Bayesian Linear Regression - CEDAR

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Machine Learning ! ! ! ! !SrihariGaussian Process with Two Samples!• Let y be a function (curve) !– of a one-dimensional variable x!• We take two samples y 1 and y 2y 2y 1corresponding to x 1 and x 2• Assume they have a bivariateGaussian distribution p(y 1 ,y 2 ) • Each point from this distribution!– has an associated probability !– It also defines a function y(x) !• Assuming that two points areenough to define a curve!• More than two points will beneeded to define a curve!– Which leads to a higherdimensional probability distribution!y 1x 1 x 1y 236
Machine Learning ! ! ! ! !SrihariGaussian Process with N samples!• A process that generatessamples over time {y 1 ,..y N } isa GP iff every set of samplesY=[y 1 ,..,y N ] is a vector-valuedGaussian random variable!• We define a distribution overall functions!– Constrained by the samples!• The samples have a jointGaussian distribution in N-dimensional space!37<strong>Regression</strong>:!Possible functions!constrained by Nsamples!Case of two samples!t 1 and t 2 that are!bivariate Gaussian!
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Bayesian Linear Regression - CEDAR

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