HMM (Smile Core 1.0.0 API)

java.lang.Object
- smile.sequence.HMM<O>

All Implemented Interfaces:

SequenceLabeler<O>
```
public class HMM<O>
extends 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.

Author:

Haifeng Li

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

Methods
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)`.
`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 String toString()
```
    Overrides:
    
    toString in class 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.

Class HMM<O>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

HMM

HMM

HMM

HMM

Method Detail

numStates

numSymbols

getInitialStateProbabilities

getStateTransitionProbabilities

getSymbolEmissionProbabilities

p

logp

p

logp

predict

learn

learn

toString

p

logp

p

logp

predict