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A class that represents a Hidden Markov Model with an arbitrary type of emission distribution. More...
Public Member Functions  
HMM (const size_t states=0, const Distribution emissions=Distribution(), const double tolerance=1e5)  
Create the Hidden Markov Model with the given number of hidden states and the given default distribution for emissions. More...  
HMM (const arma::vec &initial, const arma::mat &transition, const std::vector< Distribution > &emission, const double tolerance=1e5)  
Create the Hidden Markov Model with the given initial probability vector, the given transition matrix, and the given emission distributions. More...  
size_t  Dimensionality () const 
Get the dimensionality of observations. More...  
size_t &  Dimensionality () 
Set the dimensionality of observations. More...  
const std::vector< Distribution > &  Emission () const 
Return the emission distributions. More...  
std::vector< Distribution > &  Emission () 
Return a modifiable emission probability matrix reference. More...  
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 ForwardBackward algorithm. More...  
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 ForwardBackward algorithm. More...  
void  Filter (const arma::mat &dataSeq, arma::mat &filterSeq, size_t ahead=0) const 
HMM filtering. More...  
void  Generate (const size_t length, arma::mat &dataSequence, arma::Row< size_t > &stateSequence, const size_t startState=0) const 
Generate a random data sequence of the given length. More...  
const arma::vec &  Initial () const 
Return the vector of initial state probabilities. More...  
arma::vec &  Initial () 
Modify the vector of initial state probabilities. More...  
double  LogLikelihood (const arma::mat &dataSeq) const 
Compute the loglikelihood of the given data sequence. More...  
double  Predict (const arma::mat &dataSeq, arma::Row< size_t > &stateSeq) const 
Compute the most probable hidden state sequence for the given data sequence, using the Viterbi algorithm, returning the loglikelihood of the most likely state sequence. More...  
template < typename Archive >  
void  Serialize (Archive &ar, const unsigned int version) 
Serialize the object. More...  
void  Smooth (const arma::mat &dataSeq, arma::mat &smoothSeq) const 
HMM smoothing. More...  
double  Tolerance () const 
Get the tolerance of the BaumWelch algorithm. More...  
double &  Tolerance () 
Modify the tolerance of the BaumWelch algorithm. More...  
void  Train (const std::vector< arma::mat > &dataSeq) 
Train the model using the BaumWelch algorithm, with only the given unlabeled observations. More...  
void  Train (const std::vector< arma::mat > &dataSeq, const std::vector< arma::Row< size_t > > &stateSeq) 
Train the model using the given labeled observations; the transition and emission matrices are directly estimated. More...  
const arma::mat &  Transition () const 
Return the transition matrix. More...  
arma::mat &  Transition () 
Return a modifiable transition matrix reference. More...  
Protected Member Functions  
void  Backward (const arma::mat &dataSeq, const arma::vec &scales, arma::mat &backwardProb) const 
The Backward algorithm (part of the ForwardBackward algorithm). More...  
void  Forward (const arma::mat &dataSeq, arma::vec &scales, arma::mat &forwardProb) const 
The Forward algorithm (part of the ForwardBackward algorithm). More...  
Protected Attributes  
std::vector< Distribution >  emission 
Set of emission probability distributions; one for each state. More...  
arma::mat  transition 
Transition probability matrix. More...  
Detailed Description
template<typenameDistribution=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 loglikelihood of a given sequence.
The template parameter, Distribution, specifies the distribution which the emissions follow. The class should implement the following functions:
See the mlpack::distribution::DiscreteDistribution class for an example. One would use the DiscreteDistribution class when the observations are nonnegative 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 alreadyknown 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.
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 Train()).
 Template Parameters

Distribution Type of emission distribution for this HMM.
Constructor & Destructor Documentation
◆ HMM() [1/2]
HMM  (  const size_t  states = 0 , 
const Distribution  emissions = Distribution() , 

const double  tolerance = 1e5 

) 
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 BaumWelch algorithm can be set.
By default, the transition matrix and initial probability vector are set to contain equal probability for each state.
 Parameters

states Number of states. emissions Default distribution for emissions. tolerance Tolerance for convergence of training algorithm (BaumWelch).
◆ HMM() [2/2]
HMM  (  const arma::vec &  initial, 
const arma::mat &  transition,  
const std::vector< Distribution > &  emission,  
const double  tolerance = 1e5 

) 
Create the Hidden Markov Model with the given initial probability vector, 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 initial state probability vector should have length equal to the number of states, and each entry represents the probability of being in the given state at time T = 0 (the beginning of a sequence).
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 BaumWelch algorithm can be set.
 Parameters

initial Initial state probabilities. transition Transition matrix. emission Emission distributions. tolerance Tolerance for convergence of training algorithm (BaumWelch).
Member Function Documentation
◆ Backward()

protected 
The Backward algorithm (part of the ForwardBackward 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.
Referenced by HMM< mlpack::distribution::DiscreteDistribution >::Tolerance().
◆ Dimensionality() [1/2]

inline 
◆ Dimensionality() [2/2]

inline 
◆ Emission() [1/2]

inline 
◆ Emission() [2/2]

inline 
◆ Estimate() [1/2]
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 ForwardBackward 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 loglikelihood 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
 Loglikelihood of most likely state sequence.
◆ Estimate() [2/2]
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 ForwardBackward 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 loglikelihood of the most probable sequence is returned.
 Parameters

dataSeq Sequence of observations. stateProb Probabilities of each state at each time interval.
 Returns
 Loglikelihood of most likely state sequence.
◆ Filter()
void Filter  (  const arma::mat &  dataSeq, 
arma::mat &  filterSeq,  
size_t  ahead = 0 

)  const 
HMM filtering.
Computes the kstepahead expected emission at each time conditioned only on prior observations. That is E{ Y[t+k]  Y[0], ..., Y[t] }. The returned matrix has columns equal to the number of observations. Note that the expectation may not be meaningful for discrete emissions.
 Parameters

dataSeq Sequence of observations. filterSeq Vector in which the expected emission sequence will be stored. ahead Number of steps ahead (k) for expectations.
◆ Forward()

protected 
The Forward algorithm (part of the ForwardBackward 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.
Referenced by HMM< mlpack::distribution::DiscreteDistribution >::Tolerance().
◆ Generate()
void Generate  (  const size_t  length, 
arma::mat &  dataSequence,  
arma::Row< 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).
◆ Initial() [1/2]

inline 
◆ Initial() [2/2]

inline 
◆ LogLikelihood()
double LogLikelihood  (  const arma::mat &  dataSeq  )  const 
Compute the loglikelihood of the given data sequence.
 Parameters

dataSeq Data sequence to evaluate the likelihood of.
 Returns
 Loglikelihood of the given sequence.
◆ Predict()
double Predict  (  const arma::mat &  dataSeq, 
arma::Row< size_t > &  stateSeq  
)  const 
Compute the most probable hidden state sequence for the given data sequence, using the Viterbi algorithm, returning the loglikelihood of the most likely state sequence.
 Parameters

dataSeq Sequence of observations. stateSeq Vector in which the most probable state sequence will be stored.
 Returns
 Loglikelihood of most probable state sequence.
◆ Serialize()
void Serialize  (  Archive &  ar, 
const unsigned int  version  
) 
Serialize the object.
Referenced by HMM< mlpack::distribution::DiscreteDistribution >::Tolerance().
◆ Smooth()
void Smooth  (  const arma::mat &  dataSeq, 
arma::mat &  smoothSeq  
)  const 
HMM smoothing.
Computes expected emission at each time conditioned on all observations. That is E{ Y[t]  Y[0], ..., Y[T] }. The returned matrix has columns equal to the number of observations. Note that the expectation may not be meaningful for discrete emissions.
 Parameters

dataSeq Sequence of observations. smoothSeq Vector in which the expected emission sequence will be stored.
◆ Tolerance() [1/2]

inline 
◆ Tolerance() [2/2]

inline 
◆ Train() [1/2]
void Train  (  const std::vector< arma::mat > &  dataSeq  ) 
Train the model using the BaumWelch 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 BaumWelch algorithm can be set either in the constructor or with the Tolerance() method. When the change in loglikelihood of the model between iterations is less than the tolerance, the BaumWelch 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.
◆ Train() [2/2]
void Train  (  const std::vector< arma::mat > &  dataSeq, 
const std::vector< arma::Row< 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.
◆ Transition() [1/2]

inline 
◆ Transition() [2/2]

inline 
Member Data Documentation
◆ emission

protected 
Set of emission probability distributions; one for each state.
Definition at line 363 of file hmm.hpp.
Referenced by HMM< mlpack::distribution::DiscreteDistribution >::Emission().
◆ transition

protected 
Transition probability matrix.
Definition at line 366 of file hmm.hpp.
Referenced by HMM< mlpack::distribution::DiscreteDistribution >::Transition().
The documentation for this class was generated from the following file:
 src/mlpack/methods/hmm/hmm.hpp
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