40 lines
1.1 KiB
R
40 lines
1.1 KiB
R
# 15 LOOCV
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ridge.svd <- function(data, degre) {
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X <- data$X
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n <- nrow(X)
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A <- scale(outer(c(X), 1:degre, "^"))
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Ym <- mean(data$Y)
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Y <- data$Y - Ym
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As <- svd(A)
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d <- As$d
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function(lambda) {
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coef <- c(As$v %*% ((d / (d^2 + lambda)) * (t(As$u) %*% Y)))
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coef <- coef / attr(A,"scaled:scale")
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inter <- Ym - coef %*% attr(A,"scaled:center")
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coef <- c(inter, coef)
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trace.H <- sum(d^2 / (d^2 + lambda))
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pred <- polyeval(coef, X)
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gcv <- sum( ((Y - pred) / (1 - (trace.H / n))) ^ 2 ) / n
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list(coef = coef, gcv = gcv)
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}
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}
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ridge.loocv <- function(data, deg, lambdas) {
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errs <- double(length(lambdas))
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coefs <- matrix(data = NA, nrow = length(lambdas), ncol = 1+deg)
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ridge <- ridge.svd(data, deg)
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idx <- 1
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for(lambda in lambdas) {
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res <- ridge(lambda)
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coefs[idx,] <- res$coef
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errs[idx] <- res$gcv
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idx <- idx + 1
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}
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err.min <- min(errs)
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lambda.best <- lambdas[which(errs == err.min)]
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coef.best <- coefs[which(errs == err.min),]
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pred <- polyeval(coef.best, data$X)
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mae <- mean(abs(pred - data$Y))
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list(coef = coef.best, lambda = lambda.best, mae = mae)
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} |