epilogi {epilogi}

The epilogi Variable Selection Algorithm for Continuous Data.

Description

The \epsilonpilogi Variable Selection Algorithm for Continuous Data.

Usage

epilogi(y, x, tol = 0.01, alpha = 0.05)

Arguments

y

A vector with the continuous response variable.

x

A matrix with the continuous predictor variables.

tol

The tolerance value for the algortihm to terminate. This takes values greater than 0 and it refers to the change between two successive R^2-adjusted values.

alpha

The significance level to deem a predictor variable is statistically equivalent to a selected variable.

Details

The \epsilonpilogi variable selection algorithm (Lakiotaki et al., 2023) is a generalisation of the \gamma-OMP algorithm (Tsagris et al. 2022). It applies the aforementioned algorithm with the addition that it returns possible statistically equivalent predictor(s) for each selected predictor. Once a variable is selected the algorithm searches for possible equivalent predictors using the partial correlation between the residuals.

The heuristic method to consider two predictors R and C informationally equivalent given the current selected predictor S is determined as follows: first, the residuals r of the model using S are computed. Then, if the following two conditions hold R and C are considered equivalent: Ind(R; r | C) and Ind(r ; C | R), where Ind(R; r | C) denotes the conditional independence of R with r given C. When linearity is assumed, the test can be implemented by testing for significance the corresponding partial correlation. The tests Ind return a p-value and independence is accepted when it is larger than a threshold (significance value, argument alpha). Intuitively, R and C are heuristically considered equivalent, if C is known, then R provides no additional information for the residuals r, and if R is known, then C provides no additional information for r.

Value

A list including:

runtime

The runtime of the algorithm.

result

A matrix with two columns. The selected predictor(s) and the adjusted R^2-values.

equiv

A list with the equivalent predictors (if any) corresponding to each selected predictor.

Author(s)

Michail Tsagris.

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

References

Lakiotaki K., Papadovasilakis Z., Lagani V., Fafalios S., Charonyktakis P., Tsagris M. and Tsamardinos I. (2023). Automated machine learning for Genome Wide Association Studies. Bioinformatics.

Tsagris M., Papadovasilakis Z., Lakiotaki K. and Tsamardinos I. (2022). The \gamma-OMP algorithm for feature selection with application to gene expression data. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 19(2): 1214–1224.

See Also

pcor.equiv

Examples

#simulate a dataset with continuous data
set.seed(1234)
n <- 500
x <- matrix( rnorm(n * 50, 0, 30), ncol = 50 )

#define a simulated class variable
y <- 2 * x[, 1] - 1.5 * x[, 2] + x[, 3] + rnorm(n, 0, 15)

# define some simulated equivalences
x[, 4] <- x[, 1] + rnorm(n, 0, 1)
x[, 5] <- x[, 2] + rnorm(n, 0, 1)

epilogi(y, x, tol = 0.05)