- Implementation of Gaussian Process (GP) for regreesion with the exponential-quadratic kernel function.
- We have 100 pairs of samples (x,t) in 'gp.mat' for training & testing.
Consider the 60% as traing data, 40% as testing. - Given that the input x is limited in [0,2], predict the target t using GP.
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Calculate the kernel matrix from the first 60 samples using the following equation:
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Calculate the Covariance matrix
has values when n = m, so
is equal to
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Calculate the kernel vecotr suing testing & training input x using the following equation:
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Obtain the prediction of tset set
represent the t in train set
- The procedure is similar to the above implementation:
Replace the input for test set with all the value in x-domain like [0, 0.01, 0.02, ... 2] - Visualization:
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It was found that the results of prediction are more accurate for Train & Test set when using the parameters {1,32,5,5}.
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Further Analysis:
To validate the individual influence of theta_0, theta_1, theta_2 and theta_3, we try the combination like [1,0,0,0], [0,1,0,0], [0,0,1,0] and [0,0,0,1] for GP Regression.
It was found that the prediction will be degraded to linear regression if the other three values are all zero.