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• BackwardStepInference.java

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aima.core.probability.temporal.BackwardStepInference Maven / Gradle / Ivy

package aima.core.probability.temporal;

import java.util.List;

import aima.core.probability.CategoricalDistribution;
import aima.core.probability.proposition.AssignmentProposition;

/**
 * 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
 * 
 */
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)
	 * 
	 * 
	 * @param b_kp2t
	 *            bk+2:t
	 * @param e_kp1t
	 *            ek+1:t
	 * @return bk+1:t
	 */
	CategoricalDistribution backward(CategoricalDistribution b_kp2t,
			List e_kp1t);
}