mlpack
2.2.5
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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=1e-5) | |
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=1e-5) | |
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 Forward-Backward 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 Forward-Backward 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 log-likelihood 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 log-likelihood 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 Baum-Welch algorithm. More... | |
double & | Tolerance () |
Modify the tolerance of the Baum-Welch algorithm. More... | |
void | Train (const std::vector< arma::mat > &dataSeq) |
Train the model using the Baum-Welch 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 Forward-Backward algorithm). More... | |
void | Forward (const arma::mat &dataSeq, arma::vec &scales, arma::mat &forwardProb) const |
The Forward algorithm (part of the Forward-Backward 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 log-likelihood 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 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.
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
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Distribution Type of emission distribution for this HMM.
Constructor & Destructor Documentation
◆ HMM() [1/2]
HMM | ( | const size_t | states = 0 , |
const Distribution | emissions = Distribution() , |
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const double | tolerance = 1e-5 |
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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.
By default, the transition matrix and initial probability vector are set to contain equal probability for each state.
- Parameters
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states Number of states. emissions Default distribution for emissions. tolerance Tolerance for convergence of training algorithm (Baum-Welch).
◆ HMM() [2/2]
HMM | ( | const arma::vec & | initial, |
const arma::mat & | transition, | ||
const std::vector< Distribution > & | emission, | ||
const double | tolerance = 1e-5 |
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) |
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 Baum-Welch algorithm can be set.
- Parameters
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initial Initial state probabilities. transition Transition matrix. emission Emission distributions. tolerance Tolerance for convergence of training algorithm (Baum-Welch).
Member Function Documentation
◆ Backward()
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protected |
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
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dataSeq Data sequence to compute probabilities for. scales Vector of scaling factors. backwardProb Matrix in which backward probabilities will be saved.
Referenced by HMM< distribution::RegressionDistribution >::Tolerance().
◆ Dimensionality() [1/2]
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◆ Dimensionality() [2/2]
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◆ Emission() [1/2]
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◆ Emission() [2/2]
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◆ 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 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
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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.
◆ 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 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
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dataSeq Sequence of observations. stateProb Probabilities of each state at each time interval.
- Returns
- Log-likelihood of most likely state sequence.
◆ Filter()
void Filter | ( | const arma::mat & | dataSeq, |
arma::mat & | filterSeq, | ||
size_t | ahead = 0 |
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) | const |
HMM filtering.
Computes the k-step-ahead 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
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dataSeq Sequence of observations. filterSeq Vector in which the expected emission sequence will be stored. ahead Number of steps ahead (k) for expectations.
◆ Forward()
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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
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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< distribution::RegressionDistribution >::Tolerance().
◆ Generate()
void Generate | ( | const size_t | length, |
arma::mat & | dataSequence, | ||
arma::Row< size_t > & | stateSequence, | ||
const size_t | startState = 0 |
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) | 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
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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]
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◆ Initial() [2/2]
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◆ LogLikelihood()
double LogLikelihood | ( | const arma::mat & | dataSeq | ) | const |
Compute the log-likelihood of the given data sequence.
- Parameters
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dataSeq Data sequence to evaluate the likelihood of.
- Returns
- Log-likelihood 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 log-likelihood of the most likely state sequence.
- Parameters
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dataSeq Sequence of observations. stateSeq Vector in which the most probable state sequence will be stored.
- Returns
- Log-likelihood of most probable state sequence.
◆ Serialize()
void Serialize | ( | Archive & | ar, |
const unsigned int | version | ||
) |
Serialize the object.
Referenced by HMM< distribution::RegressionDistribution >::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
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dataSeq Sequence of observations. smoothSeq Vector in which the expected emission sequence will be stored.
◆ Tolerance() [1/2]
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◆ Tolerance() [2/2]
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◆ Train() [1/2]
void 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
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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
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dataSeq Vector of observation sequences. stateSeq Vector of state sequences, corresponding to each observation.
◆ Transition() [1/2]
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◆ Transition() [2/2]
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Member Data Documentation
◆ emission
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Set of emission probability distributions; one for each state.
Definition at line 363 of file hmm.hpp.
Referenced by HMM< distribution::RegressionDistribution >::Emission().
◆ transition
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Transition probability matrix.
Definition at line 366 of file hmm.hpp.
Referenced by HMM< distribution::RegressionDistribution >::Transition().
The documentation for this class was generated from the following file:
- src/mlpack/methods/hmm/hmm.hpp
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