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Add Tukey's Biweight and WMAPE implementations with comprehensive tests and documentation
- Introduced Tukey's Biweight as a robust loss function, including mathematical foundation, usage patterns, and performance profile. - Added WMAPE (Weighted Mean Absolute Percentage Error) implementation, emphasizing its advantages for intermittent demand forecasting. - Created unit tests for WMAPE covering various scenarios including edge cases and batch calculations. - Documented both Tukey's Biweight and WMAPE with detailed explanations, properties, and common use cases.
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Miha Kralj
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using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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namespace QuanTAlib;
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/// <summary>
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/// TukeyBiweight: Tukey's Biweight (Bisquare) Loss
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/// </summary>
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/// <remarks>
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/// Tukey's Biweight is a robust loss function that completely rejects outliers
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/// beyond a threshold c. Unlike Huber loss which downweights outliers, Tukey's
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/// biweight assigns zero weight to extreme outliers, making it highly resistant
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/// to contaminated data.
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///
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/// Formula:
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/// ρ(x) = (c²/6) * (1 - (1 - (x/c)²)³) for |x| ≤ c
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/// ρ(x) = c²/6 for |x| > c
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///
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/// Key properties:
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/// - Completely rejects outliers beyond threshold c
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/// - Redescending: influence function goes to zero for large errors
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/// - Common c values: 4.685 (95% efficiency), 6.0 (more permissive)
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/// - More robust than Huber for heavily contaminated data
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/// - Smooth and differentiable everywhere
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/// </remarks>
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[SkipLocalsInit]
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public sealed class TukeyBiweight : AbstractBase
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{
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private readonly RingBuffer _lossBuffer;
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private readonly double _c;
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private readonly double _cSquaredOver6;
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[StructLayout(LayoutKind.Auto)]
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private record struct State(double LossSum, double LastValidActual, double LastValidPredicted, int TickCount);
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private State _state;
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private State _p_state;
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private const int ResyncInterval = 1000;
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private const double DefaultC = 4.685; // 95% efficiency for normal distribution
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public TukeyBiweight(int period, double c = DefaultC)
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{
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if (period <= 0)
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throw new ArgumentException("Period must be greater than 0", nameof(period));
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if (c <= 0)
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throw new ArgumentException("Threshold c must be positive", nameof(c));
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_lossBuffer = new RingBuffer(period);
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_c = c;
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_cSquaredOver6 = (c * c) / 6.0;
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Name = $"TukeyBiweight({period},{c:F3})";
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WarmupPeriod = period;
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}
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public double C => _c;
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public override bool IsHot => _lossBuffer.IsFull;
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/// <summary>
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/// Computes Tukey's biweight loss function.
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private double BiweightLoss(double x)
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{
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double absX = Math.Abs(x);
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if (absX > _c)
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return _cSquaredOver6;
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double ratio = x / _c;
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double ratioSq = ratio * ratio;
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double oneMinusRatioSq = 1.0 - ratioSq;
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double cubed = oneMinusRatioSq * oneMinusRatioSq * oneMinusRatioSq;
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return _cSquaredOver6 * (1.0 - cubed);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public TValue Update(TValue actual, TValue predicted, bool isNew = true)
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{
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double actualVal = actual.Value;
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double predictedVal = predicted.Value;
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if (!double.IsFinite(actualVal))
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actualVal = double.IsFinite(_state.LastValidActual) ? _state.LastValidActual : 0.0;
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else
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_state.LastValidActual = actualVal;
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if (!double.IsFinite(predictedVal))
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predictedVal = double.IsFinite(_state.LastValidPredicted) ? _state.LastValidPredicted : 0.0;
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else
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_state.LastValidPredicted = predictedVal;
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double error = actualVal - predictedVal;
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double loss = BiweightLoss(error);
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if (isNew)
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{
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_p_state = _state;
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double removedLoss = _lossBuffer.Count == _lossBuffer.Capacity ? _lossBuffer.Oldest : 0.0;
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_state.LossSum = _state.LossSum - removedLoss + loss;
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_lossBuffer.Add(loss);
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_state.TickCount++;
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if (_lossBuffer.IsFull && _state.TickCount >= ResyncInterval)
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{
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_state.TickCount = 0;
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_state.LossSum = _lossBuffer.RecalculateSum();
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}
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}
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else
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{
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_state = _p_state;
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double removedLoss = _lossBuffer.Count == _lossBuffer.Capacity ? _lossBuffer.Oldest : 0.0;
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_state.LossSum = _state.LossSum - removedLoss + loss;
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_lossBuffer.UpdateNewest(loss);
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_state.LossSum = _lossBuffer.RecalculateSum();
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}
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// Mean Tukey Biweight Loss
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double result = _lossBuffer.Count > 0 ? _state.LossSum / _lossBuffer.Count : 0.0;
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Last = new TValue(actual.Time, result);
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PubEvent(Last, isNew);
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return Last;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public TValue Update(double actual, double predicted, bool isNew = true)
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{
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return Update(new TValue(DateTime.UtcNow, actual), new TValue(DateTime.UtcNow, predicted), isNew);
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}
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public override TValue Update(TValue input, bool isNew = true)
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{
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throw new NotSupportedException("TukeyBiweight requires two inputs. Use Update(actual, predicted).");
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}
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public override TSeries Update(TSeries source)
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{
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throw new NotSupportedException("TukeyBiweight requires two inputs. Use Calculate(actualSeries, predictedSeries, period, c).");
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}
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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throw new NotSupportedException("TukeyBiweight requires two inputs.");
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}
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public override void Reset()
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{
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_lossBuffer.Clear();
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_state = default;
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_p_state = default;
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Last = default;
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}
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public static TSeries Calculate(TSeries actual, TSeries predicted, int period, double c = DefaultC)
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{
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if (actual.Count != predicted.Count)
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throw new ArgumentException("Actual and predicted series must have the same length", nameof(predicted));
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int len = actual.Count;
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var t = new List<long>(len);
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var v = new List<double>(len);
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CollectionsMarshal.SetCount(t, len);
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CollectionsMarshal.SetCount(v, len);
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var tSpan = CollectionsMarshal.AsSpan(t);
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var vSpan = CollectionsMarshal.AsSpan(v);
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Batch(actual.Values, predicted.Values, vSpan, period, c);
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actual.Times.CopyTo(tSpan);
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return new TSeries(t, v);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Batch(ReadOnlySpan<double> actual, ReadOnlySpan<double> predicted, Span<double> output, int period, double c = DefaultC)
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{
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if (actual.Length != predicted.Length || actual.Length != output.Length)
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throw new ArgumentException("All spans must have the same length", nameof(output));
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if (period <= 0)
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throw new ArgumentException("Period must be greater than 0", nameof(period));
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if (c <= 0)
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throw new ArgumentException("Threshold c must be positive", nameof(c));
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int len = actual.Length;
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if (len == 0) return;
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double cSquaredOver6 = (c * c) / 6.0;
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const int StackAllocThreshold = 256;
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Span<double> lossBuffer = period <= StackAllocThreshold
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? stackalloc double[period]
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: new double[period];
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double lossSum = 0;
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double lastValidActual = 0;
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double lastValidPredicted = 0;
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for (int k = 0; k < len; k++)
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{
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if (double.IsFinite(actual[k])) { lastValidActual = actual[k]; break; }
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}
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for (int k = 0; k < len; k++)
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{
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if (double.IsFinite(predicted[k])) { lastValidPredicted = predicted[k]; break; }
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}
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int bufferIndex = 0;
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int i = 0;
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int warmupEnd = Math.Min(period, len);
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for (; i < warmupEnd; i++)
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{
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double act = actual[i];
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double pred = predicted[i];
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if (double.IsFinite(act)) lastValidActual = act; else act = lastValidActual;
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if (double.IsFinite(pred)) lastValidPredicted = pred; else pred = lastValidPredicted;
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double error = act - pred;
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double loss;
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double absError = Math.Abs(error);
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if (absError > c)
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{
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loss = cSquaredOver6;
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}
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else
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{
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double ratio = error / c;
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double ratioSq = ratio * ratio;
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double oneMinusRatioSq = 1.0 - ratioSq;
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double cubed = oneMinusRatioSq * oneMinusRatioSq * oneMinusRatioSq;
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loss = cSquaredOver6 * (1.0 - cubed);
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}
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lossSum += loss;
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lossBuffer[i] = loss;
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output[i] = lossSum / (i + 1);
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}
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int tickCount = 0;
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for (; i < len; i++)
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{
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double act = actual[i];
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double pred = predicted[i];
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if (double.IsFinite(act)) lastValidActual = act; else act = lastValidActual;
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if (double.IsFinite(pred)) lastValidPredicted = pred; else pred = lastValidPredicted;
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double error = act - pred;
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double loss;
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double absError = Math.Abs(error);
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if (absError > c)
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{
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loss = cSquaredOver6;
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}
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else
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{
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double ratio = error / c;
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double ratioSq = ratio * ratio;
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double oneMinusRatioSq = 1.0 - ratioSq;
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double cubed = oneMinusRatioSq * oneMinusRatioSq * oneMinusRatioSq;
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loss = cSquaredOver6 * (1.0 - cubed);
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}
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lossSum = lossSum - lossBuffer[bufferIndex] + loss;
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lossBuffer[bufferIndex] = loss;
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bufferIndex++;
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if (bufferIndex >= period) bufferIndex = 0;
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output[i] = lossSum / period;
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tickCount++;
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if (tickCount >= ResyncInterval)
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{
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tickCount = 0;
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double recalcSum = 0;
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for (int k = 0; k < period; k++)
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recalcSum += lossBuffer[k];
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lossSum = recalcSum;
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}
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}
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}
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}
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