Fitting a polynomial with regularization

Stefan van den Heuvel

2016 12 3

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As a means of familiarizing myself with Matlab I set out to recreate a number of figures from the book Pattern Recognition and Machine Learning (Bishop, 2006). In the first chapter already I am faced with a challange I cannot seem to get past.

To recreate figure 1.7 I will have to two plot a polynomials (of grade 9) on a training data set with a specific regularization constant, i.e. ln(lamda)=-18 and ln(lamda)=0. The regularization term goes with lambda times the square of the weights, and is added to a simple square-error-function.

Without regularization term I used polyfit and polyval to (re)produce figures. With regualization I cannot use these anymore, and now I am stuck.

Is anybody able and willing to point me in the direction of a solution ?

t.i.a.