Build two kernel density estimators(K1 and K2)for the data: one with the default kernel width value and one with a width value equal to half the default value.

Calculate the KL divergence (based on 100 equally spaced test points that cover the range of the data in x), between: o M and H1 o M and K1 o M and K2 where M is the distribution given by the mixture of 2 Gaussians. In addition to the 3 KL divergence values, provide the code used to calculate them . Include and discuss any assumptions or work- arounds you used. ? Some hints: o Recall mixture models from the clustering lecture: the distribution M above is a simple mixture with two components, each with a prior/mixing coefficient with value 0.5. o The matlab normpdf() function evaluates the density of a Gaussian at a given point. o The test points required are calculated via the ksdensity function.