# Classification Fairness¶

Demographic fairness in binary classification.

The common and simples setting, but not the only one, of fairness of a binary classifier is the demographic one. It is assume that there is one sensitive attribute or more that represents one or more demographic groups (e.g., by gender, race or age), for which a classifier should be fair.

Important

The terminology and functionality is aligned with the book Fairness and Machine Learning - Limitations and Opportunities by Solon Barocas, Moritz Hardt and Arvind Narayanan. Therefore, it is advised to get familiar with Chapter 2, as it summarized the current core knowledge regarding fairness in classification.

Currently, the ethically.fairness module has two components:

1. Metrics (ethically.fairness.metrics) for measuring unfairness.

2. Algorithmic interventions (ethically.fairness.interventions) for satisfying fairness criteria.

The demos section contains two examples of measuring the fairness of a classifier and applying intervention to adjust it:

## Metrics¶

Demographic Classification Fairness Criteria.

The objectives of the demographic classification fairness criteria is to measure unfairness towards sensitive attribute valuse.

The metrics have the same interface and behavior as the ones in sklearn.metrics (e.g., using y_true, y_pred and y_score).

One should keep in mind that the criteria are intended to measure unfairness, rather than to prove fairness, as it stated in the paper Equality of opportunity in supervised learning by Hardt et al. (2016):

… satisfying [the demographic criteria] should not be considered a conclusive proof of fairness. Similarly, violations of our condition are not meant to be a proof of unfairness. Rather we envision our framework as providing a reasonable way of discovering and measuring potential concerns that require further scrutiny. We believe that resolving fairness concerns is ultimately impossible without substantial domain-specific investigation.

The output of binary classifiers can come in two forms, either giving a binary outcome prediction for input or producing a real number score, which the common one is the probability for the positive or negative label (such as the method proba of an Estimator in sklearn). Therefore, the criteria come in two flavors, one for binary output, and the second for score output.

The fundamental concept for defining the fairness criteria is conditional independence. Using Machine Learning and Fairness book’s notions:

• A - Sensitive attribute

• Y - Binary ground truth (correct) target

• R - Estimated binary targets or score as returned by a classifier

There are three demographic fairness criteria for classification:

1. Independence - R⊥A

2. Separation - R⊥A∣Y

3. Sufficiency - Y⊥A∣R

### Independence¶

ethically.fairness.metrics.independence_binary(y_pred, x_sens, x_sens_privileged=None, labels=None, as_df=False)[source]

Compute the independence criteria for binary prediction.

In classification terminology, it is the acceptance rate grouped by the sensitive attribute.

Parameters
• y_pred – Estimated targets as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each target.

• x_sens_privileged – The privileged value in the sensitive attribute. Relevent only if there are only two values for the sensitive attribute.

• labels – List of labels to choose the negative and positive target. This may be used to reorder or select a subset of labels. If none is given, those that appear at least once in y_pred are used in sorted order; first is negative and the second is positive.

• as_df – Whether to return the results as dict (if False) or as pandas.DataFrame (if True).

Returns

Independence criteria and comparision if there are only two values for the sensitive attribute.

Return type

tuple

ethically.fairness.metrics.separation_binary(y_true, y_pred, x_sens, x_sens_privileged=None, labels=None, as_df=False)[source]

Compute the separation criteria for binary prediction.

In classification terminology, it is the TPR, FPR, TNR and FNR grouped by the sensitive attribute.

Parameters
• y_true – Binary ground truth (correct) target values.

• y_pred – Estimated binary targets as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each target.

• x_sens_privileged – The privileged value in the sensitive attribute. Relevent only if there are only two values for the sensitive attribute.

• labels – List of labels to choose the negative and positive target. This may be used to reorder or select a subset of labels. If none is given, those that appear at least once in y_pred are used in sorted order; first is negative and the second is positive.

• as_df – Whether to return the results as dict (if False) or as pandas.DataFrame (if True).

Returns

Separation criteria and comparision if there are only two values for the sensitive attribute.

Return type

tuple

### Separation¶

ethically.fairness.metrics.separation_binary(y_true, y_pred, x_sens, x_sens_privileged=None, labels=None, as_df=False)[source]

Compute the separation criteria for binary prediction.

In classification terminology, it is the TPR, FPR, TNR and FNR grouped by the sensitive attribute.

Parameters
• y_true – Binary ground truth (correct) target values.

• y_pred – Estimated binary targets as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each target.

• x_sens_privileged – The privileged value in the sensitive attribute. Relevent only if there are only two values for the sensitive attribute.

• labels – List of labels to choose the negative and positive target. This may be used to reorder or select a subset of labels. If none is given, those that appear at least once in y_pred are used in sorted order; first is negative and the second is positive.

• as_df – Whether to return the results as dict (if False) or as pandas.DataFrame (if True).

Returns

Separation criteria and comparision if there are only two values for the sensitive attribute.

Return type

tuple

ethically.fairness.metrics.separation_score(y_true, y_score, x_sens, labels=None, as_df=False)[source]

Compute the separation criteria for score prediction.

In classification terminology, it is the FPR and TPR grouped by the score and the sensitive attribute.

Parameters
• y_true – Binary ground truth (correct) target values.

• y_score – Estimated target score as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each estimated target.

• as_df – Whether to return the results as dict (if False) or as pandas.DataFrame (if True).

Returns

Separation criteria.

Return type

dict or pandas.DataFrame

#### ROC¶

The separation criterion has strong relation to the ROC, therefore these functions can generate ROC and ROC-AUC per sensitive attribute values:

ethically.fairness.metrics.roc_auc_score_by_attr(y_true, y_score, x_sens, sample_weight=None)[source]

Compute Area Under the ROC (AUC) by attribute.

Based on function:sklearn.metrics.roc_auc_score

Parameters
• y_true – Binary ground truth (correct) target values.

• y_score – Estimated target score as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each estimated target.

• sample_weight – Sample weights.

Returns

ROC AUC grouped by the sensitive attribute.

Return type

dict

ethically.fairness.metrics.roc_curve_by_attr(y_true, y_score, x_sens, pos_label=None, sample_weight=None, drop_intermediate=False)[source]

Compute Receiver operating characteristic (ROC) by attribute.

Parameters
• y_true – Binary ground truth (correct) target values.

• y_score – Estimated target score as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each estimated target.

• pos_label – Label considered as positive and others are considered negative.

• sample_weight – Sample weights.

• drop_intermediate – Whether to drop some suboptimal thresholds which would not appear on a plotted ROC curve. This is useful in order to create lighter ROC curves.

Returns

For each value of sensitive attribute: - fpr - Increasing false positive rates such

that element i is the false positive rate of predictions with score >= thresholds[i].

• fpr - Increasing true positive rates such that element i is the true positive rate of predictions with score >= thresholds[i].

• thresholds - Decreasing thresholds on the decision function used to compute fpr and tpr. thresholds[0] represents no instances being predicted and is arbitrarily set to max(y_score) + 1.

Return type

dict

#### Plotting¶

ethically.fairness.metrics.plot_roc_by_attr(y_true, y_score, x_sens, title='ROC Curves by Attribute', ax=None, figsize=None, title_fontsize='large', text_fontsize='medium')[source]

Generate the ROC curves by attribute from targets and scores.

Based on skplt.metrics.plot_roc()

Parameters
• y_true – Binary ground truth (correct) target values.

• y_score – Estimated target score as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each estimated target.

• title (str) – Title of the generated plot.

• ax – The axes upon which to plot the curve. If None, the plot is drawn on a new set of axes.

• figsize (tuple) – Tuple denoting figure size of the plot e.g. (6, 6).

• title_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

• text_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

Returns

The axes on which the plot was drawn.

Return type

matplotlib.axes.Axes

ethically.fairness.metrics.plot_roc_curves(roc_curves, aucs=None, title='ROC Curves by Attribute', ax=None, figsize=None, title_fontsize='large', text_fontsize='medium')[source]

Generate the ROC curves by attribute from (fpr, tpr, thresholds).

Based on skplt.metrics.plot_roc()

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• aucs (dict) – Area Under the ROC (AUC) by attribute.

• title (str) – Title of the generated plot.

• ax – The axes upon which to plot the curve. If None, the plot is drawn on a new set of axes.

• figsize (tuple) – Tuple denoting figure size of the plot e.g. (6, 6).

• title_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

• text_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

Returns

The axes on which the plot was drawn.

Return type

matplotlib.axes.Axes

### Sufficiency¶

ethically.fairness.metrics.sufficiency_binary(y_true, y_pred, x_sens, x_sens_privileged=None, labels=None, as_df=False)[source]

Compute the sufficiency criteria for binary prediction.

In classification terminology, it is the PPV and NPV grouped by the sensitive attribute.

Parameters
• y_true – Binary ground truth (correct) target values.

• y_pred – Binary estimated targets as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each target.

• x_sens_privileged – The privileged value in the sensitive attribute. Relevent only if there are only two values for the sensitive attribute.

• labels – List of labels to choose the negative and positive target. This may be used to reorder or select a subset of labels. If none is given, those that appear at least once in y_pred are used in sorted order; first is negative and the second is positive.

• as_df – Whether to return the results as dict (if False) or as pandas.DataFrame (if True).

Returns

Sufficiency criteria and comparision if there are only two values for the sensitive attribute.

Return type

tuple

ethically.fairness.metrics.sufficiency_score(y_true, y_score, x_sens, labels=None, within_score_percentile=False, as_df=False)[source]

Compute the sufficiency criteria for score prediction.

In classification terminology, it is the PPV and the NPV grouped by the score and the sensitive attribute.

Parameters
• y_true – Binary ground truth (correct) target values.

• y_score – Estimated target score as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each target.

• as_df – Whether to return the results as dict (if False) or as pandas.DataFrame (if True).

Returns

Sufficiency criteria.

Return type

dict or pandas.DataFrame

### Report¶

ethically.fairness.metrics.report_binary(y_true, y_pred, x_sens, labels=None)[source]

Generate a report of criteria for binary prediction.

In classification terminology, the statistics are grouped by the sensitive attribute: - Number of observations per group - Proportion of of observations per group - Base rate - Acceptance rate - FNR - TPR - PPV - NPV

Parameters
• y_true – Binary ground truth (correct) target values.

• y_pred – Binary estimated targets as returned by a classifier.

• x_sens – Sensitive attribute values corresponded to each target.

• labels – List of labels to choose the negative and positive target. This may be used to reorder or select a subset of labels. If none is given, those that appear at least once in y_pred are used in sorted order; first is negative and the second is positive.

Returns

Classification statistics grouped by the sensitive attribute.

Return type

pandas.DataFrame

### A Dictionary of criteria¶

https://fairmlbook.org/demographic.html#a-dictionary-of-criteria

## Algorithmic Interventions¶

Algorithmic intervensions for satisfying fairness criteria.

There are three families of techniques:

1. Pre-processing - Adjust features in the dataset.

2. In-processing - Adjust the learning algorithm.

3. Post-processing - Adjust the learned classifier.

### Threshold - Post-processing¶

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.

References:
ethically.fairness.interventions.threshold.find_single_threshold(roc_curves, base_rates, proportions, cost_matrix)[source]

Compute single threshold that minimizes cost.

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• base_rates (dict) – Base rate by attribute.

• proportions (dict) – Proportion of each attribute value.

• cost_matrix (sequence) – Cost matrix by [[tn, fp], [fn, tp]].

Returns

Threshold, FPR and TPR by attribute and cost value.

Return type

tuple

ethically.fairness.interventions.threshold.find_min_cost_thresholds(roc_curves, base_rates, cost_matrix)[source]

Compute thresholds by attribute values that minimize cost.

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• base_rates (dict) – Base rate by attribute.

• cost_matrix (sequence) – Cost matrix by [[tn, fp], [fn, tp]].

Returns

Thresholds, FPR and TPR by attribute and cost value.

Return type

tuple

ethically.fairness.interventions.threshold.find_independence_thresholds(roc_curves, base_rates, proportions, cost_matrix)[source]

Compute thresholds that achieve independence and minimize cost.

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• base_rates (dict) – Base rate by attribute.

• proportions (dict) – Proportion of each attribute value.

• cost_matrix (sequence) – Cost matrix by [[tn, fp], [fn, tp]].

Returns

Thresholds, FPR and TPR by attribute and cost value.

Return type

tuple

ethically.fairness.interventions.threshold.find_fnr_thresholds(roc_curves, base_rates, proportions, cost_matrix)[source]

Compute thresholds that achieve equal FNRs and minimize cost.

Also known as equal opportunity.

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• base_rates (dict) – Base rate by attribute.

• proportions (dict) – Proportion of each attribute value.

• cost_matrix (sequence) – Cost matrix by [[tn, fp], [fn, tp]].

Returns

Thresholds, FPR and TPR by attribute and cost value.

Return type

tuple

ethically.fairness.interventions.threshold.find_separation_thresholds(roc_curves, base_rate, cost_matrix)[source]

Compute thresholds that achieve separation and minimize cost.

Also known as equalized odds.

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• base_rate (float) – Overall base rate.

• cost_matrix (sequence) – Cost matrix by [[tn, fp], [fn, tp]].

Returns

Thresholds, FPR and TPR by attribute and cost value.

Return type

tuple

ethically.fairness.interventions.threshold.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)[source]

Compute thresholds that achieve various criteria and minimize cost.

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• proportions (dict) – Proportion of each attribute value.

• base_rate (float) – Overall base rate.

• base_rates (dict) – Base rate by attribute.

• cost_matrix (sequence) – Cost matrix by [[tn, fp], [fn, tp]].

• with_single (bool) – Compute single threshold.

• with_min_cost (bool) – Compute minimum cost thresholds.

• with_independence (bool) – Compute independence thresholds.

• with_fnr (bool) – Compute FNR thresholds.

• with_separation (bool) – Compute separation thresholds.

Returns

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

Return type

dict

ethically.fairness.interventions.threshold.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')[source]

Generate the ROC curves by attribute with thresholds.

Based on skplt.metrics.plot_roc()

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• thresholds_data (dict) – Thresholds by attribute from the function find_thresholds().

• aucs (dict) – Area Under the ROC (AUC) by attribute.

• title (str) – Title of the generated plot.

• ax – The axes upon which to plot the curve. If None, the plot is drawn on a new set of axes.

• figsize (tuple) – Tuple denoting figure size of the plot e.g. (6, 6).

• title_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

• text_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

Returns

The axes on which the plot was drawn.

Return type

matplotlib.axes.Axes

ethically.fairness.interventions.threshold.plot_fpt_tpr(roc_curves, title='FPR-TPR Curves by Attribute', ax=None, figsize=None, title_fontsize='large', text_fontsize='medium')[source]

Generate FPR and TPR curves by thresholds and by attribute.

Based on skplt.metrics.plot_roc()

Parameters
• roc_curves (dict) – Receiver operating characteristic (ROC) by attribute.

• title (str) – Title of the generated plot.

• ax – The axes upon which to plot the curve. If None, the plot is drawn on a new set of axes.

• figsize (tuple) – Tuple denoting figure size of the plot e.g. (6, 6).

• title_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

• text_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

Returns

The axes on which the plot was drawn.

Return type

matplotlib.axes.Axes

ethically.fairness.interventions.threshold.plot_costs(thresholds_data, title='Cost by Threshold', ax=None, figsize=None, title_fontsize='large', text_fontsize='medium')[source]

Plot cost by threshold definition and by attribute.

Based on skplt.metrics.plot_roc()

Parameters
• thresholds_data (dict) – Thresholds by attribute from the function find_thresholds().

• title (str) – Title of the generated plot.

• ax – The axes upon which to plot the curve. If None, the plot is drawn on a new set of axes.

• figsize (tuple) – Tuple denoting figure size of the plot e.g. (6, 6).

• title_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

• text_fontsize – Matplotlib-style fontsizes. Use e.g. ‘small’, ‘medium’, ‘large’ or integer-values.

Returns

The axes on which the plot was drawn.

Return type

matplotlib.axes.Axes