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SUMMARY:The EM algorithm and applications - Robert Gramacy\, University of
  Cambridge
DTSTART:20090311T163000Z
DTEND:20090311T173000Z
UID:TALK17239@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:An expectation-maximization (EM) algorithm is used in statisti
 cs for\nfinding maximum likelihood estimates of parameters in probabilisti
 c\nmodels\, where the model depends on unobserved latent variables. EM\nal
 ternates between performing an expectation (E) step\, which computes\nan e
 xpectation of the likelihood by including the latent variables as\nif they
  were observed\, and a maximization (M) step\, which computes the\nmaximum
  likelihood estimates of the parameters by maximizing the\nexpected likeli
 hood found on the E step. The parameters found on the M\nstep are then use
 d to begin another E step\, and the process is\nrepeated.\n\nThe EM algori
 thm was explained and given its name in a classic 1977\npaper by Arthur De
 mpster\, Nan Laird\, and Donald Rubin in the Journal\nof the Royal Statist
 ical Society (see link below). They pointed out\nthat the method had been 
 "proposed many times in special\ncircumstances" by other authors\, but the
  1977 paper generalized the\nmethod and developed the theory behind it.\n\
 nEM is frequently used for data clustering in machine learning and\ncomput
 er vision. In natural language processing\, two prominent\ninstances of th
 e algorithm are the Baum-Welch algorithm (also known as\nforward-backward)
  and the inside-outside algorithm for unsupervised\ninduction of probabili
 stic context-free grammars.\nIn psychometrics\, EM is almost indispensable
  for estimating item\nparameters and latent abilities of item response the
 ory models. With\nthe ability to deal with missing data and observe uniden
 tified\nvariables\, EM is becoming a useful tool to price and manage risk 
 of a\nportfolio. The EM algorithm is also widely used in medical image\nre
 construction\, especially in Positron Emission Tomography and Single\nPhot
 on Emission Computed Tomography. See below for other faster\nvariants of E
 M.\n\nWe will go through the algorithm in general\, prove an important\nco
 nvergence property\, comment on historical context\, illustrate on a\nfamo
 us application to clustering\, and talk about extensions including\nMCEM a
 nd ECM which can be used with the E-step and M-step\,\nrespectively\, are 
 not analytically tractable.\n\nhttp://www.jstor.org/stable/2984875\n
LOCATION:MR5\, CMS
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