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: Fitting complicated models can be hard How do we find an appropriate model? How do we avoid over-fitting some aspects of model?Predicting yieldFactory settingsx1 profit of32 5monetary unitsFactory settingsx2 profit of100 200monetary unitsWhich are the best settingsx1orx2?

Introduction to Gaussian Processes Iain Murray murray@cs.toronto.edu CSC2515, Introduction to Machine Learning, Fall 2008 ... Optimization In high dimensions it takes many function evaluations to be certain everywhere. Costly if experiments are involved. 0 0.2 0.4 0.6 0.8 1-1.5-1

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