Bayesian Linear Regression - CEDAR

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Machine Learning ! ! ! ! !SrihariBayesian Linear Regression Example(Straight Line Fit)• Single input variable x• Single target variable t• Goal is to fit– Linear model y(x,w) = w 0 +w 1 x• Goal of Linear Regression is to recoverw=[w 0 ,w 1 ] given the samplestx12
Machine Learning ! ! ! ! !SrihariData Generation• Synthetic data generated fromf(x,w)=w 0 +w 1 x withparameter valuesw 0 =-0.3 and w 1 =0.5t-1 x 1– First choose x n from U(x|-1,1), Then evaluate f(x n ,w)– Add Gaussian noise with st dev 0.2 to obtain targett n– Precision parameter β=(1/0.2) 2 =25 • For prior over w we choose α = 2 p(w |α ) = N(w | 0,α −1 I)13
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Bayesian Linear Regression - CEDAR

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