《Graphical Models For Machine Learning And Computer Vision》.ppt

Graphical Models for Machine Learning and Computer Vision Statistical Models Statistical Models Describe observed ‘DATA’ via an assumed likelihood: With denoting the ‘parameters’ needed to describe the data. Likelihoods measure how likely what was observed was. They implicitly assume an error mechanism (in the translation between what was observed and what was ‘supposed’ to be observed). Parameters may describe model features or even specify different models. An Example of a Statistical Model A burgler alarm is affected by both earthquakes and burgleries. It has a mechanism to communicate with the homeowner if activated. It went off at Judah Pearles house one day. Should he: a) immediately call the police under suspicion that a burglary took place, or b) go home and immediately transfer his valueables elsewhere? A Statistical Analysis Observation: The burgler alarm went off (i.e., a=1); Parameter 1: The presence or absence of an earthquake (i.e., e=1,0); Parameter 2: The presence or absence of a burglary at Judah’s house (i.e., b=1,0). LIKELIHOODS/PRIORS IN THIS CASE The Likelihood associated with the observation is: With b,e =0,1 (depending on whether a burglery,earthquake has taken place). The Priors specify the probabilities of a burglery or earthquake happenning: Example Probabilities Here are some probabilities indicating something about the likelihood and prior: LIKELIHOOD/PRIOR INTERPRETATION Burglaries are as likely (apriori) as earthquakes. It is unlikely that the alarm just went off by itself. The alarm goes off more often when a burglary happens but an earthquakes does not than (the reverse) i.e., when an earthquake happens but a burglary does not. If both a burglary and an earthquake happens tha