Nothing
require(lolR) require(ggplot2) n = 400 d = 30 r = 3
Here, we look at how to see the generalizability of a given model in the form of the cross-validated error. We simulate data with n=200
and d=30
:
testdat <- lol.sims.rtrunk(n, d) X <- testdat$X Y <- testdat$Y data <- data.frame(x1=X[,1], x2=X[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Simulated Data")
We arbitrarily select LOL as our algorithm, and look at the leave-one-out (loo) cross-validated error with the LDA classifier. We project the resulting model to 3
dimensions and visualize the first 2
:
result <- lol.xval.eval(X, Y, r, alg = lol.project.lol, alg.return="A", classifier=MASS::lda, classifier.return="class", k='loo') data <- data.frame(x1=result$model$Xr[,1], x2=result$model$Xr[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle(sprintf("Projected Data using LOL, L=%.2f", result$lhat))
result <- lol.xval.optimal_dimselect(X, Y, rs=c(5, 10, 15), alg = lol.project.lol, alg.return="A", classifier=MASS::lda, classifier.return="class", k='loo') data <- data.frame(x1=result$model$Xr[,1], x2=result$model$Xr[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle(sprintf("Projected Data using LOL, L=%.2f", result$optimal.lhat)) ggplot(result$foldmeans.data, aes(x=r, y=lhat)) + geom_line() + xlab("Embedding Dimensions, r") + ylab("Misclassification Rate, L") + ggtitle("Impact on Misclassification Rate of Embedding Dimension") print(sprintf("optimal dimension: %d", result$optimal.r)) print(sprintf("Misclassification rate at rhat = %d: %.2f", result$optimal.r, result$optimal.lhat))
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