://www.google.gr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwik9P3Yto7XAhUiCZoKHQ8XDr8QFgglMAA&url=https

Lozano A., Swirszcz G., & Abe N. (2011). Group orthogonal matching pursuit for logistic regression. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics.

The \gamma-OMP algorithm for feature selection with application to gene expression data. IEEE/ACM Transactions on Computational Biology and Bioinformatics (Accepted for publication) https://arxiv.org/pdf/2004.00281.pdf

See Also

cor.fbed, cor.fsreg, correls, fs.reg

Examples

x <- matrnorm(100, 400)
y <- rnorm(100)
a <- ompr(y, x)
a
x <- NULL