Disparate Impact (DI)
The difference in positive proportions in the predicted labels metric can be assessed in the form of a ratio.
The comparison of positive proportions in predicted labels metric can be assessed in the form of a ratio instead of as a difference, as it is with the Difference in Positive Proportions in Predicted Labels (DPPL). The disparate impact (DI) metric is defined as the ratio of the proportion of positive predictions (y’ = 1) for facet d over the proportion of positive predictions (y’ = 1) for facet a. For example, if the model predictions grant loans to 60% of a middle-aged group (facet a) and 50% other age groups (facet d), then DI = .5/.6 = 0.8, which indicates a positive bias and an adverse impact on the other aged group represented by facet d.
The formula for the ratio of proportions of the predicted labels:
DI = q'd/q'a
Where:
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q'a = n'a(1)/na is the predicted proportion of facet a who get a positive outcome of value 1. In our example, the proportion of a middle-aged facet predicted to get granted a loan. Here n'a(1) represents the number of members of facet a who get a positive predicted outcome and na the is number of members of facet a.
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q'd = n'd(1)/nd is the predicted proportion of facet d a who get a positive outcome of value 1. In our example, a facet of older and younger people predicted to get granted a loan. Here n'd(1) represents the number of members of facet d who get a positive predicted outcome and nd the is number of members of facet d.
For binary, multicategory facet, and continuous labels, the DI values range over the interval [0, ∞).
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Values less than 1 indicate that facet a has a higher proportion of predicted positive outcomes than facet d. This is referred to as positive bias.
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A value of 1 indicates demographic parity.
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Values greater than 1 indicate that facet d has a higher proportion of predicted positive outcomes than facet a. This is referred to as negative bias.