mlpg

Functions

int main(int argc, char *argv[])

mlpg [ option ] [ infile ]

• -l int

  • length of vector \((1 \le M + 1)\)

• -m int

  • order of vector \((0 \le M)\)

• -s int

  • number of past frames \((0 \le S)\)

• -q int

  • input format

    • 0 \(\boldsymbol{\mu}\), \(\boldsymbol{\varSigma}\)

    • 1 \(\boldsymbol{\mu}\), \(\boldsymbol{\varSigma}^{-1}\)

    • 2 \(\boldsymbol{\mu\varSigma}^{-1}\), \(\boldsymbol{\varSigma}^{-1}\)

• -d double+

  • delta coefficients

• -D string

  • filename of double-type delta coefficients

• -r int+

  • width of 1st (and 2nd) regression coefficients

• -magic double

  • magic number

• -R int

  • mode

    • 0 recursive (Kalman filter)

    • 1 non-recursive (Cholesky decomposition)

• infile str

  • double-type mean and variance parameter sequence

• stdout

  • double-type static parameter sequence

See also

delta

class sptk::RecursiveMaximumLikelihoodParameterGeneration

Estimate the maximum likelihood parameters from the means and the diagonal covariances of Gaussian distributions.

The input is the sequence of the mean and the diagnoal covariance of \(M\)-th order static and \(DM\)-th order dynamic feature components:

\[ \begin{array}{ccccc} \boldsymbol{\mu}_1, & \boldsymbol{\varSigma}_1, & \ldots, & \boldsymbol{\mu}_T, & \boldsymbol{\varSigma}_T, \end{array} \]

where

\[\begin{split}\begin{eqnarray} \boldsymbol{\mu}_t &=& \left[ \begin{array}{cccc} \boldsymbol{\mu}_t^{(0)}, & \boldsymbol{\mu}_t^{(1)}, & \ldots, & \boldsymbol{\mu}_t^{(D)} \end{array} \right] \\ \boldsymbol{\varSigma}_t &=& \left[ \begin{array}{cccc} \boldsymbol{\varSigma}_t^{(0)}, & \boldsymbol{\varSigma}_t^{(1)}, & \ldots, & \boldsymbol{\varSigma}_t^{(D)} \end{array} \right]. \end{eqnarray}\end{split}\]

The output is the sequence of the \(M\)-th order smoothed static feature components:

\[ \begin{array}{cccc} \boldsymbol{c}_1, & \boldsymbol{c}_2, & \ldots, & \boldsymbol{c}_T. \end{array} \]

The impelemented algorithm is based on a recursive manner using Kalman filter. The algorithm does not require entire mean and varaiance parameter sequence, but intorduces approximation error. The amount of approximation error is controlled by a parameter, \(S\).

Public Functions

RecursiveMaximumLikelihoodParameterGeneration(int num_order, int num_past_frame, const std::vector<std::vector<double>> &window_coefficients, InputSourceInterface *input_source)

Parameters

• num_order – [in] Order of coefficients, \(M\).

• num_past_frame – [in] Number of past frames, \(S\).

• window_coefficients – [in] Window coefficients. e.g.) { {-0.5, 0.0, 0.5}, {1.0, -2.0, 1.0} }

• input_source – [in] Static and dynamic components sequence.

inline int GetNumOrder() const

Returns

Order of coefficients.

inline int GetNumPastFrame() const

Returns

Number of past frames.

inline bool IsValid() const

Returns

True if this object is valid.

bool Get(std::vector<double> *smoothed_static_parameters)

Parameters

smoothed_static_parameters – [out] Smoothed static parameters.

Returns

True on success, false on failure.

class sptk::NonrecursiveMaximumLikelihoodParameterGeneration

Estimate the maximum likelihood parameters from the means and the diagonal covariances of Gaussian distributions.

The input is the sequence of the mean and the diagnoal covariance of \(M\)-th order static and \(DM\)-th order dynamic feature components:

\[ \begin{array}{ccccc} \boldsymbol{\mu}_1, & \boldsymbol{\varSigma}_1, & \ldots, & \boldsymbol{\mu}_T, & \boldsymbol{\varSigma}_T, \end{array} \]

where

\[\begin{split}\begin{eqnarray} \boldsymbol{\mu}_t &=& \left[ \begin{array}{cccc} \boldsymbol{\mu}_t^{(0)}, & \boldsymbol{\mu}_t^{(1)}, & \ldots, & \boldsymbol{\mu}_t^{(D)} \end{array} \right] \\ \boldsymbol{\varSigma}_t &=& \left[ \begin{array}{cccc} \boldsymbol{\varSigma}_t^{(0)}, & \boldsymbol{\varSigma}_t^{(1)}, & \ldots, & \boldsymbol{\varSigma}_t^{(D)} \end{array} \right]. \end{eqnarray}\end{split}\]

The output is the sequence of the \(M\)-th order smoothed static feature components:

\[ \begin{array}{cccc} \boldsymbol{c}_1, & \boldsymbol{c}_2, & \ldots, & \boldsymbol{c}_T. \end{array} \]

Public Functions

NonrecursiveMaximumLikelihoodParameterGeneration(int num_order, const std::vector<std::vector<double>> &window_coefficients, bool use_magic_number, double magic_number = 0.0)

Parameters

• num_order – [in] Order of coefficients, \(M\).

• window_coefficients – [in] Window coefficients. e.g.) { {-0.5, 0.0, 0.5}, {1.0, -2.0, 1.0} }

• use_magic_number – [in] Whether to use magic number.

• magic_number – [in] A magic number represents a discrete symbol.

inline int GetNumOrder() const

Returns

Order of coefficients.

inline double GetMagicNumber() const

Returns

Magic number.

inline bool IsValid() const

Returns

True if this object is valid.

bool Run(const std::vector<std::vector<double>> &mean_vectors, const std::vector<std::vector<double>> &variance_vectors, std::vector<std::vector<double>> *smoothed_static_parameters) const

Parameters

• mean_vectors – [in] Mean vector sequence. The shape is \([T, DM]$\).

• variance_vectors – [in] Variance vector sequence. The shape is \([T, DM]$\).

• smoothed_static_parameters – [out] Smoothed static parameters.

Returns

True on success, false on failure.

bool Run(const std::vector<std::vector<double>> &mean_vectors, const std::vector<SymmetricMatrix> &covariance_matrices, std::vector<std::vector<double>> *smoothed_static_parameters) const

Parameters

• mean_vectors – [in] Mean vector sequence. The shape is \([T, DM]$\).

• covariance_matrices – [in] Covariance matrix sequence. The shape is \([T, DM, DM]$\).

• smoothed_static_parameters – [out] Smoothed static parameters.

Returns

True on success, false on failure.