Source code for monte_carlo_analysis.uncertainty_metrics.BhattacharyaCoefficentDistributionSimilarity

"""
**Author** : Robin Camarasa

**Institution** : Erasmus Medical Center

**Position** : PhD student

**Contact** : r.camarasa@erasmusmc.nl

**Date** : 2020-10-01

**Project** : monte_carlo_analysis

**Implement class BhattacharyaCoefficentDistributionSimilarity**

"""
from monte_carlo_analysis.uncertainty_metrics import DistributionSimilarityUncertaintyMetric
import numpy as np
from monte_carlo_analysis.utils.numba_utils import numba_histogram
from numba import jit


[docs]class BhattacharyaCoefficentDistributionSimilarity(DistributionSimilarityUncertaintyMetric):
    """Implement BhattacharyaCoefficentDistributionSimilarity class. The formula applied to a pair of distributions :math:`q_{c'}(y_j|x)` and :math:`q_{c}(y_j|x)` is:

    .. math::
        S^b(q_{c'}(y_j|x), q_{c''}(y_j|x)) = \int_{0}^{1} \sqrt{q_{c'}(y_j = t | x) q_{c''}(y_j = t|x)} dt

    :param nbins: The discretization step of the integral
    """
    def __init__(self, nbins: int=100):
        super(BhattacharyaCoefficentDistributionSimilarity, self)
        self.nbins = nbins
        self.transformation = self.get_transformation(nbins)

[docs]    def get_transformation(self, nbins: int) -> callable:
        """Define the transformation applied to a pair of distributions

        :param nbins: The discretization step of the integral
        :return: transformation to apply to a pair of distributions
        """
        #@jit(nopython=True)
        def transformation(distribution_1: np.array, distribution_2) -> float:
            # discretize the distribution the division
            # by the sum is due to np.histogram implementation
            discretized_distribution_1 = numba_histogram(
                distribution_1, bins=nbins, min_value=0, max_value=1,
                normalized=True
            )[0]

            discretized_distribution_2 = numba_histogram(
                distribution_2, bins=nbins, min_value=0, max_value=1,
                normalized=True
            )[0]

            return np.sum(
                np.sqrt(discretized_distribution_1 * discretized_distribution_2)
            )
        return transformation