| Title: | The 'epilogi' Variable Selection Algorithm for Continuous Data |
|---|---|
| Description: | The 'epilogi' variable selection algorithm is implemented for the case of continuous response and predictor variables. The relevant paper is: 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, 39(9): btad545. <doi:10.1093/bioinformatics/btad545>. |
| Authors: | Michail Tsagris [aut, cre] |
| Maintainer: | Michail Tsagris <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.2 |
| Built: | 2024-12-23 19:21:19 UTC |
| Source: | CRAN |
The 'pilogi' Variable Selection Algorithm for Continuous Data.
| Package: | epilogi |
| Type: | Package |
| Version: | 1.2 |
| Date: | 2024-12-20 |
| License: | GPL-2 |
Michail Tsagris [email protected].
Michail Tsagris [email protected].
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, 39(9): btad545.
Tsagris M., Papadovasilakis Z., Lakiotaki K. and Tsamardinos I. (2022). The -OMP algorithm for feature selection with application to gene expression data. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 19(2): 1214–1224.
The pilogi Variable Selection Algorithm for Continuous Data.
epilogi(y, x, tol = 0.01, alpha = 0.05, parallel = FALSE)epilogi(y, x, tol = 0.01, alpha = 0.05, parallel = FALSE)
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 |
alpha |
The significance level to deem a predictor variable is statistically equivalent to a selected variable. |
parallel |
If set to TRUE, some of the computations take place in parallel (in C++). |
The pilogi variable selection algorithm (Lakiotaki et al., 2023) is a generalisation of the -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.
A list including:
runtime |
The runtime of the algorithm. |
result |
A matrix with two columns. The selected predictor(s) and the adjusted |
equiv |
A list with the equivalent predictors (if any) corresponding to each selected predictor. |
Michail Tsagris.
R implementation and documentation: Michail Tsagris [email protected].
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, 39(9): btad545
Tsagris M., Papadovasilakis Z., Lakiotaki K. and Tsamardinos I. (2022). The -OMP algorithm for feature selection with application to gene expression data. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 19(2): 1214–1224.
#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)#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)
Equivalence test using partial correlation.
pcor.equiv(res, y, x, alpha = 0.05)pcor.equiv(res, y, x, alpha = 0.05)
res |
A vector with the residuals of the linear model. |
y |
A vector with a selected predictor. |
x |
A matrix with other predictors. |
alpha |
The significance level to check for predictors from x that are equivalent to y. |
A vector with 0s and 1s. 0s indicate that the predictors are not equivalent, while 1s indicate the equivalent predictors.
Michail Tsagris.
R implementation and documentation: Michail Tsagris [email protected].
#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) b <- epilogi(y, x, tol = 0.05) sel <- b$result[2, 1] ## standardise the y and x first y <- (y - mean(y)) / Rfast::Var(y, std = TRUE) x <- Rfast::standardise(x) res <- resid( lm(y ~ x[, sel] ) ) sela <- b$result[2:3, 1] pcor.equiv(res, x[, sela[2]], x[, -sela] ) ## bear in mind that this gives the third variable after removing the first two, ## so this is essentially the 5th variable in the "x" matrix.#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) b <- epilogi(y, x, tol = 0.05) sel <- b$result[2, 1] ## standardise the y and x first y <- (y - mean(y)) / Rfast::Var(y, std = TRUE) x <- Rfast::standardise(x) res <- resid( lm(y ~ x[, sel] ) ) sela <- b$result[2:3, 1] pcor.equiv(res, x[, sela[2]], x[, -sela] ) ## bear in mind that this gives the third variable after removing the first two, ## so this is essentially the 5th variable in the "x" matrix.