Difference between revisions of "GeneralizedIterativeScaling"

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</math>
 
</math>
  
where <math>I</math> is an index set; the probability distribution over which has to be determined, <math>p</math> is a probability distribution and <math>\pi</math> is a subprobability function (adds to 1 but <math>\pi_i \neq 0</math> for any <math>i</math>; <math>b_{si} \neq 0</math> is constant.  
+
where <math>I</math> is an index set; the probability distribution over which has to be determined, <math>p</math> is a probability distribution and <math>\pi</math> is a subprobability function (adds to 1 but <math>\pi_i \neq 0</math> for any <math>i</math>); <math>b_{si} \neq 0</math> is constant.  
  
 
== Existence of a solution ==
 
== Existence of a solution ==
  
 
If <math>p</math> of form (1) exists satisfying (2), then it minimizes <math>KL[p, \pi]</math> and is unique.
 
If <math>p</math> of form (1) exists satisfying (2), then it minimizes <math>KL[p, \pi]</math> and is unique.

Revision as of 10:55, 27 September 2011

This is one of the earliest methods used for inference in log-linear models. Though more sophisticated and faster methods have evolved, this method provides an insight in log linear models.

What problem does it address

The objective of this method is to find a probability function of the form

satisfying the constraints

where is an index set; the probability distribution over which has to be determined, is a probability distribution and is a subprobability function (adds to 1 but for any ); is constant.

Existence of a solution

If of form (1) exists satisfying (2), then it minimizes and is unique.