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Bayesian Modelling

Bayesian ModellingZoubin GhahramaniDepartment of EngineeringUniversity of Cambridge, 2012La PalmaAn Information Revolution? We are in an era of abundant data: Society:the web, social networks, mobile networks,government, digital archives Science:large-scale scientific experiments, biomedicaldata, climate data, scientific literature Business:e-commerce, electronic trading, advertising,personalisation We need tools for Modelling , searching, visualising, andunderstanding large data ToolsOur Modelling tools should: Faithfully representuncertaintyin our model structureand parameters andnoisein our data Be automated andadaptive Exhibitrobustness Scale wellto large data setsProbabilistic Modelling A model describes data that one could observe from a system If we use the mathematics of probability theory to express allforms of uncertainty and noise associated with our.

Modeling vs toolbox views of Machine Learning Machine Learning seeks to learn models of data: de ne a space of possible ... likelihood of P( ) prior probability of P( jD) posterior of given D Prediction: P(xjD;m) = Z ... The posterior for N data points is also conjugate (by de nition), with hyperparameters + Nand + P ns(x

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  Posterior, Bayesian, Likelihood

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