gov.sandia.cognition.learning.algorithm.hmm

Class MarkovChain

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.learning.algorithm.hmm.MarkovChain

All Implemented Interfaces:

CloneableSerializable, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

HiddenMarkovModel

@PublicationReference(author="Wikipedia",
                      title="Markov chain",
                      type=WebPage,
                      year=2010,
                      url="http://en.wikipedia.org/wiki/Markov_chain")
public class MarkovChain
extends AbstractCloneableSerializable

A Markov chain is a random process that has a finite number of states with random transition probabilities between states at discrete time steps.

Since:

3.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	DEFAULT_NUM_STATES Default number of states, 3.
protected Vector	initialProbability Initial probability Vector over the states.
protected Matrix	transitionProbability Transition probability matrix.

Constructor Summary

Constructors

Constructor and Description
MarkovChain() Default constructor.
MarkovChain(int numStates) Creates a new instance of ContinuousDensityHiddenMarkovModel with uniform initial and transition probabilities.
MarkovChain(Vector initialProbability, Matrix transitionProbability) Creates a new instance of ContinuousDensityHiddenMarkovModel

Method Summary

Modifier and Type	Method and Description
MarkovChain	clone() This makes public the clone method on the Object class and removes the exception that it throws.
protected static Vector	createUniformInitialProbability(int numStates) Creates a uniform initial-probability Vector
protected static Matrix	createUniformTransitionProbability(int numStates) Creates a uniform transition-probability Matrix
Vector	getFutureStateDistribution(Vector current, int numSteps) Simulates the Markov chain into the future, given the transition Matrix and the given current state-probability distribution, for the given number of time steps into the future.
Vector	getInitialProbability() Getter for initialProbability.
int	getNumStates() Gets the number of states in the HMM.
Vector	getSteadyStateDistribution() Returns the steady-state distribution of the state distribution.
Matrix	getTransitionProbability() Getter for transitionProbability.
void	normalize() Normalizes this Markov chain.
protected void	normalizeTransitionMatrix(Matrix A) Normalizes the transition-probability matrix
protected static void	normalizeTransitionMatrix(Matrix A, int j) Normalizes a column of the transition-probability matrix
void	setInitialProbability(Vector initialProbability) Setter for initialProbability
void	setTransitionProbability(Matrix transitionProbability) Setter for transitionProbability.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_NUM_STATES

public static final int DEFAULT_NUM_STATES

Default number of states, 3.

See Also:

Constant Field Values

initialProbability

protected Vector initialProbability

Initial probability Vector over the states. Each entry must be nonnegative and the Vector must sum to 1.

transitionProbability

protected Matrix transitionProbability

Transition probability matrix. The entry (i,j) is the probability of transition from state "j" to state "i". As a corollary, all entries in the Matrix must be nonnegative and the columns of the Matrix must sum to 1.

Constructor Detail

MarkovChain

public MarkovChain()

Default constructor.

MarkovChain

public MarkovChain(int numStates)

Creates a new instance of ContinuousDensityHiddenMarkovModel with uniform initial and transition probabilities. Also uses Dirichlet PDFs as the emission functions.

Parameters:

numStates - Number of states to use.

MarkovChain

public MarkovChain(Vector initialProbability,
                   Matrix transitionProbability)

Creates a new instance of ContinuousDensityHiddenMarkovModel

Parameters:

initialProbability - Initial probability Vector over the states. Each entry must be nonnegative and the Vector must sum to 1.

transitionProbability - Transition probability matrix. The entry (i,j) is the probability of transition from state "j" to state "i". As a corollary, all entries in the Matrix must be nonnegative and the columns of the Matrix must sum to 1.

Method Detail

clone

public MarkovChain clone()

Description copied from class: AbstractCloneableSerializable

This makes public the clone method on the Object class and removes the exception that it throws. Its default behavior is to automatically create a clone of the exact type of object that the clone is called on and to copy all primitives but to keep all references, which means it is a shallow copy. Extensions of this class may want to override this method (but call super.clone() to implement a "smart copy". That is, to target the most common use case for creating a copy of the object. Because of the default behavior being a shallow copy, extending classes only need to handle fields that need to have a deeper copy (or those that need to be reset). Some of the methods in ObjectUtil may be helpful in implementing a custom clone method. Note: The contract of this method is that you must use super.clone() as the basis for your implementation.

Specified by:

clone in interface CloneableSerializable

Overrides:

clone in class AbstractCloneableSerializable

Returns:

A clone of this object.

createUniformInitialProbability

protected static Vector createUniformInitialProbability(int numStates)

Creates a uniform initial-probability Vector

Parameters:

numStates - Number of states to create the Vector for

Returns:

Uniform probability Vector.

createUniformTransitionProbability

protected static Matrix createUniformTransitionProbability(int numStates)

Creates a uniform transition-probability Matrix

Parameters:

numStates - Number of states to create the Matrix for

Returns:

Uniform probability Matrix.

getInitialProbability

public Vector getInitialProbability()

Getter for initialProbability.

Returns:

Initial probability Vector over the states. Each entry must be nonnegative and the Vector must sum to 1.

setInitialProbability

public void setInitialProbability(Vector initialProbability)

Setter for initialProbability

Parameters:

initialProbability - Initial probability Vector over the states. Each entry must be nonnegative and the Vector must sum to 1.

getTransitionProbability

public Matrix getTransitionProbability()

Getter for transitionProbability.

Returns:

Transition probability matrix. The entry (i,j) is the probability of transition from state "j" to state "i". As a corollary, all entries in the Matrix must be nonnegative and the columns of the Matrix must sum to 1.

setTransitionProbability

public void setTransitionProbability(Matrix transitionProbability)

Setter for transitionProbability.

Parameters:

transitionProbability - Transition probability matrix. The entry (i,j) is the probability of transition from state "j" to state "i". As a corollary, all entries in the Matrix must be nonnegative and the columns of the Matrix must sum to 1.

normalize

public void normalize()

Normalizes this Markov chain.

normalizeTransitionMatrix

protected static void normalizeTransitionMatrix(Matrix A,
                                                int j)

Normalizes a column of the transition-probability matrix

Parameters:

A - Transition probability matrix to normalize, modified by side effect

j - Column of the matrix to normalize

normalizeTransitionMatrix

protected void normalizeTransitionMatrix(Matrix A)

Normalizes the transition-probability matrix

Parameters:

A - Transition probability matrix to normalize, modified by side effect

getNumStates

public int getNumStates()

Gets the number of states in the HMM.

Returns:

Number of states in the HMM.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getSteadyStateDistribution

public Vector getSteadyStateDistribution()

Returns the steady-state distribution of the state distribution. This is also the largest eigenvector of the transition-probability matrix, which has an eigenvalue of 1.

Returns:

Steady-state probability distribution of state distribution.

getFutureStateDistribution

public Vector getFutureStateDistribution(Vector current,
                                         int numSteps)

Simulates the Markov chain into the future, given the transition Matrix and the given current state-probability distribution, for the given number of time steps into the future.

Parameters:

current - Current distribution of probabilities of the various states.

numSteps - Number of steps into the future to simulate.

Returns:

State-probability distribution for numSteps into the future, starting from the given state-probability distribution.