Source code for monte_carlo_analysis.uncertainty_metrics.EntropySingleDistribution

"""
**Author** : Robin Camarasa

**Institution** : Erasmus Medical Center

**Position** : PhD student

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

**Date** : 2020-09-30

**Project** : monte_carlo_analysis

**Implement class EntropySingleDistribution**

"""
from monte_carlo_analysis.uncertainty_metrics import SingleDistributionUncertaintyMetric
import numpy as np
from numba import jit


[docs]class EntropySingleDistribution(SingleDistributionUncertaintyMetric):
    """Implement EntropySingleDistribution. The formula applied to a distribution :math:`q_c(yj|x)` is:

    .. math::
        D^h(q_c(y_j|x)) = \mathcal{H}(q_c(y_j|x)) = \int_{0}^{1} - q_c(y_j=t|x) log(q_{c}(y_j=t|x)) dt

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

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

        :return: Transformation to apply to the distribution
        """
        @jit
        def transformation(distribution: np.array) -> float:
            # Discretize the distribution the division
            # by the sum is due to np.histogram implementation
            discretized_distribution = np.histogram(
                distribution, bins=nbins, range=(0, 1),
                density=True
            )[0]
            discretized_distribution /= discretized_distribution.sum()

            # Remove the 0 of the log
            log_discretized = discretized_distribution[:]
            log_discretized[np.where(log_discretized == 0)] = 1
            log_discretized = np.log(log_discretized)

            return - np.sum(discretized_distribution * log_discretized) / nbins
        return transformation