Friedman (1991) introduced several benchmark data sets create by simulation. One
ID: 3606558 • Letter: F
Question
Friedman (1991) introduced several benchmark data sets create by simulation.
One of these simulations used the following nonlinear equation to
create data:
y = 10sin(x1x2) + 20(x3 0.5)2 + 10x4 + 5x5 + N(0, 2)
where the x values are random variables uniformly distributed between [0, 1]
(there are also 5 other non-informative variables also created in the simulation).
The package mlbench contains a function called mlbench.friedman1 that
simulates these data:
> library(mlbench)
> set.seed(200)
> trainingData <- mlbench.friedman1(200, sd = 1)
> ## We convert the 'x' data from a matrix to a data frame
> ## One reason is that this will give the columns names.
> trainingData$x <- data.frame(trainingData$x)
> ## Look at the data using
> featurePlot(trainingData$x, trainingData$y)
> ## or other methods.
>
> ## This creates a list with a vector 'y' and a matrix
> ## of predictors 'x'. Also simulate a large test set to
> ## estimate the true error rate with good precision:
> testData <- mlbench.friedman1(5000, sd = 1)
> testData$x <- data.frame(testData$x)
>
Tune several models on these data. For example:
> library(caret)
> knnModel <- train(x = trainingData$x,
+ y = trainingData$y,
+ method = "knn",
+ preProc = c("center", "scale"),
+ tuneLength = 10)
> knnModel
200 samples
10 predictors
Pre-processing: centered, scaled
Resampling: Bootstrap (25 reps)
Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
Resampling results across tuning parameters:
k RMSE Rsquared RMSE SD Rsquared SD
5 3.51 0.496 0.238 0.0641
7 3.36 0.536 0.24 0.0617
9 3.3 0.559 0.251 0.0546
11 3.24 0.586 0.252 0.0501
13 3.2 0.61 0.234 0.0465
15 3.19 0.623 0.264 0.0496
17 3.19 0.63 0.286 0.0528
19 3.18 0.643 0.274 0.048
21 3.2 0.646 0.269 0.0464
23 3.2 0.652 0.267 0.0465
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was k = 19.
> knnPred <- predict(knnModel, newdata = testData$x)
> ## The function 'postResample' can be used to get the test set
> ## perforamnce values
> postResample(pred = knnPred, obs = testData$y)
RMSE Rsquared
3.2286834 0.6871735
Which models appear to give the best performance? Does MARS select the
informative predictors (those named X1–X5)?
Explanation / Answer
main.R
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