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SUMMARY:Probabilistic languages for inference - Johannes Borgstroem
DTSTART:20100809T114500Z
DTEND:20100809T130000Z
UID:TALK25437@talks.cam.ac.uk
CONTACT:Sam Staton
DESCRIPTION:The Bayesian approach to machine learning amounts to inferring
  posterior distributions of random variables from a probabilistic model of
  how the variables are related (that is\, a prior distribution) and a set 
 of observations of variables. There is a trend in machine learning towards
  expressing Bayesian models as probabilistic programs. As a foundation for
  this kind of programming\, we propose a core functional calculus with pri
 mitives for sampling prior distributions\, observing variables\, and sampl
 ing marginal distributions. Perhaps surprisingly\, the probability monad i
 s insufficient as a semantics for these kinds of programs\; instead\, we p
 ropose measure-theoretic distribution transformers as a semantics. We defi
 ne a new set of combinators for distribution transformers\, based on theor
 ems in measure theory\, and use these to obtain a rigorous semantics for o
 ur core calculus. Factor graphs are an important but low-level data struct
 ure in machine learning\; they enable many efficient inference algorithms.
  We compile our core language to a small imperative language that in addit
 ion to the distribution transformer semantics also has a straightforward s
 emantics as factor graphs\, which we evaluate using an existing inference 
 engine.\n
LOCATION:Room FW26\, Computer Laboratory\, William Gates Building
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