aima.core.probability.temporal

Interface BackwardStepInference

All Known Subinterfaces:

ForwardBackwardInference

All Known Implementing Classes:

ForwardBackward, HMMForwardBackward, HMMForwardBackwardConstantSpace

public interface BackwardStepInference

The BACKWARD operator

 bk+1:t = P(ek+1:t | Xk)
 

is defined by Equation (15.9).

 P(ek+1:t | Xk) 
 = ∑xk+1P(ek+1:t | Xk, xk+1)P(xk+1 | Xk) (conditioning on Xk+1)
 = ∑xk+1P(ek+1:t | xk+1)P(xk+1 | Xk) (by conditional independence)
 = ∑xk+1P(ek+1, ek+2:t | xk+1)P(xk+1 | Xk)
 = ∑xk+1P(ek+1 | xk+1)P(ek+2:t | xk+1)P(xk+1 | Xk)
 

Author:

Ciaran O'Reilly

Method Summary

Modifier and Type	Method and Description
CategoricalDistribution	backward(CategoricalDistribution b_kp2t, java.util.List<AssignmentProposition> e_kp1t) The BACKWARD operator

Method Detail

backward

CategoricalDistribution backward(CategoricalDistribution b_kp2t,
                                 java.util.List<AssignmentProposition> e_kp1t)

The BACKWARD operator

 bk+1:t = P(ek+1:t | Xk)
 

is defined by Equation (15.9).

 P(ek+1:t | Xk) 
 = ∑xk+1P(ek+1:t | Xk, xk+1)P(xk+1 | Xk) (conditioning on Xk+1)
 = ∑xk+1P(ek+1:t | xk+1)P(xk+1 | Xk) (by conditional independence)
 = ∑xk+1P(ek+1, ek+2:t | xk+1)P(xk+1 | Xk)
 = ∑xk+1P(ek+1 | xk+1)P(ek+2:t | xk+1)P(xk+1 | Xk)
 

Parameters:

b_kp2t - b_k+2:t

e_kp1t - e_k+1:t

Returns:

b_k+1:t