AbstractConditionalDistribution_AbstractDistribution

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riso.distributions.computes_lambda_message
Class AbstractConditionalDistribution_AbstractDistribution_AbstractDistribution

java.lang.Object
  riso.distributions.computes_lambda_message.AbstractConditionalDistribution_AbstractDistribution_AbstractDistribution

All Implemented Interfaces:: riso.distributions.LambdaMessageHelper, java.io.Serializable

public class AbstractConditionalDistribution_AbstractDistribution_AbstractDistribution
extends java.lang.Object
implements riso.distributions.LambdaMessageHelper

This class implements a lambda message helper for a variable x with one or more parents u1,...,un. Except for the parent to which we are sending the lambda message, each parent sends a pi message to x. Let us suppose that we are sending the lambda message to parent uk. The lambda message is defined as

   p( e \ e_u1(above) | uk )
     = \int p( x, e \ e_uk(above) | uk ) dx
     = \int p( x, e_x(below) + e_x(above) \ e_uk(above) | uk ) dx
     = \int p( e_x(below) | x ) p( x | e_x(above) \ e_uk(above), uk ) p( e_x(above) \ e_uk(above) | uk ) dx
     = p( e_x(above) \ e_uk(above) ) \int p( e_x(below) | x )
         \int ... \int p( x | u1,...,un ) p( u1,...,un \ uk |  e_x(above) \ e_uk(above), uk ) 
         du1 ... du_{k-1} du_{k+1} ... du_n dx

The factor p( e_x(above) \ e_uk(above) ) doesn't depend on uk so we can ignore it (a lambda message need not integrate to anything in particular). Now note that

    p( u1,...,un \ uk | e_x(above) \ e_uk(above), uk ) = \prod_{j \neq k} p( uj | e_uj(above) )

so finally we have

   p( e \ e_u1(above) | uk )
     = \int p( e_x(below) | x ) \int ... \int p( x | u1,...,un )
         \prod_{j \neq k} p( uj | e_uj(above) ) du1 ... du_{k-1} du_{k+1} ... du_n dx

In this last equation the lambda function of x appears, p( e_x(below) | x ), and the pi messages coming to x from parents other than uk, p( uj | e_uj(above) ), j \neq k. The conditional distribution of x given all its parents, p( x | u1,...,un ), links the other pieces together.

Note that this integral is a function of the parent uk. The message which is sent up the parent is NOT a Gaussian mixture or other approximation; the message is a direct representation of the integral. The evaluation of the integral is put off until the posterior or lambda of uk needs to be computed.

Constructor Summary

AbstractConditionalDistribution_AbstractDistribution_AbstractDistribution()


Method Summary

riso.distributions.Distribution compute_lambda_message(riso.distributions.ConditionalDistribution pxuuu, riso.distributions.Distribution lambda, riso.distributions.Distribution[] pi_messages)
          Compute the likelihood message from a variable to a parent.

static riso.general.SeqTriple[] description()
          Returns a description of the sequences of distributions accepted by this helper -- namely one AbstractConditionalDistribution followed by one AbstractDistribution, followed by any number of AbstractDistribution.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail