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| 1 | +#' Penalty Function Computation |
| 2 | +#' |
| 3 | +#' @description |
| 4 | +#' Compute the penalty function. |
| 5 | +#' |
| 6 | +#' @param omega A numeric scalar or vector at which the penalty is evaluated. |
| 7 | +#' |
| 8 | +#' @param penalty A character vector specifying one or more penalty types. |
| 9 | +#' Available options include: |
| 10 | +#' \enumerate{ |
| 11 | +#' \item "lasso": Least absolute shrinkage and selection operator |
| 12 | +#' \insertCite{tibshirani1996regression,friedman2008sparse}{grasps}. |
| 13 | +#' \item "atan": Arctangent type penalty \insertCite{wang2016variable}{grasps}. |
| 14 | +#' \item "exp": Exponential type penalty \insertCite{wang2018variable}{grasps}. |
| 15 | +#' \item "lq": Lq penalty \insertCite{frank1993statistical,fu1998penalized,fan2001variable}{grasps}. |
| 16 | +#' \item "lsp": Log-sum penalty \insertCite{candes2008enhancing}{grasps}. |
| 17 | +#' \item "mcp": Minimax concave penalty \insertCite{zhang2010nearly}{grasps}. |
| 18 | +#' \item "scad": Smoothly clipped absolute deviation \insertCite{fan2001variable,fan2009network}{grasps}. |
| 19 | +#' } |
| 20 | +#' |
| 21 | +#' @param lambda A non-negative scalar or vector of the same length as |
| 22 | +#' \code{penalty} specifying the regularization parameter. |
| 23 | +#' |
| 24 | +#' @param gamma A scalar or vector of the same length as \code{penalty} |
| 25 | +#' specifying the additional parameter for the penalty function. |
| 26 | +#' The defaults are: |
| 27 | +#' \enumerate{ |
| 28 | +#' \item "atan": 0.005 |
| 29 | +#' \item "exp": 0.01 |
| 30 | +#' \item "lq": 0.5 |
| 31 | +#' \item "lsp": 0.1 |
| 32 | +#' \item "mcp": 3 |
| 33 | +#' \item "scad": 3.7 |
| 34 | +#' } |
| 35 | +#' |
| 36 | +#' @return |
| 37 | +#' A data frame containing: |
| 38 | +#' \describe{ |
| 39 | +#' \item{omega}{The input \code{omega} values.} |
| 40 | +#' \item{penalty}{The penalty type for each row.} |
| 41 | +#' \item{lambda}{The regularization parameter used.} |
| 42 | +#' \item{gamma}{The additional penalty parameter used.} |
| 43 | +#' \item{value}{The computed penalty value.} |
| 44 | +#' } |
| 45 | +#' |
| 46 | +#' @references |
| 47 | +#' \insertAllCited{} |
| 48 | +#' |
| 49 | +#' @export |
| 50 | + |
| 51 | +pen <- function(omega, penalty, lambda, gamma = NULL) { |
| 52 | + |
| 53 | + n <- length(penalty) |
| 54 | + if (length(lambda) == 1) { |
| 55 | + lambda <- rep(lambda, n) |
| 56 | + } |
| 57 | + if (length(gamma) == 1) { |
| 58 | + gamma <- rep(gamma, n) |
| 59 | + } |
| 60 | + |
| 61 | + res <- do.call(rbind, lapply(seq_len(n), function(k) { |
| 62 | + pen_internal(omega = omega, penalty = penalty[k], lambda = lambda[k], gamma = gamma[k]) |
| 63 | + })) |
| 64 | + res <- as.data.frame(res) |
| 65 | + return(res) |
| 66 | +} |
| 67 | + |
| 68 | + |
| 69 | +#' @noRd |
| 70 | + |
| 71 | +pen_internal <- function(omega, penalty, lambda, gamma) { |
| 72 | + |
| 73 | + if (!(penalty %in% c("lasso", "atan", "exp", "lq", "lsp", "mcp", "scad"))) { |
| 74 | + stop('Error in `penalty`!\nAvailable options: "lasso", "atan", "exp", "lq", "lsp", "mcp", "scad".') |
| 75 | + } |
| 76 | + |
| 77 | + if (lambda < 0) { |
| 78 | + stop('The parameter `lambda` must be non-negative!') |
| 79 | + } |
| 80 | + |
| 81 | + ## default gamma by penalty |
| 82 | + if (missing(gamma) || is.null(gamma)) { |
| 83 | + gamma <- switch(penalty, |
| 84 | + "atan" = 0.005, "exp" = 0.01, "lq" = 0.5, |
| 85 | + "lsp" = 0.1, "mcp" = 3, "scad" = 3.7, NA) |
| 86 | + } |
| 87 | + |
| 88 | + a <- abs(omega) |
| 89 | + |
| 90 | + if (penalty == "atan") { |
| 91 | + if (gamma <= 0) { |
| 92 | + warning(sprintf('For "%s", typically `gamma` > 0.', penalty), call. = FALSE) |
| 93 | + } |
| 94 | + res <- lambda * (gamma + 2/pi) * atan(a / gamma) |
| 95 | + |
| 96 | + } else if (penalty == "exp") { |
| 97 | + if (gamma <= 0) { |
| 98 | + warning(sprintf('For "%s", typically `gamma` > 0.', penalty), call. = FALSE) |
| 99 | + } |
| 100 | + res <- lambda * (1 - exp(-a / gamma)) |
| 101 | + |
| 102 | + } else if (penalty == "lasso") { |
| 103 | + res <- lambda * a |
| 104 | + |
| 105 | + } else if (penalty == "lq") { |
| 106 | + if (gamma <= 0 || gamma >= 1) { |
| 107 | + warning(sprintf('For "%s", typically 0 < `gamma` < 1.', penalty), call. = FALSE) |
| 108 | + } |
| 109 | + epsilon <- 1e-10 |
| 110 | + res <- lambda * ((a + epsilon)^gamma) |
| 111 | + # res <- lambda * (pmax(a, epsilon)^gamma) |
| 112 | + # res <- lambda * (a^gamma) |
| 113 | + |
| 114 | + } else if (penalty == "lsp") { |
| 115 | + if (gamma <= 0) { |
| 116 | + warning(sprintf('For "%s", typically `gamma` > 0.', penalty), call. = FALSE) |
| 117 | + } |
| 118 | + res <- lambda * log1p(a / gamma) |
| 119 | + |
| 120 | + } else if (penalty == "mcp") { |
| 121 | + if (gamma <= 1) { |
| 122 | + warning(sprintf('For "%s", typically `gamma` > 1.', penalty), call. = FALSE) |
| 123 | + } |
| 124 | + res <- (lambda * a - a^2/(2*gamma)) * (a <= gamma * lambda) + |
| 125 | + (0.5 * gamma * lambda^2) * (a > gamma * lambda) |
| 126 | + |
| 127 | + } else if (penalty == "scad") { |
| 128 | + if (gamma <= 2) { |
| 129 | + warning(sprintf('For "%s", typically `gamma` > 2.', penalty), call. = FALSE) |
| 130 | + } |
| 131 | + res <- lambda * a * (a <= lambda) + |
| 132 | + (2 * gamma * lambda * a - a^2 - lambda^2) / (2 * (gamma-1)) * (lambda < a & a <= gamma * lambda) + |
| 133 | + lambda^2 * (gamma+1) / 2 * (a > gamma*lambda) |
| 134 | + } |
| 135 | + |
| 136 | + return(data.frame(omega = omega, penalty = penalty, lambda = lambda, gamma = gamma, value = res)) |
| 137 | +} |
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