ethically.fairness.interventions.threshold.find_thresholds() - Code Metrics - Inspection of "Merge pull request #18 from EthicallyAI/dev" - ResponsiblyAI/responsibly - Measure and Improve Code Quality continuously with Scrutinizer

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by Shlomi

created 2019-04-10 20:28 UTC

find_thresholds() B

↳ Parent: ethically.fairness.interventions.threshold

Complexity

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Total Lines	68
Code Lines	30

Duplication

Lines	0
Ratio	0 %

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Metric	Value
cc	6
eloc	30
nop	10
dl	0
loc	68
rs	8.2266
c	0
b	0
f	0

How to fix Long Method Many Parameters

"""
Post-processing fairness intervension by choosing thresholds.

There are multiple definitions for choosing the thresholds:

1. Single threshold for all the sensitive attribute values
   that minimizes cost.
2. A threshold for each sensitive attribute value
   that minimize cost.
3. A threshold for each sensitive attribute value
   that achieve independence and minimize cost.
4. A threshold for each sensitive attribute value
   that achieve equal FNR (equal opportunity) and minimize cost.
5. A threshold for each sensitive attribute value
   that achieve seperation (equalized odds) and minimize cost.

The code is based on `fairmlbook repository <https://github.com/fairmlbook/fairmlbook.github.io>`_.

References:
    - Hardt, M., Price, E., & Srebro, N. (2016).
      `Equality of opportunity in supervised learning
      <https://arxiv.org/abs/1610.02413>`_
      In Advances in neural information processing systems
      (pp. 3315-3323).
    - `Attacking discrimination with
      smarter machine learning by Google
      <https://research.google.com/bigpicture/attacking-discrimination-in-ml/>`_.

"""

# pylint: disable=no-name-in-module

import matplotlib.pylab as plt
import numpy as np
import pandas as pd
from scipy.spatial import Delaunay

from ethically.fairness.metrics.visualization import plot_roc_curves


def _ternary_search_float(f, left, right, tol):
    """Trinary search: minimize f(x) over [left, right], to within +/-tol in x.

    Works assuming f is quasiconvex.

    """
    while right - left > tol:
        left_third = (2 * left + right) / 3
        right_third = (left + 2 * right) / 3
        if f(left_third) < f(right_third):
            right = right_third
        else:
            left = left_third
    return (right + left) / 2


def _ternary_search_domain(f, domain):
    """Trinary search: minimize f(x) over a domain (sequence).

    Works assuming f is quasiconvex and domain is ascending sorted.

    """
    left = 0
    right = len(domain) - 1
    changed = True

    while changed and left != right:

        changed = False

        left_third = (2 * left + right) // 3
        right_third = (left + 2 * right) // 3

        if f(domain[left_third]) < f(domain[right_third]):
            right = right_third - 1
            changed = True
        else:
            left = left_third + 1
            changed = True

    return domain[(left + right) // 2]


def _cost_function(fpr, tpr, base_rate, cost_matrix):
    """Compute the cost of given (fpr, tpr).

    [[tn, fp], [fn, tp]]
    """

    fp = fpr * (1 - base_rate)
    tn = (1 - base_rate) - fp
    tp = tpr * base_rate
    fn = base_rate - tp

    conf_matrix = np.array([tn, fp, fn, tp])

    return (conf_matrix * np.array(cost_matrix).ravel()).sum()


def _extract_threshold(roc_curves):
    return next(iter(roc_curves.values()))[2]


def _first_index_above(array, value):
    """Find the smallest index i for which array[i] > value.

    If no such value exists, return len(array).
    """
    array = np.array(array)
    v = np.concatenate([array > value, np.ones_like(array[-1:])])
    return np.argmax(v, axis=0)


def _calc_acceptance_rate(fpr, tpr, base_rate):
    return 1 - ((fpr * (1 - base_rate)
                 + tpr * base_rate))


def find_single_threshold(roc_curves, base_rates, proportions,
                          cost_matrix):
    """Compute single threshold that minimizes cost.

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param base_rates: Base rate by attribute.
    :type base_rates: dict
    :param proportions: Proportion of each attribute value.
    :type proportions: dict
    :param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
    :type cost_matrix: sequence
    :return: Threshold, FPR and TPR by attribute and cost value.
    :rtype: tuple

    """

    def total_cost_function(index):
        total_cost = 0

        for group, roc in roc_curves.items():
            fpr = roc[0][index]
            tpr = roc[1][index]

            group_cost = _cost_function(fpr, tpr,
                                        base_rates[group], cost_matrix)
            group_cost *= proportions[group]

            total_cost += group_cost

        return -total_cost

    thresholds = _extract_threshold(roc_curves)

    cutoff_index = _ternary_search_domain(total_cost_function,
                                          range(len(thresholds)))

    fpr_tpr = {group: (roc[0][cutoff_index], roc[1][cutoff_index])
               for group, roc in roc_curves.items()}

    cost = total_cost_function(cutoff_index)

    return thresholds[cutoff_index], fpr_tpr, cost


def find_min_cost_thresholds(roc_curves, base_rates, cost_matrix):
    """Compute thresholds by attribute values that minimize cost.

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param base_rates: Base rate by attribute.
    :type base_rates: dict
    :param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
    :type cost_matrix: sequence
    :return: Thresholds, FPR and TPR by attribute and cost value.
    :rtype: tuple

    """
    # pylint: disable=cell-var-from-loop

    cutoffs = {}
    fpr_tpr = {}

    cost = 0
    thresholds = _extract_threshold(roc_curves)

    for group, roc in roc_curves.items():
        def group_cost_function(index):
            fpr = roc[0][index]
            tpr = roc[1][index]
            return -_cost_function(fpr, tpr,
                                   base_rates[group], cost_matrix)

        threshold_index = _ternary_search_domain(group_cost_function,
                                                 range(len(thresholds)))

        cutoffs[group] = thresholds[threshold_index]

        fpr_tpr[group] = (roc[0][threshold_index],
                          roc[1][threshold_index])

        cost += group_cost_function(threshold_index)

    return cutoffs, fpr_tpr, cost


def get_acceptance_rate_indices(roc_curves, base_rates,
                                acceptance_rate_value):
    indices = {}
    for group, roc in roc_curves.items():
        # can be calculated outside the function
        acceptance_rates = _calc_acceptance_rate(fpr=roc[0],
                                                 tpr=roc[1],
                                                 base_rate=base_rates[group])

        index = _first_index_above(acceptance_rates,
                                   (1 - acceptance_rate_value)) - 2

        indices[group] = index

    return indices


def find_independence_thresholds(roc_curves, base_rates, proportions,
                                 cost_matrix):
    """Compute thresholds that achieve independence and minimize cost.

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param base_rates: Base rate by attribute.
    :type base_rates: dict
    :param proportions: Proportion of each attribute value.
    :type proportions: dict
    :param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
    :type cost_matrix: sequence
    :return: Thresholds, FPR and TPR by attribute and cost value.
    :rtype: tuple

    """

    cutoffs = {}

    def total_cost_function(acceptance_rate_value):
        # todo: move demo here + multiple cost
        indices = get_acceptance_rate_indices(roc_curves, base_rates,
                                              acceptance_rate_value)

        total_cost = 0

        for group, roc in roc_curves.items():
            index = indices[group]

            fpr = roc[0][index]
            tpr = roc[1][index]

            group_cost = _cost_function(fpr, tpr,
                                        base_rates[group],
                                        cost_matrix)
            group_cost *= proportions[group]

            total_cost += group_cost

        return -total_cost

    acceptance_rate_min_cost = _ternary_search_float(total_cost_function,
                                                     0, 1, 1e-3)
    threshold_indices = get_acceptance_rate_indices(roc_curves, base_rates,
                                                    acceptance_rate_min_cost)

    thresholds = _extract_threshold(roc_curves)

    cutoffs = {group: thresholds[threshold_index]
               for group, threshold_index
               in threshold_indices.items()}

    fpr_tpr = {group: (roc[0][threshold_indices[group]],
                       roc[1][threshold_indices[group]])
               for group, roc in roc_curves.items()}

    return cutoffs, fpr_tpr, acceptance_rate_min_cost


def get_fnr_indices(roc_curves, fnr_value):
    indices = {}
    for group, roc in roc_curves.items():
        tprs = roc[1]
        index = _first_index_above(1 - tprs,
                                   (1 - fnr_value)) - 1

        indices[group] = index

    return indices


def find_fnr_thresholds(roc_curves, base_rates, proportions,

                        cost_matrix):
    """Compute thresholds that achieve equal FNRs and minimize cost.

    Also known as **equal opportunity**.

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param base_rates: Base rate by attribute.
    :type base_rates: dict
    :param proportions: Proportion of each attribute value.
    :type proportions: dict
    :param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
    :type cost_matrix: sequence
    :return: Thresholds, FPR and TPR by attribute and cost value.
    :rtype: tuple

    """

    cutoffs = {}

    def total_cost_function(fnr_value):
        # todo: move demo here + multiple cost
        indices = get_fnr_indices(roc_curves, fnr_value)

        total_cost = 0

        for group, roc in roc_curves.items():
            index = indices[group]

            fpr = roc[0][index]
            tpr = roc[1][index]

            group_cost = _cost_function(fpr, tpr,
                                        base_rates[group],
                                        cost_matrix)
            group_cost *= proportions[group]

            total_cost += group_cost

        return -total_cost

    fnr_value_min_cost = _ternary_search_float(total_cost_function,
                                               0, 1, 1e-3)
    threshold_indices = get_fnr_indices(roc_curves, fnr_value_min_cost)

    cost = total_cost_function(fnr_value_min_cost)

    fpr_tpr = {group: (roc[0][threshold_indices[group]],
                       roc[1][threshold_indices[group]])
               for group, roc in roc_curves.items()}

    thresholds = _extract_threshold(roc_curves)
    cutoffs = {group: thresholds[threshold_index]
               for group, threshold_index
               in threshold_indices.items()}

    return cutoffs, fpr_tpr, cost, fnr_value_min_cost


def _find_feasible_roc(roc_curves):
    polygons = [Delaunay(list(zip(fprs, tprs)))
                for group, (fprs, tprs, _) in roc_curves.items()]

    feasible_points = []

    for poly in polygons:
        for p in poly.points:

            if all(poly2.find_simplex(p) != -1 for poly2 in polygons):
                feasible_points.append(p)

    return np.array(feasible_points)


def find_separation_thresholds(roc_curves, base_rate, cost_matrix):
    """Compute thresholds that achieve separation and minimize cost.

    Also known as **equalized odds**.

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param base_rate: Overall base rate.
    :type base_rate: float
    :param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
    :type cost_matrix: sequence
    :return: Thresholds, FPR and TPR by attribute and cost value.
    :rtype: tuple

    """

    feasible_points = _find_feasible_roc(roc_curves)

    cost, (best_fpr, best_tpr) = max((_cost_function(fpr, tpr, base_rate,
                                                     cost_matrix),
                                      (fpr, tpr))
                                     for fpr, tpr in feasible_points)

    return {}, {'': (best_fpr, best_tpr)}, cost


def find_thresholds(roc_curves, proportions, base_rate,
                    base_rates, cost_matrix,
                    with_single=True, with_min_cost=True,
                    with_independence=True, with_fnr=True,
                    with_separation=True):
    """Compute thresholds that achieve various criteria and minimize cost.

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param proportions: Proportion of each attribute value.
    :type proportions: dict
    :param base_rate: Overall base rate.
    :type base_rate: float
    :param base_rates: Base rate by attribute.
    :type base_rates: dict
    :param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
    :type cost_matrix: sequence

    :param with_single: Compute single threshold.
    :type with_single: bool
    :param with_min_cost: Compute minimum cost thresholds.
    :type with_min_cost: bool
    :param with_independence: Compute independence thresholds.
    :type with_independence: bool
    :param with_fnr: Compute FNR thresholds.
    :type with_fnr: bool
    :param with_separation: Compute separation thresholds.
    :type with_separation: bool

    :return: Dictionary of threshold criteria,
             and for each criterion:
             thresholds, FPR and TPR by attribute and cost value.
    :rtype: dict

    """

    thresholds = {}

    if with_single:
        thresholds['single'] = find_single_threshold(roc_curves,
                                                     base_rates,
                                                     proportions,
                                                     cost_matrix)

    if with_min_cost:
        thresholds['min_cost'] = find_min_cost_thresholds(roc_curves,
                                                          base_rates,
                                                          cost_matrix)

    if with_independence:
        thresholds['independence'] = find_independence_thresholds(roc_curves,
                                                                  base_rates,
                                                                  proportions,
                                                                  cost_matrix)

    if with_fnr:
        thresholds['fnr'] = find_fnr_thresholds(roc_curves,
                                                base_rates,
                                                proportions,
                                                cost_matrix)

    if with_separation:
        thresholds['separation'] = find_separation_thresholds(roc_curves,
                                                              base_rate,
                                                              cost_matrix)

    return thresholds


def plot_roc_curves_thresholds(roc_curves, thresholds_data,
                               aucs=None,
                               title='ROC Curves by Attribute',
                               ax=None, figsize=None,
                               title_fontsize='large',
                               text_fontsize='medium'):
    """Generate the ROC curves by attribute with thresholds.

    Based on :func:`skplt.metrics.plot_roc`

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param thresholds_data: Thresholds by attribute from the
                            function
                            :func:`~ethically.interventions
                            .threshold.find_thresholds`.
    :type thresholds_data: dict
    :param aucs: Area Under the ROC (AUC) by attribute.
    :type aucs: dict
    :param str title: Title of the generated plot.
    :param ax: The axes upon which to plot the curve.
               If `None`, the plot is drawn on a new set of axes.
    :param tuple figsize: Tuple denoting figure size of the plot
                          e.g. (6, 6).
    :param title_fontsize: Matplotlib-style fontsizes.
                          Use e.g. 'small', 'medium', 'large'
                          or integer-values.
    :param text_fontsize: Matplotlib-style fontsizes.
                          Use e.g. 'small', 'medium', 'large'
                          or integer-values.
    :return: The axes on which the plot was drawn.
    :rtype: :class:`matplotlib.axes.Axes`

    """

    ax = plot_roc_curves(roc_curves, aucs,
                         title, ax, figsize, title_fontsize, text_fontsize)

    MARKERS = ['o', '^', 'x', '+', 'p']

    for (name, data), marker in zip(thresholds_data.items(), MARKERS):
        label = name.replace('_', ' ').title()
        ax.scatter(*zip(*data[1].values()),
                   marker=marker, color='k', label=label,
                   zorder=float('inf'))

    plt.legend()

    return ax


def plot_fpt_tpr(roc_curves,
                 title='FPR-TPR Curves by Attribute',
                 ax=None, figsize=None,
                 title_fontsize='large', text_fontsize='medium'):
    """Generate FPR and TPR curves by thresholds and by attribute.

    Based on :func:`skplt.metrics.plot_roc`

    :param roc_curves: Receiver operating characteristic (ROC)
                       by attribute.
    :type roc_curves: dict
    :param str title: Title of the generated plot.
    :param ax: The axes upon which to plot the curve.
               If `None`, the plot is drawn on a new set of axes.
    :param tuple figsize: Tuple denoting figure size of the plot
                          e.g. (6, 6).
    :param title_fontsize: Matplotlib-style fontsizes.
                          Use e.g. 'small', 'medium', 'large'
                          or integer-values.
    :param text_fontsize: Matplotlib-style fontsizes.
                          Use e.g. 'small', 'medium', 'large'
                          or integer-values.
    :return: The axes on which the plot was drawn.
    :rtype: :class:`matplotlib.axes.Axes`

    """

    if ax is None:
        fig, ax = plt.subplots(1, 1, figsize=figsize)  # pylint: disable=unused-variable

    ax.set_title(title, fontsize=title_fontsize)

    thresholds = _extract_threshold(roc_curves)

    prop_cycle = plt.rcParams['axes.prop_cycle']
    colors = prop_cycle.by_key()['color']

    for (group, roc), color in zip(roc_curves.items(), colors):
        plt.plot(thresholds, roc[0], '-',
                 label='{} - FPR'.format(group), color=color)
        plt.plot(thresholds, roc[1], '--',
                 label='{} - TPR'.format(group), color=color)
        plt.legend()

    ax.set_ylim([0.0, 1.05])
    ax.set_xlabel('Threshold', fontsize=text_fontsize)
    ax.set_ylabel('Probability', fontsize=text_fontsize)
    ax.tick_params(labelsize=text_fontsize)
    ax.legend(fontsize=text_fontsize)

    return ax


def plot_costs(thresholds_data,
               title='Cost by Threshold',
               ax=None, figsize=None,
               title_fontsize='large', text_fontsize='medium'):
    """Plot cost by threshold definition and by attribute.

    Based on :func:`skplt.metrics.plot_roc`

    :param thresholds_data: Thresholds by attribute from the
                            function
                            :func:`~ethically.interventions
                            .threshold.find_thresholds`.
    :type thresholds_data: dict
    :param str title: Title of the generated plot.
    :param ax: The axes upon which to plot the curve.
               If `None`, the plot is drawn on a new set of axes.
    :param tuple figsize: Tuple denoting figure size of the plot
                          e.g. (6, 6).
    :param title_fontsize: Matplotlib-style fontsizes.
                          Use e.g. 'small', 'medium', 'large'
                          or integer-values.
    :param text_fontsize: Matplotlib-style fontsizes.
                          Use e.g. 'small', 'medium', 'large'
                          or integer-values.
    :return: The axes on which the plot was drawn.
    :rtype: :class:`matplotlib.axes.Axes`

    """

    if ax is None:
        fig, ax = plt.subplots(1, 1, figsize=figsize)  # pylint: disable=unused-variable

    ax.set_title(title, fontsize=title_fontsize)

    costs = {group.replace('_', ' ').title(): cost
             for group, (_, _, cost, *_) in thresholds_data.items()}

    (pd.Series(costs)
     .sort_values(ascending=False)
     .plot(kind='barh', ax=ax))

    ax.set_xlabel('Cost', fontsize=text_fontsize)
    ax.set_ylabel('Threshold', fontsize=text_fontsize)
    ax.tick_params(labelsize=text_fontsize)

    return ax


1		"""
2		Post-processing fairness intervension by choosing thresholds.
3
4		There are multiple definitions for choosing the thresholds:
5
6		1. Single threshold for all the sensitive attribute values
7		that minimizes cost.
8		2. A threshold for each sensitive attribute value
9		that minimize cost.
10		3. A threshold for each sensitive attribute value
11		that achieve independence and minimize cost.
12		4. A threshold for each sensitive attribute value
13		that achieve equal FNR (equal opportunity) and minimize cost.
14		5. A threshold for each sensitive attribute value
15		that achieve seperation (equalized odds) and minimize cost.
16
17		The code is based on `fairmlbook repository <https://github.com/fairmlbook/fairmlbook.github.io>`_.
18
19		References:
20		- Hardt, M., Price, E., & Srebro, N. (2016).
21		`Equality of opportunity in supervised learning
22		<https://arxiv.org/abs/1610.02413>`_
23		In Advances in neural information processing systems
24		(pp. 3315-3323).
25		- `Attacking discrimination with
26		smarter machine learning by Google
27		<https://research.google.com/bigpicture/attacking-discrimination-in-ml/>`_.
28
29		"""
30
31		# pylint: disable=no-name-in-module
32
33		import matplotlib.pylab as plt
34		import numpy as np
35		import pandas as pd
36		from scipy.spatial import Delaunay
37
38		from ethically.fairness.metrics.visualization import plot_roc_curves
39
40
41		def _ternary_search_float(f, left, right, tol):
42		"""Trinary search: minimize f(x) over [left, right], to within +/-tol in x.
43
44		Works assuming f is quasiconvex.
45
46		"""
47		while right - left > tol:
48		left_third = (2 * left + right) / 3
49		right_third = (left + 2 * right) / 3
50		if f(left_third) < f(right_third):
51		right = right_third
52		else:
53		left = left_third
54		return (right + left) / 2
55
56
57		def _ternary_search_domain(f, domain):
58		"""Trinary search: minimize f(x) over a domain (sequence).
59
60		Works assuming f is quasiconvex and domain is ascending sorted.
61
62		"""
63		left = 0
64		right = len(domain) - 1
65		changed = True
66
67		while changed and left != right:
68
69		changed = False
70
71		left_third = (2 * left + right) // 3
72		right_third = (left + 2 * right) // 3
73
74		if f(domain[left_third]) < f(domain[right_third]):
75		right = right_third - 1
76		changed = True
77		else:
78		left = left_third + 1
79		changed = True
80
81		return domain[(left + right) // 2]
82
83
84		def _cost_function(fpr, tpr, base_rate, cost_matrix):
85		"""Compute the cost of given (fpr, tpr).
86
87		[[tn, fp], [fn, tp]]
88		"""
89
90		fp = fpr * (1 - base_rate)
91		tn = (1 - base_rate) - fp
92		tp = tpr * base_rate
93		fn = base_rate - tp
94
95		conf_matrix = np.array([tn, fp, fn, tp])
96
97		return (conf_matrix * np.array(cost_matrix).ravel()).sum()
98
99
100		def _extract_threshold(roc_curves):
101		return next(iter(roc_curves.values()))[2]
102
103
104		def _first_index_above(array, value):
105		"""Find the smallest index i for which array[i] > value.
106
107		If no such value exists, return len(array).
108		"""
109		array = np.array(array)
110		v = np.concatenate([array > value, np.ones_like(array[-1:])])
111		return np.argmax(v, axis=0)
112
113
114		def _calc_acceptance_rate(fpr, tpr, base_rate):
115		return 1 - ((fpr * (1 - base_rate)
116		+ tpr * base_rate))
117
118
119		def find_single_threshold(roc_curves, base_rates, proportions,
120		cost_matrix):
121		"""Compute single threshold that minimizes cost.
122
123		:param roc_curves: Receiver operating characteristic (ROC)
124		by attribute.
125		:type roc_curves: dict
126		:param base_rates: Base rate by attribute.
127		:type base_rates: dict
128		:param proportions: Proportion of each attribute value.
129		:type proportions: dict
130		:param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
131		:type cost_matrix: sequence
132		:return: Threshold, FPR and TPR by attribute and cost value.
133		:rtype: tuple
134
135		"""
136
137		def total_cost_function(index):
138		total_cost = 0
139
140		for group, roc in roc_curves.items():
141		fpr = roc[0][index]
142		tpr = roc[1][index]
143
144		group_cost = _cost_function(fpr, tpr,
145		base_rates[group], cost_matrix)
146		group_cost *= proportions[group]
147
148		total_cost += group_cost
149
150		return -total_cost
151
152		thresholds = _extract_threshold(roc_curves)
153
154		cutoff_index = _ternary_search_domain(total_cost_function,
155		range(len(thresholds)))
156
157		fpr_tpr = {group: (roc[0][cutoff_index], roc[1][cutoff_index])
158		for group, roc in roc_curves.items()}
159
160		cost = total_cost_function(cutoff_index)
161
162		return thresholds[cutoff_index], fpr_tpr, cost
163
164
165		def find_min_cost_thresholds(roc_curves, base_rates, cost_matrix):
166		"""Compute thresholds by attribute values that minimize cost.
167
168		:param roc_curves: Receiver operating characteristic (ROC)
169		by attribute.
170		:type roc_curves: dict
171		:param base_rates: Base rate by attribute.
172		:type base_rates: dict
173		:param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
174		:type cost_matrix: sequence
175		:return: Thresholds, FPR and TPR by attribute and cost value.
176		:rtype: tuple
177
178		"""
179		# pylint: disable=cell-var-from-loop
180
181		cutoffs = {}
182		fpr_tpr = {}
183
184		cost = 0
185		thresholds = _extract_threshold(roc_curves)
186
187		for group, roc in roc_curves.items():
188		def group_cost_function(index):
189		fpr = roc[0][index]
190		tpr = roc[1][index]
191		return -_cost_function(fpr, tpr,
192		base_rates[group], cost_matrix)
193
194		threshold_index = _ternary_search_domain(group_cost_function,
195		range(len(thresholds)))
196
197		cutoffs[group] = thresholds[threshold_index]
198
199		fpr_tpr[group] = (roc[0][threshold_index],
200		roc[1][threshold_index])
201
202		cost += group_cost_function(threshold_index)
203
204		return cutoffs, fpr_tpr, cost
205
206
207		def get_acceptance_rate_indices(roc_curves, base_rates,
208		acceptance_rate_value):
209		indices = {}
210		for group, roc in roc_curves.items():
211		# can be calculated outside the function
212		acceptance_rates = _calc_acceptance_rate(fpr=roc[0],
213		tpr=roc[1],
214		base_rate=base_rates[group])
215
216		index = _first_index_above(acceptance_rates,
217		(1 - acceptance_rate_value)) - 2
218
219		indices[group] = index
220
221		return indices
222
223
224	View Code Duplication	def find_independence_thresholds(roc_curves, base_rates, proportions,
225		cost_matrix):
226		"""Compute thresholds that achieve independence and minimize cost.
227
228		:param roc_curves: Receiver operating characteristic (ROC)
229		by attribute.
230		:type roc_curves: dict
231		:param base_rates: Base rate by attribute.
232		:type base_rates: dict
233		:param proportions: Proportion of each attribute value.
234		:type proportions: dict
235		:param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
236		:type cost_matrix: sequence
237		:return: Thresholds, FPR and TPR by attribute and cost value.
238		:rtype: tuple
239
240		"""
241
242		cutoffs = {}
243
244		def total_cost_function(acceptance_rate_value):
245		# todo: move demo here + multiple cost
246		indices = get_acceptance_rate_indices(roc_curves, base_rates,
247		acceptance_rate_value)
248
249		total_cost = 0
250
251		for group, roc in roc_curves.items():
252		index = indices[group]
253
254		fpr = roc[0][index]
255		tpr = roc[1][index]
256
257		group_cost = _cost_function(fpr, tpr,
258		base_rates[group],
259		cost_matrix)
260		group_cost *= proportions[group]
261
262		total_cost += group_cost
263
264		return -total_cost
265
266		acceptance_rate_min_cost = _ternary_search_float(total_cost_function,
267		0, 1, 1e-3)
268		threshold_indices = get_acceptance_rate_indices(roc_curves, base_rates,
269		acceptance_rate_min_cost)
270
271		thresholds = _extract_threshold(roc_curves)
272
273		cutoffs = {group: thresholds[threshold_index]
274		for group, threshold_index
275		in threshold_indices.items()}
276
277		fpr_tpr = {group: (roc[0][threshold_indices[group]],
278		roc[1][threshold_indices[group]])
279		for group, roc in roc_curves.items()}
280
281		return cutoffs, fpr_tpr, acceptance_rate_min_cost
282
283
284		def get_fnr_indices(roc_curves, fnr_value):
285		indices = {}
286		for group, roc in roc_curves.items():
287		tprs = roc[1]
288		index = _first_index_above(1 - tprs,
289		(1 - fnr_value)) - 1
290
291		indices[group] = index
292
293		return indices
294
295
296	View Code Duplication	def find_fnr_thresholds(roc_curves, base_rates, proportions,
		0 ignored issues – show Duplication introduced 2019-04-08 15:51 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
297		cost_matrix):
298		"""Compute thresholds that achieve equal FNRs and minimize cost.
299
300		Also known as equal opportunity.
301
302		:param roc_curves: Receiver operating characteristic (ROC)
303		by attribute.
304		:type roc_curves: dict
305		:param base_rates: Base rate by attribute.
306		:type base_rates: dict
307		:param proportions: Proportion of each attribute value.
308		:type proportions: dict
309		:param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
310		:type cost_matrix: sequence
311		:return: Thresholds, FPR and TPR by attribute and cost value.
312		:rtype: tuple
313
314		"""
315
316		cutoffs = {}
317
318		def total_cost_function(fnr_value):
319		# todo: move demo here + multiple cost
320		indices = get_fnr_indices(roc_curves, fnr_value)
321
322		total_cost = 0
323
324		for group, roc in roc_curves.items():
325		index = indices[group]
326
327		fpr = roc[0][index]
328		tpr = roc[1][index]
329
330		group_cost = _cost_function(fpr, tpr,
331		base_rates[group],
332		cost_matrix)
333		group_cost *= proportions[group]
334
335		total_cost += group_cost
336
337		return -total_cost
338
339		fnr_value_min_cost = _ternary_search_float(total_cost_function,
340		0, 1, 1e-3)
341		threshold_indices = get_fnr_indices(roc_curves, fnr_value_min_cost)
342
343		cost = total_cost_function(fnr_value_min_cost)
344
345		fpr_tpr = {group: (roc[0][threshold_indices[group]],
346		roc[1][threshold_indices[group]])
347		for group, roc in roc_curves.items()}
348
349		thresholds = _extract_threshold(roc_curves)
350		cutoffs = {group: thresholds[threshold_index]
351		for group, threshold_index
352		in threshold_indices.items()}
353
354		return cutoffs, fpr_tpr, cost, fnr_value_min_cost
355
356
357		def _find_feasible_roc(roc_curves):
358		polygons = [Delaunay(list(zip(fprs, tprs)))
359		for group, (fprs, tprs, _) in roc_curves.items()]
360
361		feasible_points = []
362
363		for poly in polygons:
364		for p in poly.points:
365
366		if all(poly2.find_simplex(p) != -1 for poly2 in polygons):
367		feasible_points.append(p)
368
369		return np.array(feasible_points)
370
371
372		def find_separation_thresholds(roc_curves, base_rate, cost_matrix):
373		"""Compute thresholds that achieve separation and minimize cost.
374
375		Also known as equalized odds.
376
377		:param roc_curves: Receiver operating characteristic (ROC)
378		by attribute.
379		:type roc_curves: dict
380		:param base_rate: Overall base rate.
381		:type base_rate: float
382		:param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
383		:type cost_matrix: sequence
384		:return: Thresholds, FPR and TPR by attribute and cost value.
385		:rtype: tuple
386
387		"""
388
389		feasible_points = _find_feasible_roc(roc_curves)
390
391		cost, (best_fpr, best_tpr) = max((_cost_function(fpr, tpr, base_rate,
392		cost_matrix),
393		(fpr, tpr))
394		for fpr, tpr in feasible_points)
395
396		return {}, {'': (best_fpr, best_tpr)}, cost
397
398
399		def find_thresholds(roc_curves, proportions, base_rate,
400		base_rates, cost_matrix,
401		with_single=True, with_min_cost=True,
402		with_independence=True, with_fnr=True,
403		with_separation=True):
404		"""Compute thresholds that achieve various criteria and minimize cost.
405
406		:param roc_curves: Receiver operating characteristic (ROC)
407		by attribute.
408		:type roc_curves: dict
409		:param proportions: Proportion of each attribute value.
410		:type proportions: dict
411		:param base_rate: Overall base rate.
412		:type base_rate: float
413		:param base_rates: Base rate by attribute.
414		:type base_rates: dict
415		:param cost_matrix: Cost matrix by [[tn, fp], [fn, tp]].
416		:type cost_matrix: sequence
417
418		:param with_single: Compute single threshold.
419		:type with_single: bool
420		:param with_min_cost: Compute minimum cost thresholds.
421		:type with_min_cost: bool
422		:param with_independence: Compute independence thresholds.
423		:type with_independence: bool
424		:param with_fnr: Compute FNR thresholds.
425		:type with_fnr: bool
426		:param with_separation: Compute separation thresholds.
427		:type with_separation: bool
428
429		:return: Dictionary of threshold criteria,
430		and for each criterion:
431		thresholds, FPR and TPR by attribute and cost value.
432		:rtype: dict
433
434		"""
435
436		thresholds = {}
437
438		if with_single:
439		thresholds['single'] = find_single_threshold(roc_curves,
440		base_rates,
441		proportions,
442		cost_matrix)
443
444		if with_min_cost:
445		thresholds['min_cost'] = find_min_cost_thresholds(roc_curves,
446		base_rates,
447		cost_matrix)
448
449		if with_independence:
450		thresholds['independence'] = find_independence_thresholds(roc_curves,
451		base_rates,
452		proportions,
453		cost_matrix)
454
455		if with_fnr:
456		thresholds['fnr'] = find_fnr_thresholds(roc_curves,
457		base_rates,
458		proportions,
459		cost_matrix)
460
461		if with_separation:
462		thresholds['separation'] = find_separation_thresholds(roc_curves,
463		base_rate,
464		cost_matrix)
465
466		return thresholds
467
468
469		def plot_roc_curves_thresholds(roc_curves, thresholds_data,
470		aucs=None,
471		title='ROC Curves by Attribute',
472		ax=None, figsize=None,
473		title_fontsize='large',
474		text_fontsize='medium'):
475		"""Generate the ROC curves by attribute with thresholds.
476
477		Based on :func:`skplt.metrics.plot_roc`
478
479		:param roc_curves: Receiver operating characteristic (ROC)
480		by attribute.
481		:type roc_curves: dict
482		:param thresholds_data: Thresholds by attribute from the
483		function
484		:func:`~ethically.interventions
485		.threshold.find_thresholds`.
486		:type thresholds_data: dict
487		:param aucs: Area Under the ROC (AUC) by attribute.
488		:type aucs: dict
489		:param str title: Title of the generated plot.
490		:param ax: The axes upon which to plot the curve.
491		If `None`, the plot is drawn on a new set of axes.
492		:param tuple figsize: Tuple denoting figure size of the plot
493		e.g. (6, 6).
494		:param title_fontsize: Matplotlib-style fontsizes.
495		Use e.g. 'small', 'medium', 'large'
496		or integer-values.
497		:param text_fontsize: Matplotlib-style fontsizes.
498		Use e.g. 'small', 'medium', 'large'
499		or integer-values.
500		:return: The axes on which the plot was drawn.
501		:rtype: :class:`matplotlib.axes.Axes`
502
503		"""
504
505		ax = plot_roc_curves(roc_curves, aucs,
506		title, ax, figsize, title_fontsize, text_fontsize)
507
508		MARKERS = ['o', '^', 'x', '+', 'p']
509
510		for (name, data), marker in zip(thresholds_data.items(), MARKERS):
511		label = name.replace('_', ' ').title()
512		ax.scatter(zip(data[1].values()),
513		marker=marker, color='k', label=label,
514		zorder=float('inf'))
515
516		plt.legend()
517
518		return ax
519
520
521		def plot_fpt_tpr(roc_curves,
522		title='FPR-TPR Curves by Attribute',
523		ax=None, figsize=None,
524		title_fontsize='large', text_fontsize='medium'):
525		"""Generate FPR and TPR curves by thresholds and by attribute.
526
527		Based on :func:`skplt.metrics.plot_roc`
528
529		:param roc_curves: Receiver operating characteristic (ROC)
530		by attribute.
531		:type roc_curves: dict
532		:param str title: Title of the generated plot.
533		:param ax: The axes upon which to plot the curve.
534		If `None`, the plot is drawn on a new set of axes.
535		:param tuple figsize: Tuple denoting figure size of the plot
536		e.g. (6, 6).
537		:param title_fontsize: Matplotlib-style fontsizes.
538		Use e.g. 'small', 'medium', 'large'
539		or integer-values.
540		:param text_fontsize: Matplotlib-style fontsizes.
541		Use e.g. 'small', 'medium', 'large'
542		or integer-values.
543		:return: The axes on which the plot was drawn.
544		:rtype: :class:`matplotlib.axes.Axes`
545
546		"""
547
548		if ax is None:
549		fig, ax = plt.subplots(1, 1, figsize=figsize) # pylint: disable=unused-variable
550
551		ax.set_title(title, fontsize=title_fontsize)
552
553		thresholds = _extract_threshold(roc_curves)
554
555		prop_cycle = plt.rcParams['axes.prop_cycle']
556		colors = prop_cycle.by_key()['color']
557
558		for (group, roc), color in zip(roc_curves.items(), colors):
559		plt.plot(thresholds, roc[0], '-',
560		label='{} - FPR'.format(group), color=color)
561		plt.plot(thresholds, roc[1], '--',
562		label='{} - TPR'.format(group), color=color)
563		plt.legend()
564
565		ax.set_ylim([0.0, 1.05])
566		ax.set_xlabel('Threshold', fontsize=text_fontsize)
567		ax.set_ylabel('Probability', fontsize=text_fontsize)
568		ax.tick_params(labelsize=text_fontsize)
569		ax.legend(fontsize=text_fontsize)
570
571		return ax
572
573
574		def plot_costs(thresholds_data,
575		title='Cost by Threshold',
576		ax=None, figsize=None,
577		title_fontsize='large', text_fontsize='medium'):
578		"""Plot cost by threshold definition and by attribute.
579
580		Based on :func:`skplt.metrics.plot_roc`
581
582		:param thresholds_data: Thresholds by attribute from the
583		function
584		:func:`~ethically.interventions
585		.threshold.find_thresholds`.
586		:type thresholds_data: dict
587		:param str title: Title of the generated plot.
588		:param ax: The axes upon which to plot the curve.
589		If `None`, the plot is drawn on a new set of axes.
590		:param tuple figsize: Tuple denoting figure size of the plot
591		e.g. (6, 6).
592		:param title_fontsize: Matplotlib-style fontsizes.
593		Use e.g. 'small', 'medium', 'large'
594		or integer-values.
595		:param text_fontsize: Matplotlib-style fontsizes.
596		Use e.g. 'small', 'medium', 'large'
597		or integer-values.
598		:return: The axes on which the plot was drawn.
599		:rtype: :class:`matplotlib.axes.Axes`
600
601		"""
602
603		if ax is None:
604		fig, ax = plt.subplots(1, 1, figsize=figsize) # pylint: disable=unused-variable
605
606		ax.set_title(title, fontsize=title_fontsize)
607
608		costs = {group.replace('_', ' ').title(): cost
609		for group, (_, _, cost, *_) in thresholds_data.items()}
610
611		(pd.Series(costs)
612		.sort_values(ascending=False)
613		.plot(kind='barh', ax=ax))
614
615		ax.set_xlabel('Cost', fontsize=text_fontsize)
616		ax.set_ylabel('Threshold', fontsize=text_fontsize)
617		ax.tick_params(labelsize=text_fontsize)
618
619		return ax
620

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