Roadmaps for risk mitigation
  • Risk mitigation roadmaps
  • Mitigation Roadmaps
    • Improving generalization through model validation
      • Step 1: Estimating generalization
      • Step 2: Model validation for hyperparameters tuning
      • Step 3: Performing algorithmic selection
      • Additional Material
    • Hyperparameter Optimisation
      • Step 1: Validation
      • Step 2: Hyperparameter Search
      • Additional Considerations
    • Handling dataset shift
      • Step 1: Understanding dataset shifts
      • Step 2: Detecting dataset shifts
      • Step 3: Handling dataset shifts
      • Additional Material
    • Adversarial training for robustness
      • Step 1: Understanding adversarial examples
      • Step 2: Finding adversarial examples
      • Step 3: Defending against adversarial examples
      • Additional Material
    • Data Minimization techniques
      • Step 1: Understanding the data minimization principle
      • Step 2: Data minimization techniques for Supervised Learning
        • Option 1: Reducing features
        • Option 2: Reducing data points
      • Step 3: Other privacy-preserving techniques
      • Additional Material
    • Measuring Bias and Discrimination
      • Step 1: Understanding bias
      • Step 2A: Measuring Bias for Classification tasks
        • Equality of Outcome metrics
        • Equality of Opportunity metrics
      • Step 2B: Measuring Bias in Regression tasks
        • Equality of Outcome metrics
        • Equality of Opportunity metrics
      • Additional Material
    • Mitigating Bias and Discrimination
      • Step 1: Understanding bias
      • Step 2: Mitigating Bias
        • Option 1: Pre-processing
        • Option 2: In-processing
        • Option 3: Post-Processing
      • Additional Material
    • Documentation for improved explainability of Machine Learning models
      • Step 1: Datasheets for Datasets
      • Step 2: Model Cards for Model Reporting
      • Additional Material
    • Extracting Explanations from Machine Learning Models
      • Step 1: Understanding algorithmic explainability
      • Step 2: In-processing methodologies for Explainability
      • Step 3: Post-processing methodologies for Explainability
      • Additional Material
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  1. Mitigation Roadmaps
  2. Measuring Bias and Discrimination
  3. Step 2A: Measuring Bias for Classification tasks

Equality of Outcome metrics

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Last updated 2 years ago

The idea of equality of outcome metrics, is to compare the rate of success in the privileged group with the rate of success in the unprivileged group. We define the success rate SRgSR_gSRg​of a particular group ggg as:

SRg=Number of individuals in g with successful outcomeNumber of individuals in gSR_g =\frac{\text{Number of individuals in g with successful outcome}}{\text{Number of individuals in g}} SRg​=Number of individuals in gNumber of individuals in g with successful outcome​

The idea is that an unbiased system would present roughly similar success rates across groups. There are two main ways of quantifying this across-groups comparison: one is by taking the ratio (disparate impact) and the other one is to take the difference (statistical parity). We will refer to the success rate for the unprivileged group as SRminSR_{min}SRmin​, and to the success rate for the privileged group as SRmajSR_{maj}SRmaj​. Typically, these metrics are used in recruitment or in an academic context.

We list here the mathematical definitions for a few common metrics:

  • Disparate Impact: Measures the ratio of success rates. The ideal value is 1. The system is considered not biased if this quantity falls between 0.8 and 1.2.

DisparateImpact=SRminSRmajDisparate Impact =\frac{SR_{min}}{SR_{maj}}DisparateImpact=SRmaj​SRmin​​

  • Statistical Parity: Measures the difference in success rates. The ideal value is 0. A negative value means that the unprivileged group is unfavoured.

StatisticalParity=SRmin−SRmajStatistical Parity=SR_{min}-SR_{maj}StatisticalParity=SRmin​−SRmaj​

  • Cohen-D: this is essentially a standardised statistical parity. This value should ideally be small or negligible.

  • 2-SD Rule: Another metric that normalises statistical parity. The ideal value is 0.

CohenD=SRmin−SRmajpoolSTDwithpoolSTD=(nmaj−1)STDmaj2+(nmin−1)STDmin2nmin+nmaj−2CohenD=\frac{SR_{min}-SR_{maj}}{poolSTD} \quad \text{with} \quad poolSTD=\frac{(n_{maj}-1)STD_{maj}^2 + (n_{min}-1)STD_{min}^2}{n_{min}+n_{maj}-2}CohenD=poolSTDSRmin​−SRmaj​​withpoolSTD=nmin​+nmaj​−2(nmaj​−1)STDmaj2​+(nmin​−1)STDmin2​​

with nmin and nmajn_{min} \text{ and } n_{maj}nmin​ and nmaj​ being the number of individuals in the minority and majority groups respectively, and:

STDmaj=SRmaj⋅(1−SRmaj)andSTDmin=SRmin⋅(1−SRmin)STD_{maj}=\sqrt{SR_{maj} \cdot (1-SR_{maj})} \quad \text{and} \quad STD_{min}=\sqrt{SR_{min} \cdot (1-SR_{min})}STDmaj​=SRmaj​⋅(1−SRmaj​)​andSTDmin​=SRmin​⋅(1−SRmin​)​
2SD=SRmin−SRmajSRtot(1−SRtot)N⋅Pmin(1−Pmin)2SD = \frac{SR_{min}-SR_{maj}}{\sqrt{\frac{SR_{tot}(1-SR_{tot})}{N\cdot P_{min}(1-P_{min})}} }2SD=N⋅Pmin​(1−Pmin​)SRtot​(1−SRtot​)​​SRmin​−SRmaj​​

where SRtotSR_{tot} SRtot​ is the total success rate (across all groups), and Pmin=nminNP_{min}=\frac{n_{min}}{N}Pmin​=Nnmin​​, with NNNbeing the total number of individuals.

An example of how to measure bias in a binary classification problem in recruitment can be found in our notebook, which can be accessed or downloaded as the following file:

here
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Measuring_Bias.ipynb