ExFairness.Metrics.DemographicParity (ExFairness v0.5.1)

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Demographic Parity (Statistical Parity) fairness metric.

Demographic parity requires that the probability of a positive prediction is equal across groups defined by the sensitive attribute.

Mathematical Definition

P(Ŷ = 1 | A = 0) = P(Ŷ = 1 | A = 1)

The disparity is measured as the absolute difference between positive prediction rates:

Δ_DP = |P(Ŷ = 1 | A = 0) - P(Ŷ = 1 | A = 1)|

When to Use

  • When equal representation in positive outcomes is required
  • Advertising and content recommendation systems
  • When base rates can legitimately differ between groups

Limitations

  • Ignores base rate differences in actual outcomes
  • May conflict with accuracy if base rates differ
  • Can be satisfied by a random classifier

References

  • Dwork, C., et al. (2012). "Fairness through awareness." ITCS.
  • Feldman, M., et al. (2015). "Certifying and removing disparate impact." KDD.

Examples

iex> predictions = Nx.tensor([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0])
iex> sensitive = Nx.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
iex> result = ExFairness.Metrics.DemographicParity.compute(predictions, sensitive)
iex> result.passes
true

Summary

Types

result()

Functions

compute(predictions, sensitive_attr, opts \\ [])

Computes demographic parity disparity between groups.

Types

result()

@type result() :: %{
  group_a_rate: float(),
  group_b_rate: float(),
  disparity: float(),
  passes: boolean(),
  threshold: float(),
  interpretation: String.t()
}

Functions

compute(predictions, sensitive_attr, opts \\ [])

@spec compute(Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: result()

Computes demographic parity disparity between groups.

Parameters

  • predictions - Binary predictions tensor (0 or 1)
  • sensitive_attr - Binary sensitive attribute tensor (0 or 1)
  • opts - Options:
    • :threshold - Maximum acceptable disparity (default: 0.1)
    • :min_per_group - Minimum samples per group for validation (default: 10)

Returns

A map containing:

  • :group_a_rate - Positive prediction rate for group A (sensitive_attr = 0)
  • :group_b_rate - Positive prediction rate for group B (sensitive_attr = 1)
  • :disparity - Absolute difference between rates
  • :passes - Whether disparity is within threshold
  • :threshold - Threshold used
  • :interpretation - Plain language explanation of the result

Examples

iex> predictions = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
iex> sensitive = Nx.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
iex> result = ExFairness.Metrics.DemographicParity.compute(predictions, sensitive)
iex> result.disparity
1.0

iex> predictions = Nx.tensor([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0])
iex> sensitive = Nx.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
iex> result = ExFairness.Metrics.DemographicParity.compute(predictions, sensitive)
iex> result.passes
true