Transcription of Introduction to Gaussian Processes
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Introduction to Gaussian Processes
Introduction to Gaussian ProcessesIain Introduction to Machine Learning, Fall 2008 Dept. Computer Science, University of TorontoThe problemLearn scalar function of vector valuesf(x) 1 f(x) 505x2x1fWe have (possibly noisy) observations{xi,yi}ni=1 Example ApplicationsReal-valued regression: Robotics: target state required torque Process engineering: predicting yield Surrogate surfaces for optimization or simulationClassification: Recognition: handwritten digits on cheques Filtering: fraud, interesting science, disease screeningOrdinal regression: User ratings ( movies or restaurants) Disease screening ( predicting Gleason score)Model complexityThe world is often 1 1 1 fitcomplex fittruthProblems.
Because marginalization in Gaussians is trivial, we can easily ignore all of the positions xithat are neither observed nor queried. Covariance functions The main part that has been missing so far is where the covariance function k(xi;xj) comes from. Also, other than making nearby points covary, what can
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