文档介绍：Graphical Models for Machine
Learning puter Vision
Statistical Models
• Statistical Models Describe observed ‘DATA’ via an
assumed likelihood: L (DATA |Θ)
• With Θ 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
(., a=1);
• Parameter 1: The presence or absence of an
earthquake (., e=1,0);
• Parameter 2: The presence or absence of a
burglary at Judah’s house
(., b=1,0).
LIKELIHOODS/PRIORS IN
THIS CASE
• The Likelihood associated with the
observation is:
L (DATA |Θ) = P ( a = 1| b , e )
• 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:
P( b = 1) = ?; P(e=1)=?;
Example Probabilities
• Here are some probabilities indicating
something about the likelihood and prior:
P( b = 0) = .9; P(b=1)=.1;
P(a=1|e=b=0)=.001; P(a=1|b=1,e=0)=.368;
P(a=1|e=1,b=0)=.135; P(a=1|b=e=1)=.607;
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) ., when an earthquake happens but a
burglary