Rare-Event Backtest and Confidence Bounds

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/** Reference implementations for D40-F05 classification and score validation. */

type AnyRecord = Record<string, any>;

function numberValue(value: unknown, name: string): number {
  if (typeof value !== "number" || !Number.isFinite(value)) throw new TypeError(`${name} must be finite numeric`);
  return value;
}

function integerValue(value: unknown, name: string): number {
  const result = numberValue(value, name);
  if (!Number.isInteger(result)) throw new RangeError(`${name} must be an integer`);
  return result;
}

function records(inputs: AnyRecord, options: { score?: boolean; probability?: boolean } = {}): AnyRecord[] {
  if (!Array.isArray(inputs.records) || inputs.records.length === 0) throw new RangeError("records must be a nonempty array");
  const cutoff = inputs.evaluation_cutoff;
  if (cutoff !== undefined && (typeof cutoff !== "string" || cutoff.length === 0)) throw new TypeError("evaluation_cutoff must be a nonempty ISO-8601 string");
  const seen = new Set<string>();
  return inputs.records.map((raw: unknown, index: number) => {
    if (!raw || typeof raw !== "object" || Array.isArray(raw)) throw new TypeError(`records[${index}] must be an object`);
    const item = raw as AnyRecord;
    if (typeof item.id !== "string" || item.id.length === 0 || seen.has(item.id)) throw new RangeError("record ids must be unique nonempty strings");
    seen.add(item.id);
    if (item.label !== 0 && item.label !== 1) throw new RangeError("labels must be numeric 0 or 1");
    const weight = numberValue(item.weight ?? 1, `records[${index}].weight`);
    if (weight <= 0) throw new RangeError("weights must be positive");
    const row: AnyRecord = { ...item, label: item.label, weight };
    if (options.score) row.score = numberValue(item.score, `records[${index}].score`);
    if (options.probability) {
      row.probability = numberValue(item.probability, `records[${index}].probability`);
      if (row.probability < 0 || row.probability > 1) throw new RangeError("probabilities must be in [0,1]");
    }
    if (cutoff !== undefined) {
      for (const key of ["score_available_at", "label_available_at"]) {
        const timestamp = item[key];
        if (timestamp !== undefined) {
          if (typeof timestamp !== "string" || timestamp.length === 0) throw new TypeError(`${key} must be a nonempty ISO-8601 string`);
          if (timestamp > cutoff) throw new RangeError(`${key} exceeds evaluation_cutoff`);
        }
      }
    }
    return row;
  });
}

function classWeights(rows: AnyRecord[]): [number, number] {
  let positive = 0, negative = 0;
  for (const row of rows) row.label === 1 ? positive += row.weight : negative += row.weight;
  return [positive, negative];
}

function scoreGroups(rows: AnyRecord[]): Array<[number, AnyRecord[]]> {
  const ordered = [...rows].sort((a, b) => b.score - a.score || String(a.id).localeCompare(String(b.id)));
  const groups: Array<[number, AnyRecord[]]> = [];
  for (const row of ordered) {
    const last = groups.at(-1);
    if (!last || last[0] !== row.score) groups.push([row.score, [row]]);
    else last[1].push(row);
  }
  return groups;
}

export function rocCurveAuc(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { score: true });
  const [positive, negative] = classWeights(rows);
  if (positive <= 0 || negative <= 0) throw new RangeError("ROC requires positive and negative weight");
  let tp = 0, fp = 0;
  const points: AnyRecord[] = [{ threshold: null, true_positive: 0, false_positive: 0, true_negative: negative, false_negative: positive, tpr: 0, fpr: 0 }];
  for (const [threshold, group] of scoreGroups(rows)) {
    for (const row of group) row.label === 1 ? tp += row.weight : fp += row.weight;
    points.push({ threshold, true_positive: tp, false_positive: fp, true_negative: negative - fp, false_negative: positive - tp, tpr: tp / positive, fpr: fp / negative });
  }
  let auc = 0;
  for (let i = 1; i < points.length; i++) auc += (points[i].fpr - points[i - 1].fpr) * (points[i].tpr + points[i - 1].tpr) / 2;
  return { points, roc_auc: auc, positive_weight: positive, negative_weight: negative, tie_group_count: points.length - 1, state: "ranking-evaluated" };
}

export function precisionRecallAuc(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { score: true });
  const [positive, negative] = classWeights(rows);
  if (positive <= 0) throw new RangeError("precision-recall requires positive weight");
  let tp = 0, fp = 0, previousRecall = 0, averagePrecision = 0;
  const points: AnyRecord[] = [{ threshold: null, true_positive: 0, false_positive: 0, precision: 1, recall: 0 }];
  for (const [threshold, group] of scoreGroups(rows)) {
    for (const row of group) row.label === 1 ? tp += row.weight : fp += row.weight;
    const precision = tp / (tp + fp), recall = tp / positive;
    averagePrecision += (recall - previousRecall) * precision;
    previousRecall = recall;
    points.push({ threshold, true_positive: tp, false_positive: fp, precision, recall });
  }
  return { points, pr_auc_average_precision: averagePrecision, baseline_prevalence: positive / (positive + negative), positive_weight: positive, negative_weight: negative, tie_group_count: points.length - 1, integration_rule: "average-precision-right-step", state: "ranking-evaluated" };
}

export function brierScore(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { probability: true });
  const total = rows.reduce((sum, row) => sum + row.weight, 0);
  const eventWeight = rows.reduce((sum, row) => sum + row.weight * row.label, 0);
  const eventRate = eventWeight / total;
  const score = rows.reduce((sum, row) => sum + row.weight * (row.probability - row.label) ** 2, 0) / total;
  const baseline = eventRate * (1 - eventRate);
  return { brier_score: score, event_rate: eventRate, baseline_brier: baseline, brier_skill: baseline === 0 ? null : 1 - score / baseline, weight_sum: total, record_count: rows.length, state: "probability-evaluated" };
}

export function binaryLogLoss(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { probability: true });
  const epsilon = numberValue(inputs.epsilon ?? 1e-15, "epsilon");
  if (epsilon <= 0 || epsilon >= 0.5) throw new RangeError("epsilon must be in (0,0.5)");
  const total = rows.reduce((sum, row) => sum + row.weight, 0);
  const eventWeight = rows.reduce((sum, row) => sum + row.weight * row.label, 0);
  let loss = 0, clippedCount = 0;
  for (const row of rows) {
    const q = Math.min(Math.max(row.probability, epsilon), 1 - epsilon);
    if (q !== row.probability) clippedCount++;
    loss += row.weight * -Math.log(row.label === 1 ? q : 1 - q);
  }
  return { log_loss: loss / total, clipped_count: clippedCount, epsilon, weight_sum: total, event_rate: eventWeight / total, state: "probability-evaluated" };
}

export function reliabilityEce(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { probability: true });
  const binCount = integerValue(inputs.bins ?? 5, "bins");
  if (binCount < 2 || binCount > 20) throw new RangeError("bins must be between 2 and 20");
  if ((inputs.bin_strategy ?? "uniform") !== "uniform") throw new RangeError("only uniform bin_strategy is supported");
  const total = rows.reduce((sum, row) => sum + row.weight, 0);
  const ledgers: AnyRecord[][] = Array.from({ length: binCount }, () => []);
  for (const row of rows) ledgers[Math.min(Math.floor(row.probability * binCount), binCount - 1)].push(row);
  const bins: AnyRecord[] = [];
  let ece = 0, mce = 0, signed = 0;
  for (let index = 0; index < binCount; index++) {
    const members = ledgers[index], lower = index / binCount, upper = (index + 1) / binCount;
    if (members.length === 0) {
      bins.push({ index: index + 1, lower, upper, right_inclusive: index === binCount - 1, record_count: 0, weight_sum: 0, mean_probability: null, event_rate: null, signed_gap: null, absolute_gap: null });
      continue;
    }
    const weight = members.reduce((sum, row) => sum + row.weight, 0);
    const meanProbability = members.reduce((sum, row) => sum + row.weight * row.probability, 0) / weight;
    const eventRate = members.reduce((sum, row) => sum + row.weight * row.label, 0) / weight;
    const signedGap = eventRate - meanProbability, absoluteGap = Math.abs(signedGap);
    ece += weight / total * absoluteGap;
    signed += weight / total * signedGap;
    mce = Math.max(mce, absoluteGap);
    bins.push({ index: index + 1, lower, upper, right_inclusive: index === binCount - 1, record_count: members.length, weight_sum: weight, mean_probability: meanProbability, event_rate: eventRate, signed_gap: signedGap, absolute_gap: absoluteGap });
  }
  return { bins, expected_calibration_error: ece, maximum_calibration_error: mce, signed_calibration_error: signed, bin_count: binCount, weight_sum: total, state: "calibration-evaluated" };
}

export function gainsLift(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { score: true });
  const bucketCount = integerValue(inputs.buckets ?? 10, "buckets");
  if (bucketCount < 2 || bucketCount > rows.length) throw new RangeError("buckets must be between 2 and record count");
  const ordered = [...rows].sort((a, b) => b.score - a.score || String(a.id).localeCompare(String(b.id)));
  const totalWeight = ordered.reduce((sum, row) => sum + row.weight, 0);
  const totalEvents = ordered.reduce((sum, row) => sum + row.weight * row.label, 0);
  if (totalEvents <= 0) throw new RangeError("gains and lift require positive event weight");
  const prevalence = totalEvents / totalWeight;
  const members: Array<Array<[number, AnyRecord]>> = Array.from({ length: bucketCount }, () => []);
  ordered.forEach((row, rank) => members[Math.min(Math.floor(rank * bucketCount / ordered.length), bucketCount - 1)].push([rank + 1, row]));
  let cumulativeWeight = 0, cumulativeEvents = 0;
  const buckets = members.map((bucket, index) => {
    const weight = bucket.reduce((sum, [, row]) => sum + row.weight, 0);
    const events = bucket.reduce((sum, [, row]) => sum + row.weight * row.label, 0);
    cumulativeWeight += weight; cumulativeEvents += events;
    const populationShare = weight / totalWeight, eventCapture = events / totalEvents;
    const cumulativePopulation = cumulativeWeight / totalWeight, cumulativeGain = cumulativeEvents / totalEvents;
    return { bucket: index + 1, rank_start: bucket[0][0], rank_end: bucket.at(-1)![0], record_count: bucket.length, population_weight: weight, event_weight: events, population_share: populationShare, event_capture: eventCapture, bucket_lift: (events / weight) / prevalence, cumulative_population: cumulativePopulation, cumulative_gain: cumulativeGain, cumulative_lift: cumulativeGain / cumulativePopulation };
  });
  return { buckets, top_decile_capture: buckets[0].event_capture, overall_prevalence: prevalence, total_events: totalEvents, total_weight: totalWeight, bucket_count: bucketCount, tie_break: "score-descending-id-ascending", state: "ranking-evaluated" };
}

export function costSensitiveThreshold(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { score: true });
  if (!inputs.costs || typeof inputs.costs !== "object" || Array.isArray(inputs.costs)) throw new TypeError("costs must be an object");
  const names = ["false_positive", "false_negative", "true_positive", "true_negative"];
  const costs: AnyRecord = {};
  for (const name of names) costs[name] = numberValue(inputs.costs[name], `costs.${name}`);
  if (names.some(name => costs[name] < 0) || (costs.false_positive === 0 && costs.false_negative === 0)) throw new RangeError("costs must be nonnegative with a positive misclassification cost");
  const total = rows.reduce((sum, row) => sum + row.weight, 0);
  const thresholds: Array<number | null> = [null, ...[...new Set(rows.map(row => row.score))].sort((a, b) => b - a)];
  const candidates = thresholds.map(threshold => {
    let tp = 0, fp = 0, tn = 0, fn = 0, selected = 0;
    for (const row of rows) {
      const predicted = threshold !== null && row.score >= threshold;
      if (predicted) selected += row.weight;
      if (predicted && row.label === 1) tp += row.weight;
      else if (predicted && row.label === 0) fp += row.weight;
      else if (!predicted && row.label === 0) tn += row.weight;
      else fn += row.weight;
    }
    const expectedCost = (costs.false_positive * fp + costs.false_negative * fn + costs.true_positive * tp + costs.true_negative * tn) / total;
    return { threshold, true_positive: tp, false_positive: fp, true_negative: tn, false_negative: fn, selected_weight: selected, selected_rate: selected / total, expected_cost: expectedCost };
  });
  const optimal = [...candidates].sort((a, b) => a.expected_cost - b.expected_cost || a.selected_weight - b.selected_weight || -((a.threshold ?? Infinity) - (b.threshold ?? Infinity)))[0];
  return { candidates, optimal_threshold: optimal.threshold, optimal_expected_cost: optimal.expected_cost, optimal_selected_rate: optimal.selected_rate, optimal_confusion: { true_positive: optimal.true_positive, false_positive: optimal.false_positive, true_negative: optimal.true_negative, false_negative: optimal.false_negative }, costs, tie_break: "minimum-cost-then-lower-selected-weight-then-higher-threshold", state: "threshold-selected" };
}

function band(score: number, edges: number[]): number {
  let result = 0;
  while (result + 1 < edges.length && score >= edges[result + 1]) result++;
  return Math.min(result, edges.length - 2);
}

export function scoreMigration(inputs: AnyRecord): AnyRecord {
  if (!Array.isArray(inputs.baseline) || inputs.baseline.length === 0 || !Array.isArray(inputs.current) || inputs.current.length === 0) throw new RangeError("baseline and current must be nonempty arrays");
  if (inputs.higher_score_higher_risk !== true) throw new RangeError("canonical orientation requires higher_score_higher_risk=true");
  if (typeof inputs.baseline_observed_at !== "string" || typeof inputs.current_observed_at !== "string" || inputs.baseline_observed_at >= inputs.current_observed_at) throw new RangeError("baseline_observed_at must be before current_observed_at");
  if (!Array.isArray(inputs.band_edges) || inputs.band_edges.length < 3) throw new RangeError("band_edges must contain at least three values");
  const edges = inputs.band_edges.map((value: unknown) => numberValue(value, "band_edges"));
  if (edges[0] !== 0 || edges.at(-1) !== 1 || edges.slice(1).some((value: number, index: number) => edges[index] >= value)) throw new RangeError("band_edges must increase strictly from 0 to 1");
  function snapshot(rawRows: unknown[], name: string): Map<string, number> {
    const result = new Map<string, number>();
    rawRows.forEach((raw, index) => {
      if (!raw || typeof raw !== "object" || Array.isArray(raw)) throw new TypeError(`${name}[${index}] must be an object`);
      const row = raw as AnyRecord;
      if (typeof row.id !== "string" || row.id.length === 0 || result.has(row.id)) throw new RangeError(`${name} ids must be unique nonempty strings`);
      const score = numberValue(row.score, `${name}[${index}].score`);
      if (score < 0 || score > 1) throw new RangeError("migration scores must be in [0,1]");
      result.set(row.id, score);
    });
    return result;
  }
  const baseline = snapshot(inputs.baseline, "baseline"), current = snapshot(inputs.current, "current");
  if (baseline.size !== current.size || [...baseline.keys()].some(id => !current.has(id))) throw new RangeError("baseline and current must contain identical ids");
  const size = edges.length - 1, matrix = Array.from({ length: size }, () => Array(size).fill(0));
  const migrations: AnyRecord[] = [];
  let stable = 0, improved = 0, worsened = 0, absoluteMove = 0, scoreChange = 0, absoluteScoreChange = 0;
  for (const id of [...baseline.keys()].sort()) {
    const before = baseline.get(id)!, after = current.get(id)!;
    const a = band(before, edges), b = band(after, edges), move = b - a, delta = after - before;
    matrix[a][b]++;
    move === 0 ? stable++ : move < 0 ? improved++ : worsened++;
    absoluteMove += Math.abs(move); scoreChange += delta; absoluteScoreChange += Math.abs(delta);
    migrations.push({ id, baseline_score: before, current_score: after, baseline_band: a + 1, current_band: b + 1, band_move: move, score_change: delta });
  }
  const rowRates = matrix.map(row => { const total = row.reduce((sum, value) => sum + value, 0); return row.map(value => total === 0 ? null : value / total); });
  const baselineCounts = matrix.map(row => row.reduce((sum, value) => sum + value, 0));
  const currentCounts = Array.from({ length: size }, (_, column) => matrix.reduce((sum, row) => sum + row[column], 0));
  const n = baseline.size, baselineShares = baselineCounts.map(value => value / n), currentShares = currentCounts.map(value => value / n);
  const tv = 0.5 * baselineShares.reduce((sum, value, index) => sum + Math.abs(value - currentShares[index]), 0);
  return { band_edges: edges, matrix, row_rates: rowRates, baseline_band_shares: baselineShares, current_band_shares: currentShares, migrations, matched_count: n, stable_count: stable, improved_count: improved, worsened_count: worsened, stable_rate: stable / n, mean_band_move: migrations.reduce((sum, row) => sum + row.band_move, 0) / n, mean_absolute_band_move: absoluteMove / n, mean_score_change: scoreChange / n, mean_absolute_score_change: absoluteScoreChange / n, band_distribution_total_variation: tv, state: "migration-evaluated" };
}

function basicMetrics(rows: AnyRecord[], epsilon: number): AnyRecord {
  const total = rows.reduce((sum, row) => sum + row.weight, 0), [positive, negative] = classWeights(rows);
  const eventRate = positive / total;
  const brier = rows.reduce((sum, row) => sum + row.weight * (row.probability - row.label) ** 2, 0) / total;
  const logloss = rows.reduce((sum, row) => { const q = Math.min(Math.max(row.probability, epsilon), 1 - epsilon); return sum + row.weight * -Math.log(row.label === 1 ? q : 1 - q); }, 0) / total;
  const auc = positive > 0 && negative > 0 ? rocCurveAuc({ records: rows }).roc_auc : null;
  return { record_count: rows.length, weight_sum: total, positive_weight: positive, negative_weight: negative, event_rate: eventRate, brier_score: brier, log_loss: logloss, roc_auc: auc };
}

export function sliceValidation(inputs: AnyRecord): AnyRecord {
  const rows = records(inputs, { score: true, probability: true });
  if (!Array.isArray(inputs.slice_fields) || inputs.slice_fields.length === 0 || new Set(inputs.slice_fields).size !== inputs.slice_fields.length || inputs.slice_fields.some((field: unknown) => typeof field !== "string" || field.length === 0)) throw new RangeError("slice_fields must be unique nonempty strings");
  const fields = inputs.slice_fields as string[], minimum = integerValue(inputs.minimum_support ?? 4, "minimum_support");
  if (minimum < 2) throw new RangeError("minimum_support must be at least 2");
  const epsilon = numberValue(inputs.epsilon ?? 1e-15, "epsilon");
  if (epsilon <= 0 || epsilon >= 0.5) throw new RangeError("epsilon must be in (0,0.5)");
  for (const field of fields) if (rows.some(row => typeof row[field] !== "string" || row[field].length === 0)) throw new RangeError(`slice field ${field} is missing or invalid`);
  const overall = basicMetrics(rows, epsilon), slices: AnyRecord[] = [], eligibleBrier: number[] = [];
  let eligible = 0, flagged = 0;
  for (const field of fields) {
    const values = [...new Set(rows.map(row => row[field] as string))].sort();
    for (const value of values) {
      const members = rows.filter(row => row[field] === value), metrics = basicMetrics(members, epsilon);
      let status = "ok";
      if (members.length < minimum) status = "insufficient-support";
      else if (metrics.positive_weight <= 0 || metrics.negative_weight <= 0) status = "single-class";
      if (status === "ok") { eligible++; eligibleBrier.push(metrics.brier_score); } else flagged++;
      slices.push({ field, value, status, ...metrics, brier_gap_from_overall: metrics.brier_score - overall.brier_score, log_loss_gap_from_overall: metrics.log_loss - overall.log_loss, roc_auc_gap_from_overall: metrics.roc_auc === null ? null : metrics.roc_auc - overall.roc_auc });
    }
  }
  if (eligibleBrier.length === 0) throw new RangeError("no slice meets the canonical support and class requirements");
  return { overall, slices, slice_fields: fields, minimum_support: minimum, worst_slice_brier: Math.max(...eligibleBrier), eligible_slice_count: eligible, flagged_slice_count: flagged, state: "slices-evaluated" };
}

export function rareEventBounds(inputs: AnyRecord): AnyRecord {
  const events = integerValue(inputs.observed_events, "observed_events"), trials = integerValue(inputs.trials, "trials");
  if (trials <= 0 || events < 0 || events > trials) throw new RangeError("require 0 <= observed_events <= trials and trials > 0");
  const expected = numberValue(inputs.expected_probability, "expected_probability");
  if (expected < 0 || expected > 1) throw new RangeError("expected_probability must be in [0,1]");
  const confidence = numberValue(inputs.confidence_level, "confidence_level");
  const zMap = new Map([[0.90, 1.6448536269514722], [0.95, 1.959963984540054], [0.99, 2.5758293035489004]]);
  const z = zMap.get(confidence);
  if (z === undefined) throw new RangeError("confidence_level must be 0.90, 0.95, or 0.99");
  if (inputs.sampling_assumption !== "independent-bernoulli-approximation") throw new RangeError("unsupported sampling_assumption");
  const observed = events / trials, denominator = 1 + z * z / trials;
  const center = (observed + z * z / (2 * trials)) / denominator;
  const half = z * Math.sqrt(observed * (1 - observed) / trials + z * z / (4 * trials * trials)) / denominator;
  const lower = events === 0 ? 0 : Math.max(0, center - half), upper = events === trials ? 1 : Math.min(1, center + half);
  const consistency = expected < lower ? "expected-below-interval" : expected > upper ? "expected-above-interval" : "inside-interval";
  return { observed_events: events, trials, observed_rate: observed, expected_probability: expected, expected_count: trials * expected, confidence_level: confidence, z_value: z, wilson_center: center, wilson_half_width: half, wilson_lower: lower, wilson_upper: upper, consistency, sampling_assumption: "independent-bernoulli-approximation", state: "rare-event-evaluated" };
}

export function calculate(topicId: string, inputs: AnyRecord): AnyRecord {
  if (!inputs || typeof inputs !== "object" || Array.isArray(inputs)) throw new TypeError("inputs must be an object");
  const dispatch: Record<string, (value: AnyRecord) => AnyRecord> = {
    "D40-F05-A01": rocCurveAuc,
    "D40-F05-A02": precisionRecallAuc,
    "D40-F05-A03": brierScore,
    "D40-F05-A04": binaryLogLoss,
    "D40-F05-A05": reliabilityEce,
    "D40-F05-A06": gainsLift,
    "D40-F05-A07": costSensitiveThreshold,
    "D40-F05-A08": scoreMigration,
    "D40-F05-A09": sliceValidation,
    "D40-F05-A10": rareEventBounds,
  };
  const implementation = dispatch[topicId];
  if (!implementation) throw new RangeError(`unsupported topic_id: ${topicId}`);
  return implementation(inputs);
}