monte_carlo_analysis.uncertainty_metrics package¶

Submodules¶

monte_carlo_analysis.uncertainty_metrics.BhattacharyaCoefficentDistributionSimilarity module¶

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

class monte_carlo_analysis.uncertainty_metrics.BhattacharyaCoefficentDistributionSimilarity.BhattacharyaCoefficentDistributionSimilarity(nbins: int = 100)[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.DistributionSimilarityUncertaintyMetric.DistributionSimilarityUncertaintyMetric

Implement BhattacharyaCoefficentDistributionSimilarity class. The formula applied to a pair of distributions \(q_{c'}(y_j|x)\) and \(q_{c}(y_j|x)\) is:

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

Parameters

nbins – The discretization step of the integral

get_transformation(nbins: int) → callable[source]¶

Define the transformation applied to a pair of distributions

Parameters

nbins – The discretization step of the integral

Returns

transformation to apply to a pair of distributions

monte_carlo_analysis.uncertainty_metrics.DistributionSimilarityUncertaintyMetric module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-10-01

Project : monte_carlo_analysis

Implement abstract class DistributionSimilarityUncertaintyMetric

class monte_carlo_analysis.uncertainty_metrics.DistributionSimilarityUncertaintyMetric.DistributionSimilarityUncertaintyMetric[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.UncertaintyMetric.UncertaintyMetric

The following classes inherits from this class:

• monte_carlo_analysis.uncertainty_metrics.BhattacharyaCoefficentDistributionSimilarity

• monte_carlo_analysis.uncertainty_metrics.KullbackLeiblerDivergenceDistributionSimilarity

• monte_carlo_analysis.uncertainty_metrics.EarthMoverDistanceDistributionSimilarity

get_transformation() → callable[source]¶

Define the transformation applied to a pair of distribution

Returns

Transformation to apply to the distribution

monte_carlo_analysis.uncertainty_metrics.EarthMoverDistanceDistributionSimilarity module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-10-13

Project : monte_carlo_analysis

Implement class EarthMoverDistanceDistributionSimilarity

class monte_carlo_analysis.uncertainty_metrics.EarthMoverDistanceDistributionSimilarity.EarthMoverDistanceDistributionSimilarity(nbins=100)[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.DistributionSimilarityUncertaintyMetric.DistributionSimilarityUncertaintyMetric

Implement EarthMoverDistanceDistributionSimilarity. The formula applied to the pair of distributions \(q_{c'}(y_j|x)\) and \(q_{c'}(y_j|x)\) is:

\[S^E(q_{c'}(y_j|x), q_{c''}(y_j|x)) = \mathcal{L}_1(\int_0^t q_{c'}(y_j = t | x),\int_0^t q_{c''}(y_j = t|x))\]

Parameters

nbins – The discretization step of the integral of the \(\mathcal{L}_1\) norm

get_transformation(nbins: int) → callable[source]¶

Define the transformation applied to a pair of distributions

Parameters

nbins – The discretization step of the integral

Returns

transformation to apply to a pair of distributions

monte_carlo_analysis.uncertainty_metrics.EntropyMultipleDistributions module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-10-14

Project : monte_carlo_analysis

Implement class EntropyMultipleDistributions

class monte_carlo_analysis.uncertainty_metrics.EntropyMultipleDistributions.EntropyMultipleDistributions[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.MultipleDistributionsUncertaintyMetric.MultipleDistributionsUncertaintyMetric

Implement EntropyMultipleDistributions. The formula applied to the family of distributions \((q_{c'}(y_j|x))_{1 \leq c \leq C}\) is:

\[M^h((q_c(y_{j}|x))_{1 \leq c \leq C}) =- \sum_{c=1}^C \mathbb{E}(q_c(y_j |x)) log(\mathbb{E}(q_c(y_j |x)))\]

get_transformation() → callable[source]¶

Define the variance transformation applied to a family of distribution

Returns

Transformation to apply a family of distribution

monte_carlo_analysis.uncertainty_metrics.EntropySingleDistribution module¶

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

class monte_carlo_analysis.uncertainty_metrics.EntropySingleDistribution.EntropySingleDistribution(nbins: int = 100)[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.SingleDistributionUncertaintyMetric.SingleDistributionUncertaintyMetric

Implement EntropySingleDistribution. The formula applied to a distribution \(q_c(yj|x)\) is:

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

Parameters

nbins – The discretization step of the integral

get_transformation(nbins: int) → callable[source]¶

Define the transformation applied to the distribution

Returns

Transformation to apply to the distribution

monte_carlo_analysis.uncertainty_metrics.KullbackLeiblerDivergenceDistributionSimilarity module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-10-13

Project : monte_carlo_analysis

Implement class KullbackLeiblerDivergenceDistributionSimilarity

class monte_carlo_analysis.uncertainty_metrics.KullbackLeiblerDivergenceDistributionSimilarity.KullbackLeiblerDivergenceDistributionSimilarity(nbins: int = 100, epsilon: float = 1e-07)[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.DistributionSimilarityUncertaintyMetric.DistributionSimilarityUncertaintyMetric

Implement KullbackLeiblerDivergenceDistributionSimilarity class. The formula applied to a pair of distributions \(q_{c'}(y_j|x)\) and \(q_{c}(y_j|x)\) is:

\[S^{k}(q_{c'}(y_j|x), q_{c''}(y_j|x)) = - D_{KL}(q_{c'}(y_j|x)||q_{c''}(y_j|x)) - D_{KL}(q_{c''}(y_j|x)||q_{c'}(y_j|x))\]

Parameters

• nbins – Number of bins of the histogram

• epsilon – Number to avoid the division by zero

get_transformation(nbins: int, epsilon) → callable[source]¶

Define the transformation applied to a pair of distributions

Parameters

nbins – The discretization step of the integral

Returns

transformation to apply to a pair of distributions

monte_carlo_analysis.uncertainty_metrics.MultipleDistributionsUncertaintyMetric module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-10-14

Project : monte_carlo_analysis

Implement abstract class MultipleDistributionsUncertaintyMetric

class monte_carlo_analysis.uncertainty_metrics.MultipleDistributionsUncertaintyMetric.MultipleDistributionsUncertaintyMetric[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.UncertaintyMetric.UncertaintyMetric

The following classes inherits from this class:

• monte_carlo_analysis.uncertainty_metrics.EntropyMultipleDistributions

• monte_carlo_analysis.uncertainty_metrics.MutualInformationMultipleDistribution

get_transformation() → callable[source]¶

Define the transformation applied to the distribution

Returns

Transformation to apply to the distribution

monte_carlo_analysis.uncertainty_metrics.MutualInformationMultipleDistribution module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-10-14

Project : monte_carlo_analysis

Implement class MutualInformationMultipleDistributions

class monte_carlo_analysis.uncertainty_metrics.MutualInformationMultipleDistribution.MutualInformationMultipleDistributions[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.MultipleDistributionsUncertaintyMetric.MultipleDistributionsUncertaintyMetric

Implement MutualInformationMultipleDistributions. The formula applied to the family of distributions \((q_{c'}(y_j|x))_{1 \leq c \leq C}\) is:

\[M^m((q_c(y_{j}|x))_{1 \leq c \leq C}) = -\sum_{c=1}^C \mathbb{E}(q_c(y_j |x)) log(\mathbb{E}(q_c(y_j |x)) + T^{-1} \sum_{t=1}^T \sum_{c=1}^C p_c(y_j | x, w=w_t) log(p_c(y_j | x, w=w_t))\]

get_transformation() → callable[source]¶

Define the variance transformation applied to the family of distributions

Returns

Transformation to apply to the family of distributions

monte_carlo_analysis.uncertainty_metrics.SingleDistributionUncertaintyMetric module¶

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 SingleDistributionUncertaintyMetric

class monte_carlo_analysis.uncertainty_metrics.SingleDistributionUncertaintyMetric.SingleDistributionUncertaintyMetric[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.UncertaintyMetric.UncertaintyMetric

get_transformation() → callable[source]¶

Define the transformation applied to the distribution

Returns

Transformation to apply to the distribution

monte_carlo_analysis.uncertainty_metrics.UncertaintyMetric module¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-09-29

Project : monte_carlo_analysis

Implement abstract class UncertaintyMetric

class monte_carlo_analysis.uncertainty_metrics.UncertaintyMetric.UncertaintyMetric[source]¶

Bases: object

Abstract class that implement the UncertaintyMetric. The following class inherit from this class:

• monte_carlo_analysis.uncertainty_metrics.DistributionSimilarityUncertaintyMetric

• monte_carlo_analysis.uncertainty_metrics.MultipleDistributionsUncertaintyMetric

• monte_carlo_analysis.uncertainty_metrics.SingleDistributionUncertaintyMetric

monte_carlo_analysis.uncertainty_metrics.VarianceSingleDistribution module¶

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 VarianceSingleDistribution

class monte_carlo_analysis.uncertainty_metrics.VarianceSingleDistribution.VarianceSingleDistribution[source]¶

Bases: monte_carlo_analysis.uncertainty_metrics.SingleDistributionUncertaintyMetric.SingleDistributionUncertaintyMetric

get_transformation() → callable[source]¶

Define the variance transformation applied to the distribution

Returns

Transformation to apply varianceto the distribution

Module contents¶

Author : Robin Camarasa

Institution : Erasmus Medical Center

Position : PhD student

Contact : r.camarasa@erasmusmc.nl

Date : 2020-09-29

Project : monte_carlo_analysis

Module that contains the uncertainty metrics