smile.sequence

Class HMM

java.lang.Object

smile.sequence.HMM

All Implemented Interfaces:

java.io.Serializable

public class HMM
extends java.lang.Object
implements java.io.Serializable

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.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
HMM(double[] pi, smile.math.matrix.Matrix a, smile.math.matrix.Matrix b) Constructor.

Method Summary

Modifier and Type	Method and Description
static HMM	fit(int[][] observations, int[][] labels) Fits an HMM by maximum likelihood estimation.
static <T> HMM	fit(T[][] observations, int[][] labels, java.util.function.ToIntFunction<T> ordinal) Fits an HMM by maximum likelihood estimation.
double[]	getInitialStateProbabilities() Returns the initial state probabilities.
smile.math.matrix.Matrix	getStateTransitionProbabilities() Returns the state transition probabilities.
smile.math.matrix.Matrix	getSymbolEmissionProbabilities() Returns the symbol emission probabilities.
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	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.
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).
java.lang.String	toString()
void	update(int[][] observations, int iterations) Updates the HMM by the Baum-Welch algorithm.
<T> void	update(T[][] observations, int iterations, java.util.function.ToIntFunction<T> ordinal) Updates the HMM by the Baum-Welch algorithm.

Methods inherited from class java.lang.Object

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

Constructor Detail

HMM

public HMM(double[] pi,
           smile.math.matrix.Matrix a,
           smile.math.matrix.Matrix 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).

Method Detail

getInitialStateProbabilities

public double[] getInitialStateProbabilities()

Returns the initial state probabilities.

getStateTransitionProbabilities

public smile.math.matrix.Matrix getStateTransitionProbabilities()

Returns the state transition probabilities.

getSymbolEmissionProbabilities

public smile.math.matrix.Matrix 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.

fit

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

Fits an HMM 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.

fit

public static <T> HMM fit(T[][] observations,
                          int[][] labels,
                          java.util.function.ToIntFunction<T> ordinal)

Fits an HMM 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.

ordinal - a lambda returning the ordinal numbers of symbols.

update

public <T> void update(T[][] observations,
                       int iterations,
                       java.util.function.ToIntFunction<T> ordinal)

Updates the HMM by the Baum-Welch algorithm.

Parameters:

observations - the training observation sequences.

iterations - the number of iterations to execute.

ordinal - a lambda returning the ordinal numbers of symbols.

update

public void update(int[][] observations,
                   int iterations)

Updates the HMM by the Baum-Welch algorithm.

Parameters:

observations - the training observation sequences.

iterations - the number of iterations to execute.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object