Module mogptk.models.sm_lmc

Classes

class SM_LMC (dataset, Q=1, Rq=1, inference=<mogptk.model.Exact object>, mean=None, name='SM-LMC')

Spectral Mixture Linear Model of Coregionalization kernel with Q components and Rq latent functions. The SM kernel as proposed by [1] is combined with the LMC kernel as proposed by [2]. The parameters will be randomly instantiated, use init_parameters() to initialize the parameters to reasonable values for the current data set.

Args

dataset : DataSet

DataSet object of data for all channels.

Q : int

Number of components.

Rq : int

Number of subcomponents.

inference

Gaussian process inference model to use, such as mogptk.Exact.

mean : Mean

The mean class.

name : str

Name of the model.

Attributes

dataset

The associated mogptk.dataset.DataSet.

gpr

The mogptk.gpr.model.Model.

Examples:

>>> import numpy as np
>>> import mogptk
>>> 
>>> t = np.linspace(0, 10, 100)
>>> y1 = np.sin(0.5 * t)
>>> y2 = 2.0 * np.sin(0.2 * t)
>>> 
>>> dataset = mogptk.DataSet(t, [y1, y2])
>>> model = mogptk.SM_LMC(dataset, Q=2)
>>> model.init_parameters()
>>> model.train()
>>> model.predict()
>>> dataset.plot()

[1] A.G. Wilson and R.P. Adams, "Gaussian Process Kernels for Pattern Discovery and Extrapolation", International Conference on Machine Learning 30, 2013 [2] P. Goovaerts, "Geostatistics for Natural Resource Evaluation", Oxford University Press, 1997

Model is the base class for multi-output Gaussian process models.

Args

dataset : DataSet, Data

DataSet with Data objects for all the channels. When a (list or dict of) Data object is passed, it will automatically be converted to a DataSet.

kernel : Kernel

The kernel class.

inference

Gaussian process inference model to use, such as mogptk.Exact.

mean : Mean

The mean class.

name : str

Name of the model.

Attributes

dataset : DataSet

Dataset.

gpr : Model

GPR model.

times : numpy.ndarray

Training times of shape (iters,).

losses : numpy.ndarray

Losses of shape (iters,).

errors : numpy.ndarray

Errors of shape (iters,).

Expand source code Browse git

class SM_LMC(Model):
    """
    Spectral Mixture Linear Model of Coregionalization kernel with `Q` components and `Rq` latent functions. The SM kernel as proposed by [1] is combined with the LMC kernel as proposed by [2]. The parameters will be randomly instantiated, use `init_parameters()` to initialize the parameters to reasonable values for the current data set.

    Args:
        dataset (mogptk.dataset.DataSet): `DataSet` object of data for all channels.
        Q (int): Number of components.
        Rq (int): Number of subcomponents.
        inference: Gaussian process inference model to use, such as `mogptk.Exact`.
        mean (mogptk.gpr.mean.Mean): The mean class.
        name (str): Name of the model.

    Attributes:
        dataset: The associated mogptk.dataset.DataSet.
        gpr: The mogptk.gpr.model.Model.

    Examples:

    >>> import numpy as np
    >>> import mogptk
    >>> 
    >>> t = np.linspace(0, 10, 100)
    >>> y1 = np.sin(0.5 * t)
    >>> y2 = 2.0 * np.sin(0.2 * t)
    >>> 
    >>> dataset = mogptk.DataSet(t, [y1, y2])
    >>> model = mogptk.SM_LMC(dataset, Q=2)
    >>> model.init_parameters()
    >>> model.train()
    >>> model.predict()
    >>> dataset.plot()

    [1] A.G. Wilson and R.P. Adams, "Gaussian Process Kernels for Pattern Discovery and Extrapolation", International Conference on Machine Learning 30, 2013\
    [2] P. Goovaerts, "Geostatistics for Natural Resource Evaluation", Oxford University Press, 1997
    """
    def __init__(self, dataset, Q=1, Rq=1, inference=Exact(), mean=None, name="SM-LMC"):
        if not isinstance(dataset, DataSet):
            dataset = DataSet(dataset)

        output_dims = dataset.get_output_dims()
        input_dims = dataset.get_input_dims()[0]
        for input_dim in dataset.get_input_dims()[1:]:
            if input_dim != input_dims:
                raise ValueError("input dimensions for all channels must match")

        spectral = [SpectralKernel(input_dims) for q in range(Q)]
        kernel = LinearModelOfCoregionalizationKernel(spectral, output_dims=output_dims, input_dims=input_dims, Q=Q, Rq=Rq)
        kernel.weight.assign(torch.rand(output_dims,Q,Rq))
        for q in range(Q):
            kernel[q].magnitude.assign(torch.rand(1))
            kernel[q].mean.assign(torch.rand(input_dims))
            kernel[q].variance.assign(torch.rand(input_dims))

        super().__init__(dataset, kernel, inference, mean, name)
        self.Q = Q
        self.Rq = Rq
        nyquist = np.amin(self.dataset.get_nyquist_estimation(), axis=0)
        for q in range(Q):
            self.gpr.kernel[q].magnitude.assign(1.0, train=False)  # handled by LMCKernel
            self.gpr.kernel[q].mean.assign(upper=np.maximum(self.gpr.kernel[q].mean.lower.detach().cpu().numpy(), nyquist))

    def init_parameters(self, method='BNSE', iters=500):
        """
        Estimate kernel parameters from the data set. The initialization can be done using three methods:

        - BNSE estimates the PSD via Bayesian non-parametris spectral estimation (Tobar 2018) and then selecting the greater Q peaks in the estimated spectrum, and use the peak's position, magnitude and width to initialize the mean, magnitude and variance of the kernel respectively.
        - LS is similar to BNSE but uses Lomb-Scargle to estimate the spectrum, which is much faster but may give poorer results.
        - SM fits independent Gaussian processes for each channel, each one with a spectral mixture kernel, and uses the fitted parameters as initial values for the multi-output kernel.

        In all cases the noise is initialized with 1/30 of the variance of each channel.

        Args:
            method (str): Method of estimation, such as BNSE, LS, or SM.
            iters (str): Number of iterations for initialization.
        """
        if not method.lower() in ['bnse', 'ls', 'sm']:
            raise ValueError("valid methods of estimation are BNSE, LS, and SM")

        if method.lower() == 'bnse':
            amplitudes, means, variances = self.dataset.get_bnse_estimation(self.Q, iters=iters)
        elif method.lower() == 'ls':
            amplitudes, means, variances = self.dataset.get_ls_estimation(self.Q)
        else:
            amplitudes, means, variances = self.dataset.get_sm_estimation(self.Q, iters=iters)
        if len(amplitudes) == 0:
            logger.warning('{} could not find peaks for SM-LMC'.format(method))
            return

        output_dims = self.dataset.get_output_dims()
        means = np.concatenate(means, axis=0)
        variances = np.concatenate(variances, axis=0)
        constant = torch.rand(output_dims, self.Q, self.Rq)
        for q in range(self.Q):
            for j in range(len(self.dataset)):
                constant[j,q,:] = amplitudes[j][q,:].mean() / self.Rq
            self.gpr.kernel[q].mean.assign(means[q,:])
            self.gpr.kernel[q].variance.assign(variances[q,:])
        self.gpr.kernel.weight.assign(constant)

        # noise
        if isinstance(self.gpr.likelihood, GaussianLikelihood):
            _, Y = self.dataset.get_train_data(transformed=True)
            Y_std = [Y[j].std() for j in range(self.dataset.get_output_dims())]
            if self.gpr.likelihood.scale().ndim == 0:
                self.gpr.likelihood.scale.assign(np.mean(Y_std))
            else:
                self.gpr.likelihood.scale.assign(Y_std)

Ancestors

• Model

Methods

def init_parameters(self, method='BNSE', iters=500)

Estimate kernel parameters from the data set. The initialization can be done using three methods:

• BNSE estimates the PSD via Bayesian non-parametris spectral estimation (Tobar 2018) and then selecting the greater Q peaks in the estimated spectrum, and use the peak's position, magnitude and width to initialize the mean, magnitude and variance of the kernel respectively.
• LS is similar to BNSE but uses Lomb-Scargle to estimate the spectrum, which is much faster but may give poorer results.
• SM fits independent Gaussian processes for each channel, each one with a spectral mixture kernel, and uses the fitted parameters as initial values for the multi-output kernel.

In all cases the noise is initialized with 1/30 of the variance of each channel.

Args

method : str

Method of estimation, such as BNSE, LS, or SM.

iters : str

Number of iterations for initialization.

Expand source code Browse git

def init_parameters(self, method='BNSE', iters=500):
    """
    Estimate kernel parameters from the data set. The initialization can be done using three methods:

    - BNSE estimates the PSD via Bayesian non-parametris spectral estimation (Tobar 2018) and then selecting the greater Q peaks in the estimated spectrum, and use the peak's position, magnitude and width to initialize the mean, magnitude and variance of the kernel respectively.
    - LS is similar to BNSE but uses Lomb-Scargle to estimate the spectrum, which is much faster but may give poorer results.
    - SM fits independent Gaussian processes for each channel, each one with a spectral mixture kernel, and uses the fitted parameters as initial values for the multi-output kernel.

    In all cases the noise is initialized with 1/30 of the variance of each channel.

    Args:
        method (str): Method of estimation, such as BNSE, LS, or SM.
        iters (str): Number of iterations for initialization.
    """
    if not method.lower() in ['bnse', 'ls', 'sm']:
        raise ValueError("valid methods of estimation are BNSE, LS, and SM")

    if method.lower() == 'bnse':
        amplitudes, means, variances = self.dataset.get_bnse_estimation(self.Q, iters=iters)
    elif method.lower() == 'ls':
        amplitudes, means, variances = self.dataset.get_ls_estimation(self.Q)
    else:
        amplitudes, means, variances = self.dataset.get_sm_estimation(self.Q, iters=iters)
    if len(amplitudes) == 0:
        logger.warning('{} could not find peaks for SM-LMC'.format(method))
        return

    output_dims = self.dataset.get_output_dims()
    means = np.concatenate(means, axis=0)
    variances = np.concatenate(variances, axis=0)
    constant = torch.rand(output_dims, self.Q, self.Rq)
    for q in range(self.Q):
        for j in range(len(self.dataset)):
            constant[j,q,:] = amplitudes[j][q,:].mean() / self.Rq
        self.gpr.kernel[q].mean.assign(means[q,:])
        self.gpr.kernel[q].variance.assign(variances[q,:])
    self.gpr.kernel.weight.assign(constant)

    # noise
    if isinstance(self.gpr.likelihood, GaussianLikelihood):
        _, Y = self.dataset.get_train_data(transformed=True)
        Y_std = [Y[j].std() for j in range(self.dataset.get_output_dims())]
        if self.gpr.likelihood.scale().ndim == 0:
            self.gpr.likelihood.scale.assign(np.mean(Y_std))
        else:
            self.gpr.likelihood.scale.assign(Y_std)

Inherited members

• Model:
  • AIC
  • BIC
  • K
  • error
  • load_kernel_parameters
  • log_marginal_likelihood
  • loss
  • num_parameters
  • num_training_points
  • parameters
  • plot_correlation
  • plot_gram
  • plot_kernel
  • plot_losses
  • plot_prediction
  • predict
  • print_parameters
  • sample
  • save
  • train