aima.core.probability.ProbabilityModel Maven / Gradle / Ivy

Show more of this group Show more artifacts with this name
Show all versions of aima-core Show documentation
AIMA-Java Core Algorithms from the book Artificial Intelligence a Modern Approach 3rd Ed.
The newest version!
package aima.core.probability;

import java.util.Set;

import aima.core.probability.proposition.Proposition;

/**
 * Artificial Intelligence A Modern Approach (3rd Edition): page 484.

 * 

 * A fully specified probability model associates a numerical probability
 * P(ω) with each possible world. The set of all possible worlds is called
 * the sample space Ω.
 * 
 * @author Ciaran O'Reilly
 */
public interface ProbabilityModel {
	/**
	 * The default threshold for rounding errors. Example, to test if
	 * probabilities sum to 1:

	 * 

	 * Math.abs(1 - probabilitySum) <
	 * ProbabilityModel.DEFAULT_ROUNDING_THRESHOLD;
	 */
	final double DEFAULT_ROUNDING_THRESHOLD = 1e-8;

	/**
	 * 
	 * @return true, if 0 <= P(ω) <= 1 for every ω and
	 *         ∑_{ω ∈ Ω} P(ω) = 1 (Equation
	 *         13.1 pg. 484 AIMA3e), false otherwise.
	 */
	boolean isValid();

	/**
	 * For any proposition φ, P(φ) = ∑_{ω ∈
	 * φ} P(ω). Refer to equation 13.2 page 485 of AIMA3e.
	 * Probabilities such as P(Total = 11) and P(doubles) are called
	 * unconditional or prior probabilities (and sometimes just "priors" for
	 * short); they refer to degrees of belief in propositions in the absence of
	 * any other information.
	 * 
	 * @param phi
	 *            the propositional terms for which a probability value is to be
	 *            returned.
	 * @return the probability of the proposition φ.
	 */
	double prior(Proposition... phi);

	/**
	 * Unlike unconditional or prior probabilities, most of the time we have
	 * some information, usually called evidence, that has already been
	 * revealed. This is the conditional or posterior probability (or just
	 * "posterior" for short). Mathematically speaking, conditional
	 * probabilities are defined in terms of unconditional probabilities as
	 * follows, for any propositions a and b, we have:

	 * 

	 * P(a | b) = P(a AND b)/P(b)

	 * 

	 * which holds whenever P(b) > 0. Refer to equation 13.3 page 485 of AIMA3e.
	 * This can be rewritten in a different form called the product rule: 

	 * 

	 * P(a AND b) = P(a | b)P(b)

	 * 

	 * and also as:

	 * 

	 * P(a AND b) = P(b | a)P(a)

	 * 

	 * whereby, equating the two right-hand sides and dividing by P(a) gives you
	 * Bayes' rule:

	 * 

	 * P(b | a) = (P(a | b)P(b))/P(a) - i.e. (likelihood * prior)/evidence
	 * 
	 * @param phi
	 *            the proposition for which a probability value is to be
	 *            returned.
	 * @param evidence
	 *            information we already have.
	 * @return the probability of the proposition φ given evidence.
	 */
	double posterior(Proposition phi, Proposition... evidence);

	/**
	 * @return a consistent ordered Set (e.g. LinkedHashSet) of the random
	 *         variables describing the atomic variable/value pairs this
	 *         probability model can take on. Refer to pg. 486 AIMA3e.
	 */
	Set getRepresentation();
}