Assignment-4
7.1. Simulate a single predictor and a nonlinear relationship, such as a sinwave shown in Fig. 7.7, and
investigate the relationship between the cost, and kernel parameters for a support vector machine
mo
...
Assignment-4
7.1. Simulate a single predictor and a nonlinear relationship, such as a sinwave shown in Fig. 7.7, and
investigate the relationship between the cost, and kernel parameters for a support vector machine
model.
(a) Fit different models using a radial basis function and different values of the cost (the C
parameter) and epsilon. Plot the fitted curve.
Cost of 1,2,4,8 and 16 is selected along with epsilon values (b) The sigma parameter can be adjusted using the kpar argument, such as kpar = list(sigma = 1). Try
different values of sigma to understand how this parameter changes the model fit. How do the cost,
epsilon, and sigma values affect the model?The Sigma values are also changed as 1,10,100,1000,10000.
The effect of cost is that when we increase the cost of the model, the error is high. Alternatively, if
the cost is low, the error is low.
The effect of epsilon is that it represent the smoothness of the curve, the loss function is
represented by epsilon. It considers the number of support vectors to make the decision boundary.
The effect of sigma represents the Bias-Variance tradeoff. As the sigma is high, the variance of the
model is high and vice-versa.
7.2. Friedman (1991) introduced several benchmark data sets create by simulation. One of these
simulations used the following nonlinear equation to create data:
y = 10 sin(πx1x2) + 20(x3 − 0.5)2 + 10x4 + 5x5 + N(0, σ2) 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
Which models appear to give the best performance?Does MARS select the informative predictors
(those named X1–X5)?
1. K Nearest Neighbors:
Train Data:Plot:
2. MARS Model:
Train Data:Plot:
3. Support Vector Machines:
TrainData:Plot:
4. Neural Networks
Train Data:
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