rv_coefficient_interdependence

Bases: statistical_kernel_based_interdependence

A statistical kernel-based interdependence class using the RV coefficient kernel.

Notes

RV coefficient based Kernel:

$$ \begin{equation} \text{kernel}(\mathbf{x}, \mathbf{y}) = \frac{ tr(\Sigma_{x,y} \Sigma_{y,x} ) }{ \sqrt{ tr(\Sigma_x^2) tr(\Sigma_y^2)}}. \end{equation} $$ where \(\Sigma_{x}\), \(\Sigma_{y}\) and \(\Sigma_{x,y}\) denote the variance/co-variance matrix of \(\mathbf{x}\) and \(\mathbf{y}\) respectively.

Attributes:

Name	Type	Description
kernel	Callable	The RV coefficient kernel function.

Methods:

Name	Description
__init__	Initializes the RV coefficient interdependence function.

Source code in tinybig/interdependence/statistical_kernel_interdependence.py

class rv_coefficient_interdependence(statistical_kernel_based_interdependence):
    r"""
        A statistical kernel-based interdependence class using the RV coefficient kernel.

        Notes
        ----------
        __RV coefficient based Kernel:__

        $$
            \begin{equation}
            \text{kernel}(\mathbf{x}, \mathbf{y}) = \frac{ tr(\Sigma_{x,y} \Sigma_{y,x} ) }{ \sqrt{ tr(\Sigma_x^2) tr(\Sigma_y^2)}}.
            \end{equation}
        $$
        where $\Sigma_{x}$, $\Sigma_{y}$ and $\Sigma_{x,y}$ denote the variance/co-variance matrix of $\mathbf{x}$ and $\mathbf{y}$ respectively.

        Attributes
        ----------
        kernel : Callable
            The RV coefficient kernel function.

        Methods
        -------
        __init__(...)
            Initializes the RV coefficient interdependence function.
    """
    def __init__(self, name: str = 'rv_coefficient_interdependence', *args, **kwargs):
        """
            Initializes the RV coefficient interdependence function.

            Parameters
            ----------
            name : str, optional
                Name of the interdependence function. Defaults to 'rv_coefficient_interdependence'.
            *args : tuple
                Additional positional arguments for the parent class.
            **kwargs : dict
                Additional keyword arguments for the parent class.
        """
        super().__init__(kernel=batch_rv_coefficient_kernel, name=name, *args, **kwargs)

__init__(name='rv_coefficient_interdependence', *args, **kwargs)

Initializes the RV coefficient interdependence function.

Parameters:

Name	Type	Description	Default
name	str	Name of the interdependence function. Defaults to 'rv_coefficient_interdependence'.	'rv_coefficient_interdependence'
*args	tuple	Additional positional arguments for the parent class.	()
**kwargs	dict	Additional keyword arguments for the parent class.	{}

Source code in tinybig/interdependence/statistical_kernel_interdependence.py

def __init__(self, name: str = 'rv_coefficient_interdependence', *args, **kwargs):
    """
        Initializes the RV coefficient interdependence function.

        Parameters
        ----------
        name : str, optional
            Name of the interdependence function. Defaults to 'rv_coefficient_interdependence'.
        *args : tuple
            Additional positional arguments for the parent class.
        **kwargs : dict
            Additional keyword arguments for the parent class.
    """
    super().__init__(kernel=batch_rv_coefficient_kernel, name=name, *args, **kwargs)