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gmm

This submodule provides implementations of Gaussian Mixture Models (GMMs) with identical covariance across components, including a periodic extension to handle data on a bounded interval via component replication.

Classes:

  • GMM –

    Defines a mixture of N Gaussians with shared scalar standard deviation. Offers methods to compute the probability density function (PDF) and its natural logarithm over input samples.

  • PeriodicGMM –

    Inherits from GMM and adds support for periodic domains [0, bound]. It replicates mixture components across multiple copies of the domain to evaluate densities that respect periodic boundary conditions.

GMM(means, std) dataclass

Gaussian Mixture Model of N Gaussians with identical covariance.

Parameters:

  • means (ndarray) –

    The means of the Gaussians.

  • std (float) –

    A scalar representing the standard deviation of the Gaussians.

pdf(X)

Calculate the probability density function (PDF) of the Gaussian Mixture Model.

Parameters:

Returns:

  • float –

    The PDF value.

Source code in src/fpsl/utils/gmm.py 
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def pdf(self, X: Float[ArrayLike, ' n_samples']) -> Float[ArrayLike, ' n_samples']:
    """
    Calculate the probability density function (PDF) of the Gaussian Mixture Model.

    Parameters
    ----------
    X : jnp.ndarray
        The input data.

    Returns
    -------
    float
        The PDF value.

    """
    return jax.scipy.stats.norm.pdf(
        X,
        loc=self.means,
        scale=self.std,
    ).mean(axis=0)

ln_pdf(X)

Calculate the natural logarithm of the probability density function (PDF) of the Gaussian Mixture Model.

Parameters:

Returns:

  • ndarray –

    The natural logarithm of the PDF value.

Source code in src/fpsl/utils/gmm.py 
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def ln_pdf(
    self,
    X: Float[ArrayLike, ' n_samples'],
) -> Float[ArrayLike, ' n_samples']:
    """
    Calculate the natural logarithm of the probability density function (PDF) of the Gaussian Mixture Model.

    Parameters
    ----------
    X : jnp.ndarray
        The input data.

    Returns
    -------
    jnp.ndarray
        The natural logarithm of the PDF value.

    """
    return jnp.log(self.pdf(X))

PeriodicGMM(means, std, bound=1.0, copies=5) dataclass

Bases: GMM, DefaultDataClass

Gaussian Mixture Model of N Gaussians with identical covariance.

Parameters:

  • means (ndarray) –

    The means of the Gaussians.

  • std (Union[ndarray, int]) –

    A scalar representing the standard deviation of the Gaussians.

  • bound (float, default: 1.0 ) –

    The data is periodic on [0, bound].

  • copies (int, default: 5 ) –

    Number of copies in each direction.

pdf(X)

Calculate the probability density function (PDF) of the Gaussian Mixture Model.

Parameters:

Returns:

Source code in src/fpsl/utils/gmm.py 
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def pdf(self, X: Float[ArrayLike, ' n_samples']) -> Float[ArrayLike, ' n_samples']:
    """
    Calculate the probability density function (PDF) of the Gaussian Mixture Model.

    Parameters
    ----------
    X : jnp.ndarray
        The input data.

    Returns
    -------
    jnp.ndarray
        The PDF values.

    """
    return jnp.array([
        jax.scipy.stats.norm.pdf(
            X + offset,
            loc=self.means,
            scale=self.std,
        ).mean(axis=0)
        for offset in self.offsets
    ]).sum(axis=0)