mlpack::hmm::HMM< Distribution > Class Template Reference

A class that represents a Hidden Markov Model with an arbitrary type of emission distribution. More...

List of all members.

Public Member Functions

 HMM (const arma::mat &transition, const std::vector< Distribution > &emission, const double tolerance=1e-5)
 Create the Hidden Markov Model with the given transition matrix and the given emission distributions.
 HMM (const size_t states, const Distribution emissions, const double tolerance=1e-5)
 Create the Hidden Markov Model with the given number of hidden states and the given default distribution for emissions.
size_t & Dimensionality ()
 Set the dimensionality of observations.
size_t Dimensionality () const
 Get the dimensionality of observations.
std::vector< Distribution > & Emission ()
 Return a modifiable emission probability matrix reference.
const std::vector< Distribution > & Emission () const
 Return the emission distributions.
double Estimate (const arma::mat &dataSeq, arma::mat &stateProb) const
 Estimate the probabilities of each hidden state at each time step of each given data observation, using the Forward-Backward algorithm.
double Estimate (const arma::mat &dataSeq, arma::mat &stateProb, arma::mat &forwardProb, arma::mat &backwardProb, arma::vec &scales) const
 Estimate the probabilities of each hidden state at each time step for each given data observation, using the Forward-Backward algorithm.
void Generate (const size_t length, arma::mat &dataSequence, arma::Col< size_t > &stateSequence, const size_t startState=0) const
 Generate a random data sequence of the given length.
double LogLikelihood (const arma::mat &dataSeq) const
 Compute the log-likelihood of the given data sequence.
double Predict (const arma::mat &dataSeq, arma::Col< size_t > &stateSeq) const
 Compute the most probable hidden state sequence for the given data sequence, using the Viterbi algorithm, returning the log-likelihood of the most likely state sequence.
double & Tolerance ()
 Modify the tolerance of the Baum-Welch algorithm.
double Tolerance () const
 Get the tolerance of the Baum-Welch algorithm.
void Train (const std::vector< arma::mat > &dataSeq, const std::vector< arma::Col< size_t > > &stateSeq)
 Train the model using the given labeled observations; the transition and emission matrices are directly estimated.
void Train (const std::vector< arma::mat > &dataSeq)
 Train the model using the Baum-Welch algorithm, with only the given unlabeled observations.
arma::mat & Transition ()
 Return a modifiable transition matrix reference.
const arma::mat & Transition () const
 Return the transition matrix.

Private Member Functions

void Backward (const arma::mat &dataSeq, const arma::vec &scales, arma::mat &backwardProb) const
 The Backward algorithm (part of the Forward-Backward algorithm).
void Forward (const arma::mat &dataSeq, arma::vec &scales, arma::mat &forwardProb) const
 The Forward algorithm (part of the Forward-Backward algorithm).

Private Attributes

size_t dimensionality
 Dimensionality of observations.
std::vector< Distribution > emission
 Set of emission probability distributions; one for each state.
double tolerance
 Tolerance of Baum-Welch algorithm.
arma::mat transition
 Transition probability matrix.

Detailed Description

template<typename Distribution = distribution::DiscreteDistribution>
class mlpack::hmm::HMM< Distribution >

A class that represents a Hidden Markov Model with an arbitrary type of emission distribution.

This HMM class supports training (supervised and unsupervised), prediction of state sequences via the Viterbi algorithm, estimation of state probabilities, generation of random sequences, and calculation of the log-likelihood of a given sequence.

The template parameter, Distribution, specifies the distribution which the emissions follow. The class should implement the following functions:

 class Distribution
 {
  public:
   // The type of observation used by this distribution.
   typedef something DataType;

   // Return the probability of the given observation.
   double Probability(const DataType& observation) const;

   // Estimate the distribution based on the given observations.
   void Estimate(const std::vector<DataType>& observations);

   // Estimate the distribution based on the given observations, given also
   // the probability of each observation coming from this distribution.
   void Estimate(const std::vector<DataType>& observations,
                 const std::vector<double>& probabilities);
 };

See the mlpack::distribution::DiscreteDistribution class for an example. One would use the DiscreteDistribution class when the observations are non-negative integers. Other distributions could be Gaussians, a mixture of Gaussians (GMM), or any other probability distribution implementing the four Distribution functions.

Usage of the HMM class generally involves either training an HMM or loading an already-known HMM and taking probability measurements of sequences. Example code for supervised training of a Gaussian HMM (that is, where the emission output distribution is a single Gaussian for each hidden state) is given below.

 extern arma::mat observations; // Each column is an observation.
 extern arma::Col<size_t> states; // Hidden states for each observation.
 // Create an untrained HMM with 5 hidden states and default (N(0, 1))
 // Gaussian distributions with the dimensionality of the dataset.
 HMM<GaussianDistribution> hmm(5, GaussianDistribution(observations.n_rows));

 // Train the HMM (the labels could be omitted to perform unsupervised
 // training).
 hmm.Train(observations, states);

Once initialized, the HMM can evaluate the probability of a certain sequence (with LogLikelihood()), predict the most likely sequence of hidden states (with Predict()), generate a sequence (with Generate()), or estimate the probabilities of each state for a sequence of observations (with Estimate()).

Template Parameters:
Distribution Type of emission distribution for this HMM.

Definition at line 93 of file hmm.hpp.


Constructor & Destructor Documentation

template<typename Distribution = distribution::DiscreteDistribution>
mlpack::hmm::HMM< Distribution >::HMM ( const size_t  states,
const Distribution  emissions,
const double  tolerance = 1e-5 
)

Create the Hidden Markov Model with the given number of hidden states and the given default distribution for emissions.

The dimensionality of the observations is taken from the emissions variable, so it is important that the given default emission distribution is set with the correct dimensionality. Alternately, set the dimensionality with Dimensionality(). Optionally, the tolerance for convergence of the Baum-Welch algorithm can be set.

Parameters:
states Number of states.
emissions Default distribution for emissions.
tolerance Tolerance for convergence of training algorithm (Baum-Welch).
template<typename Distribution = distribution::DiscreteDistribution>
mlpack::hmm::HMM< Distribution >::HMM ( const arma::mat &  transition,
const std::vector< Distribution > &  emission,
const double  tolerance = 1e-5 
)

Create the Hidden Markov Model with the given transition matrix and the given emission distributions.

The dimensionality of the observations of the HMM are taken from the given emission distributions. Alternately, the dimensionality can be set with Dimensionality().

The transition matrix should be such that T(i, j) is the probability of transition to state i from state j. The columns of the matrix should sum to 1.

The emission matrix should be such that E(i, j) is the probability of emission i while in state j. The columns of the matrix should sum to 1.

Optionally, the tolerance for convergence of the Baum-Welch algorithm can be set.

Parameters:
transition Transition matrix.
emission Emission distributions.
tolerance Tolerance for convergence of training algorithm (Baum-Welch).

Member Function Documentation

template<typename Distribution = distribution::DiscreteDistribution>
void mlpack::hmm::HMM< Distribution >::Backward ( const arma::mat &  dataSeq,
const arma::vec &  scales,
arma::mat &  backwardProb 
) const [private]

The Backward algorithm (part of the Forward-Backward algorithm).

Computes backward probabilities for each state for each observation in the given data sequence, using the scaling factors found (presumably) by Forward(). The returned matrix has rows equal to the number of hidden states and columns equal to the number of observations.

Parameters:
dataSeq Data sequence to compute probabilities for.
scales Vector of scaling factors.
backwardProb Matrix in which backward probabilities will be saved.
template<typename Distribution = distribution::DiscreteDistribution>
size_t& mlpack::hmm::HMM< Distribution >::Dimensionality (  )  [inline]

Set the dimensionality of observations.

Definition at line 281 of file hmm.hpp.

References mlpack::hmm::HMM< Distribution >::dimensionality.

template<typename Distribution = distribution::DiscreteDistribution>
size_t mlpack::hmm::HMM< Distribution >::Dimensionality (  )  const [inline]

Get the dimensionality of observations.

Definition at line 279 of file hmm.hpp.

References mlpack::hmm::HMM< Distribution >::dimensionality.

template<typename Distribution = distribution::DiscreteDistribution>
std::vector<Distribution>& mlpack::hmm::HMM< Distribution >::Emission (  )  [inline]

Return a modifiable emission probability matrix reference.

Definition at line 276 of file hmm.hpp.

template<typename Distribution = distribution::DiscreteDistribution>
const std::vector<Distribution>& mlpack::hmm::HMM< Distribution >::Emission (  )  const [inline]

Return the emission distributions.

Definition at line 274 of file hmm.hpp.

template<typename Distribution = distribution::DiscreteDistribution>
double mlpack::hmm::HMM< Distribution >::Estimate ( const arma::mat &  dataSeq,
arma::mat &  stateProb 
) const

Estimate the probabilities of each hidden state at each time step of each given data observation, using the Forward-Backward algorithm.

The returned matrix of state probabilities has columns equal to the number of data observations, and rows equal to the number of hidden states in the model. The log-likelihood of the most probable sequence is returned.

Parameters:
dataSeq Sequence of observations.
stateProb Probabilities of each state at each time interval.
Returns:
Log-likelihood of most likely state sequence.
template<typename Distribution = distribution::DiscreteDistribution>
double mlpack::hmm::HMM< Distribution >::Estimate ( const arma::mat &  dataSeq,
arma::mat &  stateProb,
arma::mat &  forwardProb,
arma::mat &  backwardProb,
arma::vec &  scales 
) const

Estimate the probabilities of each hidden state at each time step for each given data observation, using the Forward-Backward algorithm.

Each matrix which is returned has columns equal to the number of data observations, and rows equal to the number of hidden states in the model. The log-likelihood of the most probable sequence is returned.

Parameters:
dataSeq Sequence of observations.
stateProb Matrix in which the probabilities of each state at each time interval will be stored.
forwardProb Matrix in which the forward probabilities of each state at each time interval will be stored.
backwardProb Matrix in which the backward probabilities of each state at each time interval will be stored.
scales Vector in which the scaling factors at each time interval will be stored.
Returns:
Log-likelihood of most likely state sequence.
template<typename Distribution = distribution::DiscreteDistribution>
void mlpack::hmm::HMM< Distribution >::Forward ( const arma::mat &  dataSeq,
arma::vec &  scales,
arma::mat &  forwardProb 
) const [private]

The Forward algorithm (part of the Forward-Backward algorithm).

Computes forward probabilities for each state for each observation in the given data sequence. The returned matrix has rows equal to the number of hidden states and columns equal to the number of observations.

Parameters:
dataSeq Data sequence to compute probabilities for.
scales Vector in which scaling factors will be saved.
forwardProb Matrix in which forward probabilities will be saved.
template<typename Distribution = distribution::DiscreteDistribution>
void mlpack::hmm::HMM< Distribution >::Generate ( const size_t  length,
arma::mat &  dataSequence,
arma::Col< size_t > &  stateSequence,
const size_t  startState = 0 
) const

Generate a random data sequence of the given length.

The data sequence is stored in the dataSequence parameter, and the state sequence is stored in the stateSequence parameter. Each column of dataSequence represents a random observation.

Parameters:
length Length of random sequence to generate.
dataSequence Vector to store data in.
stateSequence Vector to store states in.
startState Hidden state to start sequence in (default 0).
template<typename Distribution = distribution::DiscreteDistribution>
double mlpack::hmm::HMM< Distribution >::LogLikelihood ( const arma::mat &  dataSeq  )  const

Compute the log-likelihood of the given data sequence.

Parameters:
dataSeq Data sequence to evaluate the likelihood of.
Returns:
Log-likelihood of the given sequence.
template<typename Distribution = distribution::DiscreteDistribution>
double mlpack::hmm::HMM< Distribution >::Predict ( const arma::mat &  dataSeq,
arma::Col< size_t > &  stateSeq 
) const

Compute the most probable hidden state sequence for the given data sequence, using the Viterbi algorithm, returning the log-likelihood of the most likely state sequence.

Parameters:
dataSeq Sequence of observations.
stateSeq Vector in which the most probable state sequence will be stored.
Returns:
Log-likelihood of most probable state sequence.
template<typename Distribution = distribution::DiscreteDistribution>
double& mlpack::hmm::HMM< Distribution >::Tolerance (  )  [inline]

Modify the tolerance of the Baum-Welch algorithm.

Definition at line 286 of file hmm.hpp.

References mlpack::hmm::HMM< Distribution >::tolerance.

template<typename Distribution = distribution::DiscreteDistribution>
double mlpack::hmm::HMM< Distribution >::Tolerance (  )  const [inline]

Get the tolerance of the Baum-Welch algorithm.

Definition at line 284 of file hmm.hpp.

References mlpack::hmm::HMM< Distribution >::tolerance.

template<typename Distribution = distribution::DiscreteDistribution>
void mlpack::hmm::HMM< Distribution >::Train ( const std::vector< arma::mat > &  dataSeq,
const std::vector< arma::Col< size_t > > &  stateSeq 
)

Train the model using the given labeled observations; the transition and emission matrices are directly estimated.

Each matrix in the vector of data sequences corresponds to a vector in the vector of state sequences. Each point in each individual data sequence should be a column in the matrix, and its state should be the corresponding element in the state sequence vector. For instance, dataSeq[0].col(3) corresponds to the fourth observation in the first data sequence, and its state is stateSeq[0][3]. The number of rows in each matrix should be equal to the dimensionality of the HMM (which is set in the constructor).

Note:
Train() can be called multiple times with different sequences; each time it is called, it uses the current parameters of the HMM as a starting point for training.
Parameters:
dataSeq Vector of observation sequences.
stateSeq Vector of state sequences, corresponding to each observation.
template<typename Distribution = distribution::DiscreteDistribution>
void mlpack::hmm::HMM< Distribution >::Train ( const std::vector< arma::mat > &  dataSeq  ) 

Train the model using the Baum-Welch algorithm, with only the given unlabeled observations.

Instead of giving a guess transition and emission matrix here, do that in the constructor. Each matrix in the vector of data sequences holds an individual data sequence; each point in each individual data sequence should be a column in the matrix. The number of rows in each matrix should be equal to the dimensionality of the HMM (which is set in the constructor).

It is preferable to use the other overload of Train(), with labeled data. That will produce much better results. However, if labeled data is unavailable, this will work. In addition, it is possible to use Train() with labeled data first, and then continue to train the model using this overload of Train() with unlabeled data.

The tolerance of the Baum-Welch algorithm can be set either in the constructor or with the Tolerance() method. When the change in log-likelihood of the model between iterations is less than the tolerance, the Baum-Welch algorithm terminates.

Note:
Train() can be called multiple times with different sequences; each time it is called, it uses the current parameters of the HMM as a starting point for training.
Parameters:
dataSeq Vector of observation sequences.
template<typename Distribution = distribution::DiscreteDistribution>
arma::mat& mlpack::hmm::HMM< Distribution >::Transition (  )  [inline]

Return a modifiable transition matrix reference.

Definition at line 271 of file hmm.hpp.

template<typename Distribution = distribution::DiscreteDistribution>
const arma::mat& mlpack::hmm::HMM< Distribution >::Transition (  )  const [inline]

Return the transition matrix.

Definition at line 269 of file hmm.hpp.


Member Data Documentation

template<typename Distribution = distribution::DiscreteDistribution>
size_t mlpack::hmm::HMM< Distribution >::dimensionality [private]

Dimensionality of observations.

Definition at line 327 of file hmm.hpp.

Referenced by mlpack::hmm::HMM< Distribution >::Dimensionality().

template<typename Distribution = distribution::DiscreteDistribution>
std::vector<Distribution> mlpack::hmm::HMM< Distribution >::emission [private]

Set of emission probability distributions; one for each state.

Definition at line 324 of file hmm.hpp.

template<typename Distribution = distribution::DiscreteDistribution>
double mlpack::hmm::HMM< Distribution >::tolerance [private]

Tolerance of Baum-Welch algorithm.

Definition at line 330 of file hmm.hpp.

Referenced by mlpack::hmm::HMM< Distribution >::Tolerance().

template<typename Distribution = distribution::DiscreteDistribution>
arma::mat mlpack::hmm::HMM< Distribution >::transition [private]

Transition probability matrix.

Definition at line 321 of file hmm.hpp.


The documentation for this class was generated from the following file:

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