Bayesian Linear Regression - CEDAR

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Machine Learning ! ! ! ! !SrihariEquivalent Kernel for Sigmoidal BasisFunction"ϕ j(x) = σ $#x − µ js%1' where σ (a) =&1+ exp(−a)k(x,x’)=βφ(x) T S N φ(x’)Localized function of x’ even thoughcorresponding basis function is nonlocal28
Machine Learning ! ! ! ! !SrihariCovariance between y(x) and y(x’)cov [y(x) , y(x’)] = cov[φ(x) T w, w T φ(x’)]= φ(x) T S N φ(x’)= β -1 k(x,x’)The kernel captures the covarianceFrom the form of the equivalent kernel,the predictive mean at nearby points y(x) , y(x’) will be highly correlatedFor more distant pairs correlation is smaller29
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Bayesian Linear Regression - CEDAR

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