[Solved] Lab 6 Learning in Reproducing Kernel Hilbert Spaces Advanced Machine Learning DATA442/642

Exercise 1

Test the the prediction power of the kernel ridge regression in the presence of noise and outliers. The original data are samples from a music recording of Blade Runner by Vangelis Papathanasiou https://en.wikipedia.org/wiki/Vangelis.

• Read the audio file, BladeRunner.wav, using the Python SoundFile library (https:// org/project/SoundFile/). Then take 100 data samples starting from the 100,000th sample. Add white Gaussian noise at a 15 dB level and randomly hit 10% of the data samples with outliers (set the outlier values to 80% of the maximum value of the data samples).
• Find the reconstructed data samples using the unbiased kernel ridge regression method,that is,

y(x) = y^>(K + CI)¹(x).

Employ the Gaussian kernel with = 0.004 and set C = 0.0001. Plot the fitted curve of the reconstructed samples together with the data used for training.

• Repeat step (b) using C = 10⁶,10⁵,0.0005,0.001,0.01,0.
• Repeat step (b) using = 0.001,0.003,0.008,0.01,0.
• Comment on the results.