ExFairness - Future Directions and Technical Roadmap

Date: October 20, 2025 Version: 0.1.0 → 1.0.0 Author: North Shore AI Research Team

Executive Summary

ExFairness has achieved a production-ready state with comprehensive core functionality:

• ✅ 4 group fairness metrics (Demographic Parity, Equalized Odds, Equal Opportunity, Predictive Parity)
• ✅ Legal compliance detection (EEOC 80% rule)
• ✅ Mitigation technique (Reweighting)
• ✅ Multi-format reporting (Markdown/JSON)
• ✅ 134 tests, all passing, zero warnings
• ✅ 1,437 line comprehensive README with 15+ academic citations

Current Status: ~60% of complete buildout plan implemented

Next Phase: Expand to advanced metrics, additional mitigation techniques, and statistical inference capabilities to reach v1.0.0 production release.

Implementation Status Overview

Completed (Production Ready)

Priority 1: Critical Path to v1.0.0

1. Statistical Inference & Confidence Intervals

Status: Not implemented Priority: HIGH Estimated Effort: 2-3 weeks Dependencies: None (uses existing infrastructure)

Why Critical

• Required for scientific rigor
• Needed for publication in academic venues
• Essential for legal defense of fairness claims
• Industry standard in Python libraries (AIF360, Fairlearn)

Technical Specification

Bootstrap Confidence Intervals:

defmodule ExFairness.Utils.Bootstrap do
  @moduledoc """
  Bootstrap confidence interval computation for fairness metrics.

  Uses stratified bootstrap to preserve group proportions.
  """

  @doc """
  Computes bootstrap confidence interval for a statistic.

  ## Algorithm

  1. For i = 1 to n_samples:
     a. Sample with replacement (stratified by sensitive attribute)
     b. Compute statistic on bootstrap sample
     c. Store bootstrap_statistics[i]

  2. Sort bootstrap_statistics

  3. Compute percentiles:
     CI_lower = percentile(alpha/2)
     CI_upper = percentile(1 - alpha/2)

  ## Parameters

    * `data` - List of tensors [predictions, labels, sensitive_attr]
    * `statistic_fn` - Function to compute on bootstrap samples
    * `opts`:
      * `:n_samples` - Number of bootstrap samples (default: 1000)
      * `:confidence_level` - Confidence level (default: 0.95)
      * `:stratified` - Preserve group proportions (default: true)
      * `:parallel` - Use parallel bootstrap (default: true)
      * `:seed` - Random seed for reproducibility

  ## Returns

  Tuple {lower, upper} representing confidence interval

  ## Examples

      iex> predictions = Nx.tensor([...])
      iex> sensitive = Nx.tensor([...])
      iex> statistic_fn = fn [preds, sens] ->
      ...>   ExFairness.Metrics.DemographicParity.compute(preds, sens).disparity
      ...> end
      iex> {lower, upper} = ExFairness.Utils.Bootstrap.confidence_interval(
      ...>   [predictions, sensitive],
      ...>   statistic_fn,
      ...>   n_samples: 1000
      ...> )
      iex> IO.puts "95% CI: [#{lower}, #{upper}]"

  """
  @spec confidence_interval([Nx.Tensor.t()], function(), keyword()) :: {float(), float()}
  def confidence_interval(data, statistic_fn, opts \\ []) do
    n_samples = Keyword.get(opts, :n_samples, 1000)
    confidence_level = Keyword.get(opts, :confidence_level, 0.95)
    stratified = Keyword.get(opts, :stratified, true)
    parallel = Keyword.get(opts, :parallel, true)
    seed = Keyword.get(opts, :seed, :erlang.system_time())

    # Get sample size
    n = elem(Nx.shape(hd(data)), 0)

    # Generate bootstrap samples
    bootstrap_statistics = if parallel do
      # Parallel bootstrap using Task.async_stream
      1..n_samples
      |> Task.async_stream(fn i ->
        bootstrap_sample(data, n, seed + i, stratified)
        |> statistic_fn.()
      end, max_concurrency: System.schedulers_online())
      |> Enum.map(fn {:ok, stat} -> stat end)
      |> Enum.sort()
    else
      # Sequential bootstrap
      for i <- 1..n_samples do
        bootstrap_sample(data, n, seed + i, stratified)
        |> statistic_fn.()
      end
      |> Enum.sort()
    end

    # Compute percentiles
    alpha = 1 - confidence_level
    lower_idx = floor(n_samples * alpha / 2)
    upper_idx = ceil(n_samples * (1 - alpha / 2)) - 1

    lower = Enum.at(bootstrap_statistics, lower_idx)
    upper = Enum.at(bootstrap_statistics, upper_idx)

    {lower, upper}
  end

  defp bootstrap_sample(data, n, seed, stratified) do
    # Implementation details...
  end
end

Statistical Significance Testing:

defmodule ExFairness.Utils.StatisticalTests do
  @moduledoc """
  Hypothesis testing for fairness metrics.
  """

  @doc """
  Two-proportion Z-test for demographic parity.

  H0: P(Ŷ=1|A=0) = P(Ŷ=1|A=1) (no disparity)
  H1: P(Ŷ=1|A=0) ≠ P(Ŷ=1|A=1) (disparity exists)

  ## Test Statistic

  Under H0, the standard error is:

      SE = sqrt(p̂ * (1 - p̂) * (1/n_A + 1/n_B))

  where p̂ = (n_A * p_A + n_B * p_B) / (n_A + n_B)

  Z-statistic:

      Z = (p_A - p_B) / SE

  P-value (two-tailed):

      p = 2 * P(|Z| > |z_observed|)

  ## Returns

  %{
    z_statistic: float(),
    p_value: float(),
    significant: boolean(),
    alpha: float()
  }
  """
  @spec two_proportion_test(Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: map()
  def two_proportion_test(predictions, sensitive_attr, opts \\ []) do
    # Implementation
  end

  @doc """
  Permutation test for any fairness metric.

  Non-parametric test that doesn't assume normal distribution.

  ## Algorithm

  1. Compute observed statistic on actual data
  2. For i = 1 to n_permutations:
     a. Randomly permute sensitive attributes
     b. Compute statistic on permuted data
     c. Store permuted_statistics[i]
  3. P-value = proportion of permuted statistics >= observed

  ## Parameters

    * `predictions` - Predictions tensor
    * `labels` - Labels tensor (optional, for some metrics)
    * `sensitive_attr` - Sensitive attribute
    * `metric_fn` - Function to compute metric
    * `opts`:
      * `:n_permutations` - Number of permutations (default: 10000)
      * `:alpha` - Significance level (default: 0.05)
      * `:alternative` - 'two-sided', 'greater', 'less' (default: 'two-sided')
  """
  @spec permutation_test(Nx.Tensor.t(), Nx.Tensor.t() | nil, Nx.Tensor.t(), function(), keyword()) :: map()
  def permutation_test(predictions, labels, sensitive_attr, metric_fn, opts \\ []) do
    # Implementation
  end
end

Updated Metric Signatures:

# All metrics should support statistical inference
result = ExFairness.demographic_parity(predictions, sensitive_attr,
  include_ci: true,
  bootstrap_samples: 1000,
  confidence_level: 0.95,
  statistical_test: :z_test  # or :permutation
)

# Returns enhanced result:
# %{
#   group_a_rate: 0.50,
#   group_b_rate: 0.60,
#   disparity: 0.10,
#   passes: false,
#   threshold: 0.05,
#   confidence_interval: {0.05, 0.15},  # NEW
#   p_value: 0.023,                      # NEW
#   statistically_significant: true,     # NEW
#   interpretation: "..."
# }

Implementation Tasks:

1. Implement ExFairness.Utils.Bootstrap module (150 lines, 15 tests)
2. Implement ExFairness.Utils.StatisticalTests module (200 lines, 20 tests)
3. Add :include_ci option to all 4 metrics (50 lines each, 5 tests each)
4. Add :statistical_test option to all 4 metrics
5. Update documentation with statistical inference examples
6. Add property-based tests using StreamData

Research Citations:

• Efron, B., & Tibshirani, R. J. (1994). "An introduction to the bootstrap." CRC press.
• Good, P. (2013). "Permutation tests: a practical guide to resampling methods for testing hypotheses." Springer Science & Business Media.

2. Calibration Metric

Status: Not implemented Priority: HIGH Estimated Effort: 1-2 weeks Dependencies: None

Why Important

• Critical for probability-based decisions (risk scores, medical predictions)
• Required for many healthcare and financial applications
• Complements other fairness metrics

Technical Specification

Mathematical Definition:

For each predicted probability bin b:

P(Y = 1 | S(X) ∈ bin_b, A = 0) = P(Y = 1 | S(X) ∈ bin_b, A = 1)

Disparity Measure:

Δ_Cal = max_over_bins |P(Y=1|S∈b,A=0) - P(Y=1|S∈b,A=1)|

Expected Calibration Error (ECE):

ECE = Σ_b (n_b / n) * |actual_rate_b - predicted_prob_b|

Implementation Plan:

defmodule ExFairness.Metrics.Calibration do
  @moduledoc """
  Calibration fairness metric.

  Ensures that predicted probabilities match actual outcomes
  across groups.
  """

  @doc """
  Computes calibration disparity between groups.

  ## Parameters

    * `probabilities` - Predicted probabilities tensor (0.0 to 1.0)
    * `labels` - Binary labels tensor (0 or 1)
    * `sensitive_attr` - Binary sensitive attribute tensor
    * `opts`:
      * `:n_bins` - Number of probability bins (default: 10)
      * `:strategy` - Binning strategy (:uniform or :quantile, default: :uniform)
      * `:threshold` - Max acceptable calibration disparity (default: 0.1)

  ## Returns

  %{
    group_a_calibration: [bin calibrations],
    group_b_calibration: [bin calibrations],
    max_disparity: float(),
    ece_a: float(),  # Expected Calibration Error for group A
    ece_b: float(),  # Expected Calibration Error for group B
    passes: boolean(),
    calibration_curves: %{group_a: [...], group_b: [...]},  # For plotting
    interpretation: String.t()
  }

  ## Algorithm

  1. Create probability bins [0, 0.1), [0.1, 0.2), ..., [0.9, 1.0]
  2. For each group and each bin:
     a. Find samples with predicted prob in bin
     b. Compute actual positive rate
     c. Compute expected prob (bin midpoint or mean)
     d. Calibration error = |actual_rate - expected_prob|
  3. Compute max disparity across bins
  4. Compute ECE for each group

  ## Examples

      iex> probabilities = Nx.tensor([0.1, 0.3, 0.5, 0.7, 0.9, ...])
      iex> labels = Nx.tensor([0, 0, 1, 1, 1, ...])
      iex> sensitive = Nx.tensor([0, 0, 0, 1, 1, ...])
      iex> result = ExFairness.Metrics.Calibration.compute(probabilities, labels, sensitive, n_bins: 10)
      iex> result.passes
      true
  """
  @spec compute(Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: map()
  def compute(probabilities, labels, sensitive_attr, opts \\ []) do
    n_bins = Keyword.get(opts, :n_bins, 10)

    # Create bins
    bins = create_bins(n_bins)

    # Compute calibration for each group
    group_a_cal = compute_group_calibration(probabilities, labels, sensitive_attr, 0, bins)
    group_b_cal = compute_group_calibration(probabilities, labels, sensitive_attr, 1, bins)

    # Find max disparity across bins
    max_disparity = compute_max_calibration_disparity(group_a_cal, group_b_cal)

    # Compute ECE
    ece_a = compute_ece(group_a_cal)
    ece_b = compute_ece(group_b_cal)

    # Generate result
    %{
      group_a_calibration: group_a_cal,
      group_b_calibration: group_b_cal,
      max_disparity: max_disparity,
      ece_a: ece_a,
      ece_b: ece_b,
      passes: max_disparity <= threshold,
      interpretation: generate_interpretation(...)
    }
  end
end

Test Requirements:

• 15+ unit tests covering:
  • Perfect calibration (all bins match)
  • Poor calibration (large gaps)
  • Different binning strategies (uniform, quantile)
  • Edge cases (empty bins, all in one bin)
  • Calibration curves generation
  • ECE computation

Research Citations:

• Pleiss, G., Raghavan, M., Wu, F., Kleinberg, J., & Weinberger, K. Q. (2017). "On fairness and calibration." NeurIPS.
• Corbett-Davies, S., Pierson, E., Feller, A., Goel, S., & Huq, A. (2017). "Algorithmic decision making and the cost of fairness." KDD.

3. Intersectional Fairness Analysis

Status: Not implemented Priority: HIGH Estimated Effort: 2 weeks Dependencies: Core metrics already implemented

Why Important

• Real-world bias is often intersectional (e.g., race × gender)
• Required for comprehensive fairness assessment
• Legal requirement in some jurisdictions
• Kimberlé Crenshaw's intersectionality theory

Technical Specification

Mathematical Foundation:

For attributes A₁, A₂, ..., Aₖ, create all combinations:

Groups = {(a₁, a₂, ..., aₖ) : aᵢ ∈ values(Aᵢ)}

For each subgroup g ∈ Groups, compute fairness metric:

metric_g = compute_metric(data[subgroup == g])

Find reference group (typically majority or best-performing):

reference = argmax_g(metric_g)  or  argmax_g(count_g)

Compute disparities:

disparity_g = |metric_g - metric_reference|

Implementation Plan:

defmodule ExFairness.Detection.Intersectional do
  @moduledoc """
  Intersectional fairness analysis across multiple sensitive attributes.

  Analyzes fairness for all combinations of sensitive attributes to
  detect bias that may be hidden in single-attribute analysis.

  ## Example

  Race × Gender analysis:
  - (White, Male)
  - (White, Female)
  - (Black, Male)
  - (Black, Female)

  May reveal that Black women face unique disadvantages not captured
  by analyzing race or gender alone.
  """

  @doc """
  Performs intersectional fairness analysis.

  ## Parameters

    * `predictions` - Binary predictions
    * `labels` - Binary labels (optional for some metrics)
    * `sensitive_attrs` - List of sensitive attribute tensors
    * `opts`:
      * `:metric` - Metric to use (default: :demographic_parity)
      * `:attr_names` - Names for attributes (for reporting)
      * `:min_samples_per_subgroup` - Min samples (default: 30)
      * `:reference_group` - Reference subgroup (default: :largest)

  ## Returns

  %{
    subgroup_results: %{
      {attr1_val, attr2_val, ...} => metric_result
    },
    max_disparity: float(),
    most_disadvantaged_group: tuple(),
    least_disadvantaged_group: tuple(),
    disparity_matrix: Nx.Tensor.t(),  # For heatmap visualization
    interpretation: String.t()
  }

  ## Examples

      iex> gender = Nx.tensor([0, 0, 1, 1, 0, 0, 1, 1, ...])
      iex> race = Nx.tensor([0, 1, 0, 1, 0, 1, 0, 1, ...])
      iex> result = ExFairness.Detection.Intersectional.analyze(
      ...>   predictions,
      ...>   labels,
      ...>   [gender, race],
      ...>   attr_names: ["gender", "race"],
      ...>   metric: :equalized_odds
      ...> )
      iex> result.most_disadvantaged_group
      {1, 1}  # Female, Black
  """
  @spec analyze(Nx.Tensor.t(), Nx.Tensor.t() | nil, [Nx.Tensor.t()], keyword()) :: map()
  def analyze(predictions, labels, sensitive_attrs, opts \\ []) do
    metric = Keyword.get(opts, :metric, :demographic_parity)
    attr_names = Keyword.get(opts, :attr_names, Enum.map(1..length(sensitive_attrs), &"attr#{&1}"))

    # 1. Create all combinations (Cartesian product)
    subgroups = create_subgroups(sensitive_attrs)

    # 2. Compute metric for each subgroup
    subgroup_results = Enum.map(subgroups, fn subgroup_vals ->
      mask = create_subgroup_mask(sensitive_attrs, subgroup_vals)

      # Filter to subgroup
      subgroup_preds = filter_by_mask(predictions, mask)
      subgroup_labels = if labels, do: filter_by_mask(labels, mask), else: nil

      # Compute metric (need to handle single-group case)
      metric_result = compute_metric_for_subgroup(subgroup_preds, subgroup_labels, metric)

      {subgroup_vals, metric_result}
    end) |> Map.new()

    # 3. Find reference group
    reference = find_reference_group(subgroup_results)

    # 4. Compute disparities
    disparities = compute_subgroup_disparities(subgroup_results, reference)

    # 5. Find most/least disadvantaged
    {most_disadvantaged, max_disparity} = Enum.max_by(disparities, fn {_g, d} -> d end)
    {least_disadvantaged, min_disparity} = Enum.min_by(disparities, fn {_g, d} -> d end)

    # 6. Create disparity matrix for visualization
    disparity_matrix = create_disparity_matrix(disparities, sensitive_attrs)

    %{
      subgroup_results: subgroup_results,
      disparities: disparities,
      max_disparity: max_disparity,
      most_disadvantaged_group: most_disadvantaged,
      least_disadvantaged_group: least_disadvantaged,
      disparity_matrix: disparity_matrix,
      interpretation: generate_interpretation(...)
    }
  end
end

Visualization Support:

# Generate heatmap data for 2D intersectional analysis
defmodule ExFairness.Visualization do
  @doc """
  Prepares data for heatmap visualization of intersectional disparities.

  Returns data suitable for VegaLite or other plotting libraries.
  """
  def prepare_heatmap_data(intersectional_result) do
    # Convert disparity matrix to plottable format
  end
end

Test Requirements:

• 20+ tests covering:
  • 2-attribute combinations (race × gender)
  • 3-attribute combinations (race × gender × age)
  • Different metrics (demographic parity, equalized odds)
  • Minimum sample size enforcement
  • Reference group selection strategies
  • Disparity matrix generation

Research Citations:

• Crenshaw, K. (1989). "Demarginalizing the intersection of race and sex." University of Chicago Legal Forum.
• Buolamwini, J., & Gebru, T. (2018). "Gender shades: Intersectional accuracy disparities in commercial gender classification." FAccT.
• Foulds, J. R., Islam, R., Keya, K. N., & Pan, S. (2020). "An intersectional definition of fairness." FAccT.

4. Threshold Optimization (Post-processing)

Status: Not implemented Priority: HIGH Estimated Effort: 2 weeks Dependencies: Core metrics

Why Important

• Practical mitigation without retraining
• Can be applied to any trained model
• Pareto-optimal fairness-accuracy tradeoff
• Used in production at Microsoft (Fairlearn)

Technical Specification

Mathematical Problem:

Find thresholds (t_A, t_B) that:

Maximize: Accuracy (or other utility metric)
Subject to: Fairness constraint (e.g., |TPR_A - TPR_B| ≤ ε)

Algorithm (Grid Search):

1. Initialize best = (0.5, 0.5, -∞)
2. For t_A in [0, 0.01, 0.02, ..., 1.0]:
     For t_B in [0, 0.01, 0.02, ..., 1.0]:
       a. Apply thresholds: pred_A = (prob_A >= t_A), pred_B = (prob_B >= t_B)
       b. Check fairness constraint
       c. If satisfies constraint:
          - Compute utility (accuracy, F1, etc.)
          - If utility > best.utility:
              best = (t_A, t_B, utility)
3. Return best

Implementation:

defmodule ExFairness.Mitigation.ThresholdOptimization do
  @moduledoc """
  Post-processing threshold optimization for fairness.

  Finds group-specific decision thresholds that optimize accuracy
  subject to fairness constraints.
  """

  @doc """
  Finds optimal thresholds for each group.

  ## Parameters

    * `probabilities` - Predicted probabilities tensor (0.0 to 1.0)
    * `labels` - Binary labels tensor
    * `sensitive_attr` - Binary sensitive attribute
    * `opts`:
      * `:target_metric` - Fairness metric to satisfy
        (:equalized_odds, :equal_opportunity, :demographic_parity)
      * `:epsilon` - Allowed fairness violation (default: 0.05)
      * `:utility_metric` - What to maximize (default: :accuracy)
        Options: :accuracy, :f1_score, :balanced_accuracy
      * `:grid_resolution` - Threshold grid step size (default: 0.01)
      * `:method` - :grid_search or :gradient_based (default: :grid_search)

  ## Returns

  %{
    group_a_threshold: float(),
    group_b_threshold: float(),
    utility: float(),
    fairness_achieved: map(),
    pareto_frontier: [...],  # List of {threshold_a, threshold_b, utility, fairness}
    interpretation: String.t()
  }

  ## Examples

      iex> probabilities = Nx.tensor([0.3, 0.7, 0.8, 0.6, ...])
      iex> labels = Nx.tensor([0, 1, 1, 0, ...])
      iex> sensitive = Nx.tensor([0, 0, 1, 1, ...])
      iex> result = ExFairness.Mitigation.ThresholdOptimization.optimize(
      ...>   probabilities,
      ...>   labels,
      ...>   sensitive,
      ...>   target_metric: :equalized_odds,
      ...>   epsilon: 0.05
      ...> )
      iex> result.group_a_threshold
      0.47
  """
  @spec optimize(Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: map()
  def optimize(probabilities, labels, sensitive_attr, opts \\ []) do
    # Grid search implementation
  end

  @doc """
  Applies optimized thresholds to make predictions.
  """
  @spec apply_thresholds(Nx.Tensor.t(), Nx.Tensor.t(), map()) :: Nx.Tensor.t()
  def apply_thresholds(probabilities, sensitive_attr, thresholds) do
    # Apply group-specific thresholds
  end

  @doc """
  Computes Pareto frontier of fairness-accuracy tradeoff.

  Explores different fairness constraints to show tradeoff curve.
  """
  @spec pareto_frontier(Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: list()
  def pareto_frontier(probabilities, labels, sensitive_attr, opts \\ []) do
    # Compute frontier
  end
end

Test Requirements:

• 20+ tests including:
  • Grid search correctness
  • Fairness constraint satisfaction
  • Utility maximization
  • Edge cases (all same threshold, extreme thresholds)
  • Pareto frontier generation
  • Different utility metrics
  • Different fairness targets

Research Citations:

• Hardt, M., Price, E., & Srebro, N. (2016). "Equality of Opportunity in Supervised Learning." NeurIPS.
• Agarwal, A., Beygelzimer, A., Dudík, M., Langford, J., & Wallach, H. (2018). "A reductions approach to fair classification." ICML.

Priority 2: Enhanced Detection Capabilities

5. Statistical Parity Testing

Status: Not implemented Priority: MEDIUM Estimated Effort: 1 week

Builds on: Statistical inference work from Priority 1

defmodule ExFairness.Detection.StatisticalParity do
  @doc """
  Hypothesis testing for demographic parity violations.

  Combines multiple statistical tests:
  - Two-proportion Z-test
  - Chi-square test
  - Permutation test (for small samples)
  - Fisher's exact test (for very small samples)

  With multiple testing correction:
  - Bonferroni correction
  - Benjamini-Hochberg (FDR control)
  """
  @spec test(Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: map()
  def test(predictions, sensitive_attr, opts \\ []) do
    # Multiple test implementations
  end
end

Research Citations:

• Holm, S. (1979). "A simple sequentially rejective multiple test procedure." Scandinavian Journal of Statistics.
• Benjamini, Y., & Hochberg, Y. (1995). "Controlling the false discovery rate." Journal of the Royal Statistical Society.

6. Temporal Drift Detection

Status: Not implemented Priority: MEDIUM Estimated Effort: 1-2 weeks

Purpose: Monitor fairness metrics over time to detect degradation

Algorithms:

CUSUM (Cumulative Sum Control Chart):

S_pos[t] = max(0, S_pos[t-1] + (metric[t] - baseline) - allowance)
S_neg[t] = max(0, S_neg[t-1] - (metric[t] - baseline) - allowance)

If S_pos[t] > threshold or S_neg[t] > threshold:
  Alert: Drift detected at time t

EWMA (Exponentially Weighted Moving Average):

EWMA[t] = λ * metric[t] + (1-λ) * EWMA[t-1]

If |EWMA[t] - baseline| > threshold:
  Alert: Drift detected

Implementation:

defmodule ExFairness.Detection.TemporalDrift do
  @doc """
  Detects fairness drift over time using control charts.

  ## Parameters

    * `time_series` - List of {timestamp, metric_value} tuples
    * `opts`:
      * `:method` - :cusum or :ewma (default: :cusum)
      * `:baseline` - Baseline metric value
      * `:threshold` - Alert threshold
      * `:allowance` - CUSUM allowance parameter
      * `:lambda` - EWMA smoothing parameter

  ## Returns

  %{
    drift_detected: boolean(),
    change_point: DateTime.t() | nil,
    drift_magnitude: float(),
    alert_level: :none | :warning | :critical,
    control_chart_data: [...],  # For plotting
    interpretation: String.t()
  }
  """
  @spec detect(list({DateTime.t(), float()}), keyword()) :: map()
  def detect(time_series, opts \\ []) do
    # CUSUM or EWMA implementation
  end
end

Research Citations:

• Page, E. S. (1954). "Continuous inspection schemes." Biometrika.
• Roberts, S. W. (1959). "Control chart tests based on geometric moving averages." Technometrics.
• Lu, C. W., & Reynolds Jr, M. R. (1999). "EWMA control charts for monitoring the mean of autocorrelated processes." Journal of Quality Technology.

7. Label Bias Detection

Status: Not implemented Priority: MEDIUM Estimated Effort: 2 weeks

Purpose: Detect bias in training labels themselves

Algorithm:

1. For each group:
   a. Find similar feature vectors across groups (k-NN)
   b. Compare labels for similar individuals
   c. Compute label discrepancy

2. Statistical test:
   H0: No label bias (discrepancies random)
   H1: Label bias exists (systematic discrepancy)

3. Test statistic:
   Compare observed discrepancy to random baseline using permutation test

Implementation:

defmodule ExFairness.Detection.LabelBias do
  @doc """
  Detects bias in training labels.

  ## Method

  Uses k-nearest neighbors to find similar individuals across groups.
  If similar individuals have systematically different labels between
  groups, this suggests label bias.

  ## Parameters

    * `features` - Feature matrix
    * `labels` - Labels to test for bias
    * `sensitive_attr` - Sensitive attribute
    * `opts`:
      * `:k` - Number of nearest neighbors (default: 5)
      * `:distance_metric` - :euclidean or :cosine (default: :euclidean)
      * `:min_pairs` - Minimum similar pairs required (default: 100)

  ## Returns

  %{
    bias_detected: boolean(),
    avg_label_discrepancy: float(),
    p_value: float(),
    similar_pairs_found: integer(),
    interpretation: String.t()
  }
  """
  @spec detect(Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: map()
  def detect(features, labels, sensitive_attr, opts \\ []) do
    # k-NN based label bias detection
  end
end

Research Citations:

• Jiang, H., & Nachum, O. (2020). "Identifying and correcting label bias in machine learning." AISTATS.

Priority 3: Additional Mitigation Techniques

8. Resampling (Pre-processing)

Status: Not implemented Priority: MEDIUM Estimated Effort: 1 week

Techniques:

1. Random Oversampling: Duplicate minority group samples
2. Random Undersampling: Remove majority group samples
3. SMOTE: Synthetic Minority Oversampling (for continuous features)

Implementation:

defmodule ExFairness.Mitigation.Resampling do
  @doc """
  Resamples data to achieve fairness.

  ## Strategies

  - `:oversample` - Duplicate minority group samples
  - `:undersample` - Remove majority group samples
  - `:combined` - Both oversample and undersample
  - `:smote` - Generate synthetic samples (for continuous features)

  ## Parameters

    * `features` - Feature tensor
    * `labels` - Labels tensor
    * `sensitive_attr` - Sensitive attribute
    * `opts`:
      * `:strategy` - Resampling strategy (default: :combined)
      * `:target_ratio` - Desired group balance (default: 1.0)
      * `:k_neighbors` - For SMOTE (default: 5)

  ## Returns

  {resampled_features, resampled_labels, resampled_sensitive}
  """
  @spec resample(Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t(), keyword()) ::
    {Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t()}
  def resample(features, labels, sensitive_attr, opts \\ []) do
    # Implementation
  end
end

Research Citations:

• Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). "SMOTE: synthetic minority over-sampling technique." JAIR.
• Kamiran, F., & Calders, T. (2012). "Data preprocessing techniques for classification without discrimination." KAIS.

Priority 4: Advanced Fairness Metrics

9. Individual Fairness

Status: Not implemented Priority: MEDIUM Estimated Effort: 2-3 weeks

Mathematical Definition (Dwork et al. 2012):

d(Ŷ(x₁), Ŷ(x₂)) ≤ L · d(x₁, x₂)

Lipschitz continuity: Similar inputs produce similar outputs.

Measurement:

Fairness Score = (1/|P|) Σ_{(i,j)∈P} 𝟙[|f(xᵢ) - f(xⱼ)| ≤ ε]

Where P is set of "similar pairs".

Implementation:

defmodule ExFairness.Metrics.IndividualFairness do
  @doc """
  Measures individual fairness via Lipschitz continuity.

  ## Parameters

    * `features` - Feature tensor
    * `predictions` - Predictions (can be probabilities)
    * `opts`:
      * `:similarity_metric` - :euclidean, :cosine, :manhattan, or custom
      * `:k_neighbors` - Number of nearest neighbors to check (default: 10)
      * `:epsilon` - Acceptable prediction difference (default: 0.1)
      * `:lipschitz_constant` - Expected constant (default: 1.0)

  ## Returns

  %{
    individual_fairness_score: float(),  # 0.0 to 1.0
    lipschitz_violations: integer(),
    estimated_lipschitz_constant: float(),
    passes: boolean(),
    interpretation: String.t()
  }
  """
  @spec compute(Nx.Tensor.t(), Nx.Tensor.t(), keyword()) :: map()
  def compute(features, predictions, opts \\ []) do
    # 1. For each sample, find k nearest neighbors
    # 2. Compute prediction consistency
    # 3. Estimate Lipschitz constant
    # 4. Report violations
  end
end

Challenges:

• Defining similarity metric is domain-specific
• Computationally expensive (O(n²) for pairwise)
• Approximate nearest neighbors (Annoy, FAISS) may be needed

Research Citations:

• Dwork, C., et al. (2012). "Fairness through awareness." ITCS.
• Yona, G., & Rothblum, G. N. (2018). "Probably approximately metric-fair learning." ICML.

10. Counterfactual Fairness

Status: Not implemented Priority: LOW (Requires causal inference) Estimated Effort: 3-4 weeks

Mathematical Definition (Kusner et al. 2017):

P(Ŷ_{A←a}(U) = y | X = x, A = a) = P(Ŷ_{A←a'}(U) = y | X = x, A = a)

Requirements:

• Causal graph specification (domain knowledge)
• Counterfactual generation (causal inference)
• Intervention operators (do-calculus)

Implementation Sketch:

defmodule ExFairness.Metrics.Counterfactual do
  @doc """
  Measures counterfactual fairness.

  Requires specifying causal relationships between variables.

  ## Parameters

    * `features` - Feature tensor
    * `predictions` - Model predictions
    * `sensitive_attr` - Sensitive attribute
    * `causal_graph` - Causal DAG structure
    * `opts`:
      * `:counterfactual_generator` - Function to generate counterfactuals
      * `:threshold` - Max acceptable counterfactual difference
  """
  @spec compute(Nx.Tensor.t(), Nx.Tensor.t(), Nx.Tensor.t(), map(), keyword()) :: map()
  def compute(features, predictions, sensitive_attr, causal_graph, opts \\ []) do
    # Requires significant causal inference infrastructure
  end
end

Research Citations:

• Kusner, M. J., Loftus, J., Russell, C., & Silva, R. (2017). "Counterfactual fairness." NeurIPS.
• Pearl, J. (2009). "Causality: Models, reasoning and inference." Cambridge University Press.

Note: This is the most complex metric and may require a separate causal inference library for Elixir.

Priority 5: Production Features

11. Fairness Monitoring Dashboard

Status: Concept stage Priority: MEDIUM Estimated Effort: 2-3 weeks

Vision: Phoenix LiveView dashboard for real-time fairness monitoring

Features:

• Real-time fairness metric visualization
• Historical trend charts
• Alert configuration
• Report generation UI
• Metric comparison across models/versions

Technical Stack:

• Phoenix LiveView for reactive UI
• VegaLite for visualizations
• GenServer for background monitoring
• PostgreSQL for metric storage

12. Automated Fairness Testing

Status: Concept stage Priority: MEDIUM Estimated Effort: 1 week

Vision: ExUnit integration for fairness as part of test suite

defmodule MyModel.FairnessTest do
  use ExUnit.Case
  use ExFairness.Test

  test "model satisfies demographic parity" do
    assert_fairness :demographic_parity,
      predictions: @test_predictions,
      sensitive_attr: @test_sensitive,
      threshold: 0.05
  end

  test "model passes EEOC 80% rule" do
    assert_passes_80_percent_rule @test_predictions, @test_sensitive
  end
end

Technical Debt & Refactoring Opportunities

Code Quality Improvements

1. Property-Based Testing with StreamData

   • Current: Unit tests only
   • Future: Add property tests for:
     • Symmetry properties (swapping groups shouldn't change disparity)
     • Monotonicity (worse fairness → higher disparity)
     • Boundedness (disparities in [0, 1])
     • Invariants (normalization preserves fairness)

2. Performance Benchmarking

   • Add benchmark suite using Benchee
   • Target performance requirements:
     • 10,000 samples: < 100ms for basic metrics
     • 100,000 samples: < 1s for basic metrics
     • Bootstrap CI (1000 samples): < 5s

3. Multi-Group Support

   • Current: Binary sensitive attributes only (0/1)
   • Future: Support k-way attributes (race: White, Black, Hispanic, Asian, etc.)
   • Challenge: Pairwise comparisons (k choose 2) grow quadratically

4. Streaming/Online Metrics

   • Current: Batch computation only
   • Future: Online algorithms for streaming data
   • Use case: Real-time monitoring without storing all data

Integration & Ecosystem Development

13. Scholar Integration

Status: Planned Priority: HIGH (for adoption)

Goals:

• Pre-built fair classifiers in Scholar
• Sample weight support in Scholar models
• Direct integration examples

Example API:

# Hypothetical Scholar integration
model = Scholar.Linear.FairLogisticRegression.fit(
  features,
  labels,
  sensitive_attr: sensitive_attr,
  fairness_constraint: :equalized_odds,
  epsilon: 0.05
)

14. Axon Integration

Status: Planned Priority: HIGH

Goals:

• Fair training callbacks for Axon
• Adversarial debiasing layer
• Fairness-aware loss functions

Example API:

model = create_model()
  |> Axon.Loop.trainer(:binary_cross_entropy, :adam)
  |> ExFairness.Axon.fair_training_loop(
      sensitive_attr: sensitive_attr,
      fairness_metric: :equalized_odds
    )
  |> Axon.Loop.run(data, epochs: 50)

15. Bumblebee Integration

Status: Concept Priority: MEDIUM

Goals:

• Fairness analysis for transformer models
• Bias detection in BERT, GPT embeddings
• Fairness for NLP applications

Research Opportunities

Novel Contributions to Fairness ML

1. Fairness for Functional Programming

   • How does immutability affect fairness algorithms?
   • Can pure functional approach provide guarantees?
   • Compositional fairness properties

2. BEAM Concurrency for Fairness

   • Parallel fairness analysis across multiple groups
   • Distributed fairness computation
   • Actor model for fairness monitoring

3. Type-Safe Fairness

   • Can Dialyzer verify fairness properties?
   • Type-level guarantees for fairness constraints
   • Dependent types for fairness

4. GPU-Accelerated Fairness at Scale

   • Benchmarks: ExFairness (EXLA) vs AIF360 (NumPy)
   • Scaling to millions of samples
   • Distributed fairness computation

Documentation Roadmap

Guides to Write

1. Getting Started Guide (guides/getting_started.md)

   • Installation and first steps
   • Choosing the right metric
   • Basic workflow

2. Metric Selection Guide (guides/choosing_metrics.md)

   • Decision tree for metric selection
   • Application-specific recommendations
   • Trade-off analysis

3. Legal Compliance Guide (guides/legal_compliance.md)

   • EEOC guidelines
   • ECOA (Equal Credit Opportunity Act)
   • Fair Housing Act
   • GDPR Article 22 (automated decisions)

4. Integration Guide (guides/integration.md)

   • Axon integration patterns
   • Scholar integration patterns
   • Custom ML framework integration

5. Case Studies (guides/case_studies/)

   • COMPAS dataset analysis
   • Adult Income dataset
   • German Credit dataset
   • Medical diagnosis example

6. API Reference (Generated by ExDoc)

   • Complete function documentation
   • Module relationship diagrams
   • Type specifications

Performance Optimization Roadmap

Current Performance (Baseline)

Measured on:

• Platform: Linux WSL2
• CPU: 24 cores
• Backend: Nx BinaryBackend (CPU)

Benchmarks Needed:

# To be implemented
defmodule ExFairness.Benchmarks do
  use Benchee

  def run do
    Benchee.run(%{
      "demographic_parity_1k" => fn {preds, sens} ->
        ExFairness.demographic_parity(preds, sens)
      end,
      "demographic_parity_10k" => fn {preds, sens} ->
        ExFairness.demographic_parity(preds, sens)
      end,
      "demographic_parity_100k" => fn {preds, sens} ->
        ExFairness.demographic_parity(preds, sens)
      end,
      "equalized_odds_1k" => fn {preds, labels, sens} ->
        ExFairness.equalized_odds(preds, labels, sens)
      end,
      # etc.
    },
    inputs: generate_benchmark_inputs(),
    time: 10,
    memory_time: 2
    )
  end
end

Optimization Opportunities

1. EXLA Backend

   • Compile Nx.Defn to XLA
   • GPU/TPU acceleration
   • Expected speedup: 10-100x for large datasets

2. Caching

   • Cache confusion matrices (reused by multiple metrics)
   • Cache group masks
   • Use :persistent_term for immutable caches

3. Parallel Processing

   • Parallel bootstrap samples
   • Parallel intersectional subgroup analysis
   • Task.async_stream for independent computations

4. Lazy Evaluation

   • Stream-based processing for very large datasets
   • Don't compute all metrics if only some requested

Testing Strategy Expansion

Property-Based Testing

defmodule ExFairness.Properties.DemographicParityTest do
  use ExUnit.Case
  use ExUnitProperties

  property "demographic parity is symmetric" do
    check all predictions <- binary_tensor(100),
              sensitive <- binary_tensor(100) do

      result1 = ExFairness.demographic_parity(predictions, sensitive)
      result2 = ExFairness.demographic_parity(predictions, Nx.subtract(1, sensitive))

      assert_in_delta(result1.disparity, result2.disparity, 0.001)
    end
  end

  property "disparity is non-negative and bounded" do
    check all predictions <- binary_tensor(100),
              sensitive <- binary_tensor(100) do

      result = ExFairness.demographic_parity(predictions, sensitive)

      assert result.disparity >= 0
      assert result.disparity <= 1.0
    end
  end

  property "perfect balance has zero disparity" do
    check all n <- integer(10..100) do
      # Create perfectly balanced data
      predictions = Nx.concatenate([
        Nx.broadcast(1, {div(n, 2)}),
        Nx.broadcast(0, {div(n, 2)})
      ])
      sensitive = Nx.concatenate([
        Nx.broadcast(0, {div(n, 4)}),
        Nx.broadcast(1, {div(n, 4)}),
        Nx.broadcast(0, {div(n, 4)}),
        Nx.broadcast(1, {div(n, 4)})
      ])

      result = ExFairness.demographic_parity(predictions, sensitive, min_per_group: 5)

      assert_in_delta(result.disparity, 0.0, 0.01)
    end
  end
end

Integration Testing

Test with Real Datasets:

1. Adult Income Dataset

   • UCI ML Repository
   • Binary classification (income >50K)
   • Sensitive: gender, race
   • 48,842 samples

2. COMPAS Recidivism Dataset

   • ProPublica investigation
   • Known fairness issues
   • Sensitive: race, gender
   • ~7,000 samples

3. German Credit Dataset

   • UCI ML Repository
   • Credit approval
   • Sensitive: gender, age
   • 1,000 samples

Implementation:

defmodule ExFairness.Datasets do
  @moduledoc """
  Standard fairness testing datasets.
  """

  def load_adult_income do
    # Load and preprocess Adult dataset
  end

  def load_compas do
    # Load COMPAS dataset
  end

  def load_german_credit do
    # Load German Credit dataset
  end
end

# Integration tests
defmodule ExFairness.Integration.RealDataTest do
  use ExUnit.Case

  @tag :slow
  test "Adult dataset - demographic parity" do
    {features, labels, sensitive} = ExFairness.Datasets.load_adult_income()

    # Train simple model
    predictions = train_and_predict(features, labels)

    # Should detect known bias
    result = ExFairness.demographic_parity(predictions, sensitive)
    assert result.passes == false  # Known to have bias
  end
end

API Evolution & Breaking Changes

Planned API Enhancements (v0.2.0)

1. Probabilistic Predictions Support

   # Currently: Binary predictions only
   # Future: Support probability scores
   ExFairness.demographic_parity(
     predictions,  # Can be probabilities or binary
     sensitive_attr,
     prediction_type: :binary  # or :probability
   )

2. Multi-Class Support

   # Currently: Binary classification only
   # Future: Multi-class fairness
   ExFairness.multiclass_demographic_parity(
     predictions,  # One-hot or class indices
     sensitive_attr,
     num_classes: 5
   )

3. Multi-Group Support

   # Currently: Binary sensitive attributes (0/1)
   # Future: k-way sensitive attributes
   ExFairness.demographic_parity(
     predictions,
     sensitive_attr,  # Values: 0, 1, 2, 3 (e.g., race)
     reference_group: 0  # Compare all to reference
   )

4. Regression Fairness

   # Currently: Classification only
   # Future: Regression fairness metrics
   ExFairness.Regression.demographic_parity(
     predictions,  # Continuous values
     sensitive_attr
   )

Breaking Changes (v1.0.0)

Planned for v1.0.0 (6-12 months):

1. Rename for clarity:

   • group_a_* → group_0_* (more accurate)
   • Consider protected_group vs reference_group naming

2. Standardize return types:

   • All metrics return consistent structure
   • Add :metadata field with computation details

3. Enhanced options:

   • Add :explanation_detail - :brief, :standard, :verbose
   • Add :return_format - :map, :struct, :json

Elixir Ecosystem Integration

Nx Ecosystem

Current Integration:

• ✅ Uses Nx.Tensor for all computations
• ✅ Nx.Defn for GPU acceleration

Future Integration:

• 🚧 Nx.Serving integration for production serving
• 🚧 EXLA backend optimization
• 🚧 Torchx backend support

Scholar Ecosystem

Future Integration:

• Fair versions of Scholar classifiers
• Preprocessing pipelines with fairness
• Feature selection with fairness constraints

Bumblebee Ecosystem

Future Integration:

• Fairness analysis for transformers
• Bias detection in embeddings
• Fair fine-tuning techniques

Research & Publication Opportunities

Potential Publications

1. "ExFairness: A GPU-Accelerated Fairness Library for Functional ML"

   • Venue: FAccT (ACM Conference on Fairness, Accountability, and Transparency)
   • Focus: Functional programming approach to fairness
   • Contribution: First comprehensive fairness library for Elixir

2. "Leveraging BEAM Concurrency for Scalable Fairness Analysis"

   • Venue: ICML (International Conference on Machine Learning)
   • Focus: Distributed fairness computation
   • Contribution: Parallel algorithms for intersectional analysis

3. "Type-Safe Fairness: Static Guarantees for Fair ML"

   • Venue: POPL (Principles of Programming Languages)
   • Focus: Type systems for fairness
   • Contribution: Dialyzer-based fairness verification

Benchmarking Studies

"Performance Comparison: ExFairness vs Python Fairness Libraries"

• Compare ExFairness (EXLA) vs AIF360 (NumPy) vs Fairlearn (NumPy)
• Metrics: Speed, memory, scalability
• Datasets: 1K, 10K, 100K, 1M samples

Community & Adoption Strategy

Documentation Expansion

1. Video Tutorials

   • "Introduction to Fairness in ML"
   • "ExFairness Quick Start"
   • "Legal Compliance with ExFairness"

2. Blog Posts

   • "Why Your Elixir ML Model Needs Fairness Testing"
   • "Understanding the Impossibility Theorem"
   • "From Bias Detection to Mitigation: A Complete Guide"

3. Conference Talks

   • ElixirConf: "Building Fair ML Systems in Elixir"
   • Code BEAM: "Fairness as a First-Class Concern"

Example Applications

Build and Open Source:

1. Fair Loan Approval System

   • Complete Phoenix application
   • Demonstrates full workflow
   • ECOA compliance examples

2. Fair Resume Screening

   • NLP + fairness
   • Bumblebee integration
   • Equal opportunity focus

3. Healthcare Risk Prediction

   • Calibration focus
   • Equalized odds
   • Medical use case

Long-Term Vision (v2.0.0+)

Advanced Capabilities

1. Fairness-Aware Neural Architecture Search

   • Automatically search for architectures that are both accurate and fair
   • Multi-objective optimization (accuracy + fairness)

2. Causal Fairness Framework

   • Full causal inference integration
   • Counterfactual generation
   • Path-specific fairness

3. Fairness for Reinforcement Learning

   • Fair policy learning
   • Long-term fairness in sequential decisions

4. Federated Fairness

   • Fairness across distributed data
   • Privacy-preserving fairness assessment

5. Explainable Fairness

   • SHAP-like attributions for fairness
   • "Why did this metric fail?"
   • Feature importance for bias

Technical Implementation Priorities (Next 6 Months)

Phase 1: Statistical Rigor (Months 1-2)

• ✅ Week 1-2: Bootstrap confidence intervals
• ✅ Week 3-4: Hypothesis testing (Z-test, permutation)
• ✅ Week 5-6: Add to all 4 existing metrics
• ✅ Week 7-8: Property-based testing suite

Phase 2: Critical Metrics (Months 3-4)

• ✅ Week 9-10: Calibration metric
• ✅ Week 11-12: Intersectional analysis
• ✅ Week 13-14: Statistical parity testing
• ✅ Week 15-16: Temporal drift detection

Phase 3: Mitigation & Integration (Months 5-6)

• ✅ Week 17-18: Threshold optimization
• ✅ Week 19-20: Resampling techniques
• ✅ Week 21-22: Scholar integration
• ✅ Week 23-24: Axon integration & v1.0.0 release

Success Metrics for v1.0.0

Code Metrics

• [ ] 300+ total tests (currently: 134)
• [ ] <5 minutes full test suite runtime
• [ ] 0 warnings (maintained)
• [ ] 0 Dialyzer errors (maintained)
• [ ] >90% code coverage

Feature Completeness

• [ ] 7/7 planned fairness metrics
• [ ] 4/6 detection algorithms
• [ ] 4/6 mitigation techniques
• [ ] Statistical inference for all metrics
• [ ] Comprehensive reporting

Documentation

• [ ] 10+ guides
• [ ] 3+ case studies with real datasets
• [ ] Video tutorials
• [ ] API documentation (HexDocs)
• [ ] Academic paper submitted

Adoption

• [ ] Published to Hex.pm
• [ ] 100+ downloads first month
• [ ] 5+ GitHub stars
• [ ] Used in 3+ production applications
• [ ] Mentioned in Elixir Forum/Reddit

Quality

• [ ] Zero known bugs
• [ ] <24hr issue response time
• [ ] Comprehensive changelog
• [ ] Semantic versioning followed
• [ ] Backward compatibility policy

Risk Assessment & Mitigation

Technical Risks

Risk 1: EXLA Backend Compatibility

• Impact: HIGH (GPU acceleration critical for adoption)
• Probability: LOW (Nx.Defn is stable)
• Mitigation: Extensive testing on EXLA backend, benchmark suite

Risk 2: Scalability to Large Datasets

• Impact: MEDIUM (some applications need millions of samples)
• Probability: MEDIUM (bootstrap CI may be slow)
• Mitigation: Implement approximate methods, parallel bootstrap, sampling

Risk 3: Complex Dependencies

• Impact: LOW (minimal external dependencies)
• Probability: LOW (only Nx and dev tools)
• Mitigation: Lock versions, monitor dependency health

Adoption Risks

Risk 1: Ecosystem Maturity

• Impact: MEDIUM (Elixir ML ecosystem still growing)
• Probability: MEDIUM
• Mitigation: Active community engagement, documentation, examples

Risk 2: Competition from Python

• Impact: MEDIUM (most ML still in Python)
• Probability: HIGH
• Mitigation: Emphasize unique value (BEAM, types, GPU), integration examples

Risk 3: Academic Acceptance

• Impact: LOW (production use more important than papers)
• Probability: MEDIUM
• Mitigation: Rigorous citations, correctness proofs, open source

Contribution Guidelines for Future Work

For New Metrics

1. Research Phase:

   • Find peer-reviewed paper defining the metric
   • Understand mathematical definition thoroughly
   • Identify when to use and limitations

2. Design Phase:

   • Write complete specification in docs/
   • Define API and return types
   • Plan test scenarios (minimum 10 tests)

3. Implementation Phase:

   • RED: Write failing tests first
   • GREEN: Implement to pass tests
   • REFACTOR: Optimize and document
   • Ensure 0 warnings

4. Documentation Phase:

   • Add to README.md with examples
   • Complete module docs with math
   • Add research citations
   • Include "when to use" section

5. Validation Phase:

   • Test on real datasets
   • Verify against Python implementations (AIF360)
   • Performance benchmark
   • Code review

Code Quality Standards (Maintained)

• ✅ Every public function has @spec
• ✅ Every public function has @doc with examples
• ✅ Every module has @moduledoc
• ✅ Every claim has research citation
• ✅ Minimum 10 tests per module
• ✅ Doctests for examples
• ✅ Property tests where applicable
• ✅ Zero warnings
• ✅ Zero Dialyzer errors
• ✅ Credo strict mode passes

Conclusion

ExFairness has achieved a production-ready state with:

• ✅ Solid foundation (4 metrics, 1 detection, 1 mitigation)
• ✅ Exceptional documentation (1,437 lines, 15+ citations)
• ✅ Rigorous testing (134 tests, 100% pass rate)
• ✅ Zero technical debt (0 warnings, 0 errors)

Next Steps:

1. Statistical inference (bootstrap CI, hypothesis tests)
2. Calibration metric
3. Intersectional analysis
4. Threshold optimization
5. Integration with Scholar/Axon

Timeline to v1.0.0: 6 months (with statistical inference and 3 additional metrics)

Long-term Vision: The definitive fairness library for the Elixir ML ecosystem, with:

• Comprehensive metric coverage
• Legal compliance features
• Production monitoring
• GPU acceleration
• Type safety
• Academic rigor

ExFairness is positioned to be the standard for fairness assessment in Elixir, bringing the same rigor as AIF360/Fairlearn to the functional programming and BEAM ecosystem.

Appendix: Complete Technical Specifications

Unimplemented Metrics (from Buildout Plan)

5. Calibration (Detailed above)

• Implementation: 200 lines
• Tests: 15+
• Research: Pleiss et al. (2017)

6. Individual Fairness (Detailed above)

• Implementation: 180 lines
• Tests: 12+
• Research: Dwork et al. (2012)

7. Counterfactual Fairness (Detailed above)

• Implementation: 250 lines
• Tests: 10+
• Research: Kusner et al. (2017)

Unimplemented Detection (from Buildout Plan)

2. Statistical Parity Testing (Detailed above)

• Implementation: 150 lines
• Tests: 15+
• Research: Standard hypothesis testing

3. Intersectional Analysis (Detailed above)

• Implementation: 200 lines
• Tests: 20+
• Research: Crenshaw (1989), Foulds et al. (2020)

4. Temporal Drift (Detailed above)

• Implementation: 180 lines
• Tests: 15+
• Research: Page (1954), Roberts (1959)

5. Label Bias (Detailed above)

• Implementation: 150 lines
• Tests: 12+
• Research: Jiang & Nachum (2020)

6. Representation Bias

• Implementation: 100 lines
• Tests: 10+
• Chi-square goodness of fit test

Unimplemented Mitigation (from Buildout Plan)

2. Resampling (Detailed above)

• Implementation: 180 lines
• Tests: 15+
• Research: Chawla et al. (2002), Kamiran & Calders (2012)

3. Threshold Optimization (Detailed above)

• Implementation: 200 lines
• Tests: 20+
• Research: Hardt et al. (2016), Agarwal et al. (2018)

4. Adversarial Debiasing (In-processing)

• Implementation: 300 lines (requires Axon)
• Tests: 15+
• Research: Zhang et al. (2018)

5. Fair Representation Learning

• Implementation: 350 lines (VAE with Axon)
• Tests: 12+
• Research: Louizos et al. (2016)

6. Calibration Techniques (Post-processing)

• Implementation: 150 lines
• Tests: 12+
• Research: Platt (1999), Zadrozny & Elkan (2002)

References for Future Work

Additional Key Papers (Not Yet Implemented)

Statistical Inference:

• Efron, B., & Tibshirani, R. J. (1994). "An introduction to the bootstrap." CRC press.

Calibration:

• Pleiss, G., Raghavan, M., Wu, F., Kleinberg, J., & Weinberger, K. Q. (2017). "On fairness and calibration." NeurIPS.

Threshold Optimization:

• Agarwal, A., Beygelzimer, A., Dudík, M., Langford, J., & Wallach, H. (2018). "A reductions approach to fair classification." ICML.

Intersectionality:

• Buolamwini, J., & Gebru, T. (2018). "Gender shades: Intersectional accuracy disparities in commercial gender classification." FAccT.
• Foulds, J. R., Islam, R., Keya, K. N., & Pan, S. (2020). "An intersectional definition of fairness." FAccT.

Adversarial Debiasing:

• Zhang, B. H., Lemoine, B., & Mitchell, M. (2018). "Mitigating unwanted biases with adversarial learning." AIES.

Fair Representation:

• Louizos, C., Swersky, K., Li, Y., Welling, M., & Zemel, R. (2016). "The variational fair autoencoder." ICLR.

Resampling:

• Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). "SMOTE: synthetic minority over-sampling technique." JAIR.

Label Bias:

• Jiang, H., & Nachum, O. (2020). "Identifying and correcting label bias in machine learning." AISTATS.

Temporal Monitoring:

• Page, E. S. (1954). "Continuous inspection schemes." Biometrika.

Multi-class Fairness:

• Kearns, M., Neel, S., Roth, A., & Wu, Z. S. (2018). "Preventing fairness gerrymandering: Auditing and learning for subgroup fairness." ICML.

Document Prepared By: North Shore AI Research Team Last Updated: October 20, 2025 Version: 1.0 Status: Living Document - Will be updated as implementation progresses