Merge pull request #2142 from aabghari/master
HMM: calculate likelihood for data stream with/without pre-calculated emission probability
This commit is contained in:
Ryan Curtin
@@ -12,6 +12,9 @@
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* Add Triplet Margin Loss function (#2762).
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* Add finalizers to Julia binding model types to fix memory handling (#2756).
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* HMM: add functions to calculate likelihood for data stream with/without
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pre-calculated emission probability (#2142).
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### mlpack 3.4.2
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###### 2020-10-26
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@@ -290,6 +290,79 @@ class HMM
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*/
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double LogLikelihood(const arma::mat& dataSeq) const;
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/**
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* Compute the log of the scaling factor of the given emission probability
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* at time t. To calculate the log-likelihood for the whole sequence,
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* accumulate log scale over the entire sequence
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* This is meant for incremental or streaming computation of the
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* log-likelihood of a sequence. For the first data point, provide an empty
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* forwardLogProb vector.
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*
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* @param emissionLogProb emission probability at time t.
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* @param forwardLogProb Vector in which forward probabilities will be saved.
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* Passing forwardLogProb as an empty vector indicates the start of the
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* sequence (i.e. time t=0).
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* @return Log scale factor of the given sequence of emission at time t.
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*/
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double EmissionLogScaleFactor(const arma::vec& emissionLogProb,
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arma::vec& forwardLogProb) const;
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/**
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* Compute the log-likelihood of the given emission probability up to time t,
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* storing the result in logLikelihood.
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* This is meant for incremental or streaming computation of the
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* log-likelihood of a sequence. For the first data point, provide an empty
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* forwardLogProb vector.
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*
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* @param emissionLogProb emission probability at time t.
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* @param logLikelihood Log-likelihood of the given sequence of emission
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* probability up to time t-1. This will be overwritten with the log-likelihood
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* of the given emission probability up to time t.
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* @param forwardLogProb Vector in which forward probabilities will be saved.
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* Passing forwardLogProb as an empty vector indicates the start of the
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* sequence (i.e. time t=0).
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* @return Log-likelihood of the given sequence of emission up to time t.
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*/
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double EmissionLogLikelihood(const arma::vec& emissionLogProb,
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double &logLikelihood,
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arma::vec& forwardLogProb) const;
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/**
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* Compute the log of the scaling factor of the given data at time t.
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* To calculate the log-likelihood for the whole sequence, accumulate the
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* log scale factor (the return value of this function) over the entire
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* sequence.
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* This is meant for incremental or streaming computation of the
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* log-likelihood of a sequence. For the first data point, provide an empty
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* forwardLogProb vector.
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*
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* @param data observation at time t.
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* @param forwardLogProb Vector in which forward probabilities will be saved.
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* Passing forwardLogProb as an empty vector indicates the start of the
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* sequence (i.e. time t=0).
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* @return Log scale factor of the given sequence of data up at time t.
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*/
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double LogScaleFactor(const arma::vec &data,
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arma::vec& forwardLogProb) const;
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/**
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* Compute the log-likelihood of the given data up to time t, storing the
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* result in logLikelihood.
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* This is meant for incremental or streaming computation of the
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* log-likelihood of a sequence. For the first data point, provide an empty
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* forwardLogProb vector.
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*
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* @param data observation at time t.
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* @param logLikelihood Log-likelihood of the given sequence of data
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* up to time t-1.
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* @param forwardLogProb Vector in which forward probabilities will be saved.
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* Passing forwardLogProb as an empty vector indicates the start of the
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* sequence (i.e. time t=0).
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* @return Log-likelihood of the given sequence of data up to time t.
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*/
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double LogLikelihood(const arma::vec &data,
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double &logLikelihood,
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arma::vec& forwardLogProb) const;
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/**
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* HMM filtering. Computes the k-step-ahead expected emission at each time
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* conditioned only on prior observations. That is
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@@ -366,6 +439,30 @@ class HMM
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void save(Archive& ar, const uint32_t version) const;
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protected:
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/**
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* Given emission probabilities, computes forward probabilities at time t=0.
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*
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* @param emissionLogProb Emission probability at time t=0.
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* @param logScales Vector in which the log of scaling factors will be saved.
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* @return Forward probabilities
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*/
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arma::vec ForwardAtT0(
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const arma::vec& emissionLogProb,
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double& logScales) const;
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/**
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* Given emission probabilities, computes forward probabilities for time t>0.
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*
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* @param emissionLogProb Emission probability at time t>0.
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* @param logScales Vector in which the log of scaling factors will be saved.
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* @param prevForwardLogProb Previous forward probabilities.
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* @return Forward probabilities
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*/
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arma::vec ForwardAtTn(
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const arma::vec& emissionLogProb,
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double& logScales,
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const arma::vec& prevForwardLogProb) const;
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// Helper functions.
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/**
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* The Forward algorithm (part of the Forward-Backward algorithm). Computes
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@@ -374,7 +471,7 @@ class HMM
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* states and columns equal to the number of observations.
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*
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* @param dataSeq Data sequence to compute probabilities for.
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* @param logScales Vector in which scaling factors will be saved.
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* @param logScales Vector in which the log of scaling factors will be saved.
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* @param forwardLogProb Matrix in which forward probabilities will be saved.
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*/
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void Forward(const arma::mat& dataSeq,
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@@ -389,7 +486,7 @@ class HMM
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* columns equal to the number of observations.
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*
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* @param dataSeq Data sequence to compute probabilities for.
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* @param logScales Vector of scaling factors.
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* @param logScales Vector of log of scaling factors.
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* @param backwardLogProb Matrix in which backward probabilities will be saved.
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*/
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void Backward(const arma::mat& dataSeq,
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@@ -166,7 +166,7 @@ double HMM<Distribution>::Train(const std::vector<arma::mat>& dataSeq)
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{
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// Estimate of T_ij (probability of transition from state j to state
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// i). We postpone multiplication of the old T_ij until later.
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for (size_t i = 0; i < logTransition.n_rows; ++i)
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for (size_t i = 0; i < logTransition.n_rows; i++)
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{
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newLogTransition(i, j) = math::LogAdd(newLogTransition(i, j),
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forwardLog(j, t) + backwardLog(i, t + 1) +
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@@ -204,7 +204,7 @@ double HMM<Distribution>::Train(const std::vector<arma::mat>& dataSeq)
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logTransition += newLogTransition;
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// Now we normalize the transition matrix.
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for (size_t i = 0; i < logTransition.n_cols; ++i)
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for (size_t i = 0; i < logTransition.n_cols; i++)
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{
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const double sum = math::AccuLog(logTransition.col(i));
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if (std::isfinite(sum))
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@@ -309,7 +309,7 @@ void HMM<Distribution>::Train(const std::vector<arma::mat>& dataSeq,
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if (emissionList[state].size() > 0)
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{
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arma::mat emissions(dimensionality, emissionList[state].size());
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for (size_t i = 0; i < emissions.n_cols; ++i)
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for (size_t i = 0; i < emissions.n_cols; i++)
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{
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emissions.col(i) = dataSeq[emissionList[state][i].first].col(
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emissionList[state][i].second);
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@@ -486,7 +486,7 @@ double HMM<Distribution>::Predict(const arma::mat& dataSeq,
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// Assemble the state probability for this element.
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// Given that we are in state j, we use state with the highest probability
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// of being the previous state.
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for (size_t j = 0; j < logTransition.n_rows; ++j)
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for (size_t j = 0; j < logTransition.n_rows; j++)
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{
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arma::vec prob = logStateProb.col(t - 1) + logTransition.row(j).t();
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logStateProb(j, t) = prob.max(index) +
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@@ -522,6 +522,80 @@ double HMM<Distribution>::LogLikelihood(const arma::mat& dataSeq) const
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return accu(logScales);
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}
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/**
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* Compute the log of the scaling factor of the given emission probability
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* at time t. To calculate the log-likelihood for the whole sequence,
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* accumulate log scale over the entire sequence
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*/
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template<typename Distribution>
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double HMM<Distribution>::EmissionLogScaleFactor(
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const arma::vec& emissionLogProb,
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arma::vec& forwardLogProb) const
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{
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double curLogScale;
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if (forwardLogProb.empty())
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{
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// We are at the start of the sequence (i.e. time t=0).
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forwardLogProb = ForwardAtT0(emissionLogProb, curLogScale);
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}
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else
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{
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forwardLogProb = ForwardAtTn(emissionLogProb, curLogScale,
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forwardLogProb);
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}
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return curLogScale;
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}
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/**
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* Compute the log-likelihood of the given emission probability up to time t
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*/
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template<typename Distribution>
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double HMM<Distribution>::EmissionLogLikelihood(
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const arma::vec& emissionLogProb,
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double& logLikelihood,
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arma::vec& forwardLogProb) const
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{
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bool isStartOfSeq = forwardLogProb.empty();
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double curLogScale = EmissionLogScaleFactor(emissionLogProb,
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forwardLogProb);
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logLikelihood = isStartOfSeq ? curLogScale : curLogScale + logLikelihood;
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return logLikelihood;
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}
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/**
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* Compute the log of the scaling factor of the given data at time t.
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* To calculate the log-likelihood for the whole sequence, accumulate log
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* scale over the entire sequence
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*/
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template<typename Distribution>
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double HMM<Distribution>::LogScaleFactor(const arma::vec &data,
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arma::vec& forwardLogProb) const
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{
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arma::vec emissionLogProb(logTransition.n_rows);
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for (size_t state = 0; state < logTransition.n_rows; state++)
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{
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emissionLogProb(state) = emission[state].LogProbability(data);
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}
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return EmissionLogScaleFactor(emissionLogProb, forwardLogProb);
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}
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/**
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* Compute the log-likelihood of the given data up to time t
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*/
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template<typename Distribution>
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double HMM<Distribution>::LogLikelihood(const arma::vec& data,
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double& logLikelihood,
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arma::vec& forwardLogProb) const
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{
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bool isStartOfSeq = forwardLogProb.empty();
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double curLogScale = LogScaleFactor(data, forwardLogProb);
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logLikelihood = isStartOfSeq ? curLogScale : curLogScale + logLikelihood;
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return logLikelihood;
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}
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/**
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* HMM filtering.
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*/
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@@ -544,7 +618,7 @@ void HMM<Distribution>::Filter(const arma::mat& dataSeq,
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// Compute expected emissions.
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// Will not work for distributions without a Mean() function.
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filterSeq.zeros(dimensionality, dataSeq.n_cols);
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for (size_t i = 0; i < emission.size(); ++i)
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for (size_t i = 0; i < emission.size(); i++)
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filterSeq += emission[i].Mean() * forwardProb.row(i);
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}
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@@ -566,10 +640,67 @@ void HMM<Distribution>::Smooth(const arma::mat& dataSeq,
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// Compute expected emissions.
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// Will not work for distributions without a Mean() function.
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smoothSeq.zeros(dimensionality, dataSeq.n_cols);
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for (size_t i = 0; i < emission.size(); ++i)
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for (size_t i = 0; i < emission.size(); i++)
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smoothSeq += emission[i].Mean() * exp(stateLogProb.row(i));
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}
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/**
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* The Forward procedure (part of the Forward-Backward algorithm).
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*/
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template<typename Distribution>
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arma::vec HMM<Distribution>::ForwardAtT0(const arma::vec& emissionLogProb,
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double& logScales) const
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{
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// Our goal is to calculate the forward probabilities:
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// P(X_k | o_{1:k}) for all possible states X_k, for each time point k.
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ConvertToLogSpace();
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arma::vec forwardLogProb(logTransition.n_rows);
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forwardLogProb.fill(-std::numeric_limits<double>::infinity());
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// The first entry in the forward algorithm uses the initial state
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// probabilities. Note that MATLAB assumes that the starting state (at
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// t = -1) is state 0; this is not our assumption here. To force that
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// behavior, you could append a single starting state to every single data
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// sequence and that should produce results in line with MATLAB.
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forwardLogProb = logInitial + emissionLogProb;
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// Normalize probability.
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logScales = math::AccuLog(forwardLogProb);
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if (std::isfinite(logScales))
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forwardLogProb -= logScales;
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return forwardLogProb;
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}
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/**
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* The Forward procedure (part of the Forward-Backward algorithm).
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*/
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template<typename Distribution>
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arma::vec HMM<Distribution>::ForwardAtTn(const arma::vec& emissionLogProb,
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double& logScales,
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const arma::vec& prevForwardLogProb) const
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{
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// Our goal is to calculate the forward probabilities:
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// P(X_k | o_{1:k}) for all possible states X_k, for each time point k.
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arma::vec forwardLogProb(logTransition.n_rows);
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forwardLogProb.fill(-std::numeric_limits<double>::infinity());
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// Now compute the probabilities for each successive observation.
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for (size_t state = 0; state < logTransition.n_rows; state++) {
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// The forward probability of state j at time t is the sum over all
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// states of the probability of the previous state transitioning to
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// the current state and emitting the given observation.
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arma::vec tmp = prevForwardLogProb + logTransition.row(state).t();
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forwardLogProb(state) = math::AccuLog(tmp) + emissionLogProb(state);
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}
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// Normalize probability.
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logScales = math::AccuLog(forwardLogProb);
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if (std::isfinite(logScales))
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forwardLogProb -= logScales;
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return forwardLogProb;
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}
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/**
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* The Forward procedure (part of the Forward-Backward algorithm).
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*/
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@@ -585,41 +716,32 @@ void HMM<Distribution>::Forward(const arma::mat& dataSeq,
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logScales.resize(dataSeq.n_cols);
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logScales.fill(-std::numeric_limits<double>::infinity());
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ConvertToLogSpace();
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// The first entry in the forward algorithm uses the initial state
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// probabilities. Note that MATLAB assumes that the starting state (at
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// t = -1) is state 0; this is not our assumption here. To force that
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// behavior, you could append a single starting state to every single data
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// sequence and that should produce results in line with MATLAB.
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arma::vec emissionLogProb(logTransition.n_rows);
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for (size_t state = 0; state < logTransition.n_rows; state++)
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{
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forwardLogProb(state, 0) = logInitial(state) +
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emissionLogProb(state) =
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emission[state].LogProbability(dataSeq.unsafe_col(0));
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}
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// Then normalize the column.
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logScales[0] = math::AccuLog(forwardLogProb.col(0));
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if (std::isfinite(logScales[0]))
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forwardLogProb.col(0) -= logScales[0];
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forwardLogProb.col(0) = ForwardAtT0(emissionLogProb, logScales(0));
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// Now compute the probabilities for each successive observation.
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for (size_t t = 1; t < dataSeq.n_cols; t++)
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{
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for (size_t j = 0; j < logTransition.n_rows; ++j)
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for (size_t state = 0; state < logTransition.n_rows; state++)
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{
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// The forward probability of state j at time t is the sum over all states
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// of the probability of the previous state transitioning to the current
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// state and emitting the given observation.
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arma::vec tmp = forwardLogProb.col(t - 1) + logTransition.row(j).t();
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forwardLogProb(j, t) = math::AccuLog(tmp) +
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emission[j].LogProbability(dataSeq.unsafe_col(t));
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emissionLogProb(state) =
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emission[state].LogProbability(dataSeq.unsafe_col(t));
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}
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// Normalize probability.
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logScales[t] = math::AccuLog(forwardLogProb.col(t));
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if (std::isfinite(logScales[t]))
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forwardLogProb.col(t) -= logScales[t];
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forwardLogProb.col(t) =
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ForwardAtTn(emissionLogProb, logScales(t), forwardLogProb.col(t-1));
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}
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}
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@@ -639,7 +761,7 @@ void HMM<Distribution>::Backward(const arma::mat& dataSeq,
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// Now step backwards through all other observations.
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for (size_t t = dataSeq.n_cols - 2; t + 1 > 0; t--)
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{
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for (size_t j = 0; j < logTransition.n_rows; ++j)
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for (size_t j = 0; j < logTransition.n_rows; j++)
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{
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// The backward probability of state j at time t is the sum over all state
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// of the probability of the next state having been a transition from the
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@@ -660,7 +782,8 @@ void HMM<Distribution>::Backward(const arma::mat& dataSeq,
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}
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/**
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* Make sure the variables in log space are in sync with the linear counter parts
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* Make sure the variables in log space are in sync with the linear
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* counterparts.
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*/
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template<typename Distribution>
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void HMM<Distribution>::ConvertToLogSpace() const
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@@ -800,6 +800,7 @@ TEST_CASE("GaussianHMMPredictTest", "[HMMTest]")
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emission.Covariance(cov.at(i));
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}
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// 100 2D observations.
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arma::mat obs = {
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{
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-0.0424, -0.0395, -0.0336, -0.0294, -0.0299, -0.032, -0.0289, -0.0148,
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@@ -832,9 +833,261 @@ TEST_CASE("GaussianHMMPredictTest", "[HMMTest]")
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0.0521, 0.0313, 0.0188, 0.0113, 0.0068, 0.0042, 0.0026, 0.0018, 0.0014
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}
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};
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//100 pre-calculated emission probabilities each for 10 states
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std::vector<arma::vec> emissionProb = {
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{ -2.7301e+03, 1.7874e+00, -1.9428e+00, -3.6365e+00, -4.0397e-01,
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-1.5115e-01, -1.0328e+00, -1.1071e+00, 5.2876e-01, -1.0643e-01 },
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{ -2.3684e+03, 1.8059e+00, -2.2058e+00, -4.0514e+00, -5.0935e-01,
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-2.1126e-01, -1.1962e+00, -1.2567e+00, 4.1247e-01, -3.0199e-01 },
|
||||
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|
||||
{ -5.0308e+05, -1.5078e+01, -2.5824e+00, -1.6122e+00, -1.1850e-01,
|
||||
-7.0720e-01, -1.0690e+00, -3.7916e-01, 2.0948e-01, -3.9737e+00 },
|
||||
{ -4.2417e+05, -1.1613e+01, -2.7333e+00, -2.2592e+00, -2.1392e-01,
|
||||
-6.2529e-01, -1.2691e+00, -5.9232e-01, 3.8196e-01, -3.8021e+00 },
|
||||
{ -3.4311e+05, -8.4490e+00, -2.9262e+00, -2.9840e+00, -3.6201e-01,
|
||||
-6.0612e-01, -1.5036e+00, -8.4657e-01, 3.8172e-01, -3.6994e+00 },
|
||||
{ -2.6553e+05, -5.7959e+00, -3.0657e+00, -3.6135e+00, -5.0450e-01,
|
||||
-6.1056e-01, -1.6893e+00, -1.0726e+00, 2.9263e-01, -3.5310e+00 },
|
||||
{ -1.6581e+05, -2.8806e+00, -2.9242e+00, -3.9480e+00, -5.5108e-01,
|
||||
-5.3603e-01, -1.6743e+00, -1.1832e+00, 2.8121e-01, -2.8215e+00 },
|
||||
{ -6.3112e+04, -4.4355e-02, -2.4673e+00, -3.8848e+00, -4.8010e-01,
|
||||
-3.5415e-01, -1.4075e+00, -1.1547e+00, 4.0803e-01, -1.5227e+00 },
|
||||
{ -5.4196e+03, 1.6750e+00, -1.9272e+00, -3.5655e+00, -3.8433e-01,
|
||||
-1.5578e-01, -1.0312e+00, -1.0745e+00, 5.4628e-01, -1.8838e-01 },
|
||||
{ -7.9742e+03, 1.9542e+00, -1.5297e+00, -3.2224e+00, -3.5023e-01,
|
||||
-2.9557e-02, -7.1541e-01, -1.0340e+00, 5.7335e-01, 7.0234e-01 },
|
||||
{ -4.6838e+04, 1.3383e+00, -1.2840e+00, -2.9202e+00, -3.6943e-01,
|
||||
2.1035e-02, -4.9879e-01, -1.0295e+00, 5.0388e-01, 1.1296e+00 },
|
||||
{ -9.2965e+04, 5.0293e-01, -1.1033e+00, -2.6251e+00, -4.0461e-01,
|
||||
2.4992e-02, -3.5062e-01, -1.0246e+00, 3.8909e-01, 1.2595e+00 },
|
||||
{ -1.3250e+05, -2.3738e-01, -9.9398e-01, -2.4136e+00, -4.4740e-01,
|
||||
6.0968e-03, -2.6559e-01, -1.0308e+00, 2.6684e-01, 1.2440e+00 },
|
||||
{ -1.7149e+05, -9.7999e-01, -9.1698e-01, -2.2384e+00, -4.9912e-01,
|
||||
-2.5475e-02, -2.0762e-01, -1.0468e+00, 1.3078e-01, 1.1599e+00 },
|
||||
{ -2.2091e+05, -1.9350e+00, -8.5497e-01, -2.0582e+00, -5.7508e-01,
|
||||
-7.7816e-02, -1.6138e-01, -1.0794e+00, -5.6045e-02, 9.8875e-01 },
|
||||
{ -2.8140e+05, -3.1219e+00, -8.2568e-01, -1.8962e+00, -6.7862e-01,
|
||||
-1.5242e-01, -1.3554e-01, -1.1353e+00, -2.9320e-01, 7.2082e-01 },
|
||||
{ -3.4167e+05, -4.3171e+00, -8.2824e-01, -1.7733e+00, -7.8907e-01,
|
||||
-2.3483e-01, -1.3167e-01, -1.2015e+00, -5.3627e-01, 4.0854e-01 },
|
||||
{ -3.7868e+05, -5.0537e+00, -8.3691e-01, -1.7046e+00, -8.6035e-01,
|
||||
-2.9036e-01, -1.3690e-01, -1.2447e+00, -6.9304e-01, 1.9260e-01 },
|
||||
{ -3.7429e+05, -4.9406e+00, -7.8456e-01, -1.6323e+00, -8.6203e-01,
|
||||
-3.0644e-01, -1.3159e-01, -1.2267e+00, -7.3358e-01, 1.3468e-01 },
|
||||
{ -3.3293e+05, -4.0758e+00, -6.6873e-01, -1.5416e+00, -8.0032e-01,
|
||||
-2.8877e-01, -1.1346e-01, -1.1498e+00, -6.7458e-01, 2.1365e-01 },
|
||||
{ -2.7541e+05, -2.9085e+00, -5.3210e-01, -1.4470e+00, -7.0706e-01,
|
||||
-2.5517e-01, -9.1435e-02, -1.0445e+00, -5.6402e-01, 3.5113e-01 },
|
||||
{ -2.2010e+05, -1.8209e+00, -4.1116e-01, -1.3627e+00, -6.1220e-01,
|
||||
-2.2144e-01, -7.3319e-02, -9.4005e-01, -4.4660e-01, 4.7992e-01 },
|
||||
{ -1.7809e+05, -1.0242e+00, -3.2646e-01, -1.3011e+00, -5.3612e-01,
|
||||
-1.9567e-01, -6.2291e-02, -8.5731e-01, -3.5032e-01, 5.7022e-01 },
|
||||
{ -1.5426e+05, -5.8691e-01, -2.8121e-01, -1.2660e+00, -4.9111e-01,
|
||||
-1.8141e-01, -5.7387e-02, -8.0842e-01, -2.9317e-01, 6.1601e-01 },
|
||||
};
|
||||
|
||||
const double loglikelihoodRef = -2734.43;
|
||||
|
||||
// Test log-likelihood calculation for the whole data.
|
||||
{
|
||||
const double loglikelihood = hmm.LogLikelihood(obs);
|
||||
REQUIRE(loglikelihood == Approx(loglikelihoodRef).epsilon(1e-3));
|
||||
}
|
||||
|
||||
// Test loglikelihood calculation in an incremental way.
|
||||
// It simulates the case where we have a stream of data.
|
||||
{
|
||||
double loglikelihood;
|
||||
arma::vec forwardLogProb;
|
||||
for (size_t t = 0; t<obs.n_cols; ++t)
|
||||
{
|
||||
loglikelihood = hmm.LogLikelihood(obs.col(t), loglikelihood,
|
||||
forwardLogProb);
|
||||
}
|
||||
REQUIRE(loglikelihood == Approx(loglikelihoodRef).epsilon(1e-3));
|
||||
}
|
||||
|
||||
// Test loglikelihood calculation in an incremental way.
|
||||
// It simulates the case where we have a stream of data.
|
||||
// In this case the accumulation of the log scales factor to calculate
|
||||
// the log-likelihood value is done outside of the loop
|
||||
{
|
||||
double loglikelihood = 0;
|
||||
arma::vec forwardLogProb;
|
||||
for (size_t t = 0; t<obs.n_cols; ++t)
|
||||
{
|
||||
double logScale = hmm.LogScaleFactor(obs.col(t), forwardLogProb);
|
||||
loglikelihood += logScale;
|
||||
}
|
||||
REQUIRE(loglikelihood == Approx(loglikelihoodRef).epsilon(1e-3));
|
||||
}
|
||||
|
||||
// Test loglikelihood calculation in an incremental way.
|
||||
// It simulates the case where we have emission probabilities pre-calculated.
|
||||
{
|
||||
double loglikelihood = 0;
|
||||
arma::vec forwardLogProb;
|
||||
for (size_t t = 0; t<emissionProb.size(); ++t)
|
||||
{
|
||||
loglikelihood = hmm.EmissionLogLikelihood(emissionProb.at(t),
|
||||
loglikelihood, forwardLogProb);
|
||||
}
|
||||
REQUIRE(loglikelihood == Approx(loglikelihoodRef).epsilon(1e-1));
|
||||
}
|
||||
|
||||
arma::Row<size_t> stateSeq;
|
||||
auto likelihood = hmm.LogLikelihood(obs);
|
||||
hmm.Predict(obs, stateSeq);
|
||||
|
||||
arma::Row<size_t> stateSeqRef = { 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
||||
@@ -843,8 +1096,6 @@ TEST_CASE("GaussianHMMPredictTest", "[HMMTest]")
|
||||
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9,
|
||||
9, 9, 9, 9, 9, 9, 9, 9, 9, 9 };
|
||||
|
||||
REQUIRE(likelihood == Approx(-2734.43).epsilon(1e-5));
|
||||
|
||||
for (size_t i = 0; i < stateSeqRef.n_cols; ++i)
|
||||
{
|
||||
REQUIRE(stateSeqRef.at(i) == stateSeq.at(i));
|
||||
|
||||
Reference in New Issue
Block a user