Bayesian Linear Regression - CEDAR

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Machine Learning ! ! ! ! !SrihariSampling p(w) and p(w|t) • Each sample represents a straight line indata spacew 1 Distribution Six samplesp(w) w 0 p(w|t) Goal of Bayesian Linear Regression:Determine p(w|t) 10
Machine Learning ! ! ! ! !SrihariInteresting Relationship to MLE• Since• Log of Posterior isln p(w | t) = − β 2Np(w | t) = ∏ N t n| w T φ(x n), β −1 N(w | 0,α −1 I)n=1N∑n=1{ t n− w T φ(x n)}• Thus Maximization of posterior distribution wrtw is equivalent to minimization of sum-ofsquareserror functionE(w) = 1 2N∑n=1( ){ t n− w T φ(x n) } 2+ λ 2 wT wwith addition of quadratic regularization term w T wwith λ=α/β 112− α 2 wT w + const
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Bayesian Linear Regression - CEDAR

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