smile.sequence

Class HMM<O>

java.lang.Object

smile.sequence.HMM<O>

All Implemented Interfaces:

SequenceLabeler<O>

public class HMM<O>
extends java.lang.Object
implements SequenceLabeler<O>

First-order Hidden Markov Model. A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network.

In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a hidden Markov model, the state is not directly visible, but output, dependent on the state, is visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states.

Constructor Summary

Constructors

Constructor and Description
HMM(double[] pi, double[][] a, double[][] b) Constructor.
HMM(double[] pi, double[][] a, double[][] b, O[] symbols) Constructor.
HMM(int[][] observations, int[][] labels) Learn an HMM from labeled observation sequences by maximum likelihood estimation.
HMM(O[][] observations, int[][] labels) Learn an HMM from labeled observation sequences by maximum likelihood estimation.

Method Summary

Modifier and Type	Method and Description
double[]	getInitialStateProbabilities() Returns the initial state probabilities.
double[][]	getStateTransitionProbabilities() Returns the state transition probabilities.
double[][]	getSymbolEmissionProbabilities() Returns the symbol emission probabilities.
HMM<O>	learn(int[][] observations, int iterations) With this HMM as the initial model, learn an HMM by the Baum-Welch algorithm.
HMM<O>	learn(O[][] observations, int iterations) With this HMM as the initial model, learn an HMM by the Baum-Welch algorithm.
double	logp(int[] o) Returns the logarithm probability of an observation sequence given this HMM.
double	logp(int[] o, int[] s) Returns the log joint probability of an observation sequence along a state sequence given this HMM.
double	logp(O[] o) Returns the logarithm probability of an observation sequence given this HMM.
double	logp(O[] o, int[] s) Returns the log joint probability of an observation sequence along a state sequence given this HMM.
int	numStates() Returns the number of states.
int	numSymbols() Returns the number of emission symbols.
double	p(int[] o) Returns the probability of an observation sequence given this HMM.
double	p(int[] o, int[] s) Returns the joint probability of an observation sequence along a state sequence given this HMM.
double	p(O[] o) Returns the probability of an observation sequence given this HMM.
double	p(O[] o, int[] s) Returns the joint probability of an observation sequence along a state sequence given this HMM.
int[]	predict(int[] o) Returns the most likely state sequence given the observation sequence by the Viterbi algorithm, which maximizes the probability of P(I | O, HMM).
int[]	predict(O[] o) Returns the most likely state sequence given the observation sequence by the Viterbi algorithm, which maximizes the probability of P(I | O, HMM).
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

HMM

public HMM(double[] pi,
           double[][] a,
           double[][] b)

Constructor.

Parameters:

pi - the initial state probabilities.

a - the state transition probabilities, of which a[i][j] is P(s_j | s_i);

b - the symbol emission probabilities, of which b[i][j] is P(o_j | s_i).

HMM

public HMM(double[] pi,
           double[][] a,
           double[][] b,
           O[] symbols)

Constructor.

Parameters:

pi - the initial state probabilities.

a - the state transition probabilities, of which a[i][j] is P(s_j | s_i);

b - the symbol emission probabilities, of which b[i][j] is P(o_j | s_i).

symbols - the list of emission symbols.

HMM

public HMM(int[][] observations,
           int[][] labels)

Learn an HMM from labeled observation sequences by maximum likelihood estimation.

Parameters:

observations - the observation sequences, of which symbols take values in [0, n), where n is the number of unique symbols.

labels - the state labels of observations, of which states take values in [0, p), where p is the number of hidden states.

HMM

public HMM(O[][] observations,
           int[][] labels)

Learn an HMM from labeled observation sequences by maximum likelihood estimation.

Parameters:

observations - the observation sequences.

labels - the state labels of observations, of which states take values in [0, p), where p is the number of hidden states.

Method Detail

numStates

public int numStates()

Returns the number of states.

numSymbols

public int numSymbols()

Returns the number of emission symbols.

getInitialStateProbabilities

public double[] getInitialStateProbabilities()

Returns the initial state probabilities.

getStateTransitionProbabilities

public double[][] getStateTransitionProbabilities()

Returns the state transition probabilities.

getSymbolEmissionProbabilities

public double[][] getSymbolEmissionProbabilities()

Returns the symbol emission probabilities.

p

public double p(int[] o,
                int[] s)

Returns the joint probability of an observation sequence along a state sequence given this HMM.

Parameters:

o - an observation sequence.

s - a state sequence.

Returns:

the joint probability P(o, s | H) given the model H.

logp

public double logp(int[] o,
                   int[] s)

Returns the log joint probability of an observation sequence along a state sequence given this HMM.

Parameters:

o - an observation sequence.

s - a state sequence.

Returns:

the log joint probability P(o, s | H) given the model H.

p

public double p(int[] o)

Returns the probability of an observation sequence given this HMM.

Parameters:

o - an observation sequence.

Returns:

the probability of this sequence.

logp

public double logp(int[] o)

Returns the logarithm probability of an observation sequence given this HMM. A scaling procedure is used in order to avoid underflows when computing the probability of long sequences.

Parameters:

o - an observation sequence.

Returns:

the log probability of this sequence.

predict

public int[] predict(int[] o)

Returns the most likely state sequence given the observation sequence by the Viterbi algorithm, which maximizes the probability of P(I | O, HMM). In the calculation, we may get ties. In this case, one of them is chosen randomly.

Parameters:

o - an observation sequence.

Returns:

the most likely state sequence.

learn

public HMM<O> learn(O[][] observations,
                    int iterations)

With this HMM as the initial model, learn an HMM by the Baum-Welch algorithm.

Parameters:

observations - the observation sequences on which the learning is based. Each sequence must have a length higher or equal to 2.

iterations - the number of iterations to execute.

Returns:

the updated HMM.

learn

public HMM<O> learn(int[][] observations,
                    int iterations)

With this HMM as the initial model, learn an HMM by the Baum-Welch algorithm.

Parameters:

observations - the observation sequences on which the learning is based. Each sequence must have a length higher or equal to 2.

iterations - the number of iterations to execute.

Returns:

the updated HMM.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

p

public double p(O[] o,
                int[] s)

Returns the joint probability of an observation sequence along a state sequence given this HMM.

Parameters:

o - an observation sequence.

s - a state sequence.

Returns:

the joint probability P(o, s | H) given the model H.

logp

public double logp(O[] o,
                   int[] s)

Returns the log joint probability of an observation sequence along a state sequence given this HMM.

Parameters:

o - an observation sequence.

s - a state sequence.

Returns:

the log joint probability P(o, s | H) given the model H.

p

public double p(O[] o)

Returns the probability of an observation sequence given this HMM.

Parameters:

o - an observation sequence.

Returns:

the probability of this sequence.

logp

public double logp(O[] o)

Returns the logarithm probability of an observation sequence given this HMM. A scaling procedure is used in order to avoid underflows when computing the probability of long sequences.

Parameters:

o - an observation sequence.

Returns:

the log probability of this sequence.

predict

public int[] predict(O[] o)

Returns the most likely state sequence given the observation sequence by the Viterbi algorithm, which maximizes the probability of P(I | O, HMM). In the calculation, we may get ties. In this case, one of them is chosen randomly.

Specified by:

predict in interface SequenceLabeler<O>

Parameters:

o - an observation sequence.

Returns:

the most likely state sequence.