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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
86fe32a682
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com> Co-authored-by: aider (openrouter/anthropic/claude-sonnet-4) <aider@aider.chat> Co-authored-by: Warp <agent@warp.dev>
88 lines
5.0 KiB
Markdown
88 lines
5.0 KiB
Markdown
# Errors
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> "All models are wrong. Error metrics tell you how wrong." — Adapted from George Box
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Error metrics and loss functions for model/strategy evaluation. All error indicators accept two input series (actual and predicted values) and compute rolling error metrics over a configurable period.
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## Two-Input Pattern
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All error indicators in this category follow a consistent dual-input API:
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```csharp
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// Streaming mode
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var mae = new Mae(period: 14);
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var result = mae.Update(actualValue, predictedValue);
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// Batch mode
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var maeSeries = Mae.Calculate(actualSeries, predictedSeries, period: 14);
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// Span mode (zero-allocation)
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Mae.Batch(actualSpan, predictedSpan, outputSpan, period: 14);
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```
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## Indicator Status
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| Indicator | Full Name | Status | Description |
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| :--- | :--- | :---: | :--- |
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| [HUBER](lib/errors/huber/Huber.md) | Huber Loss | ✅ | Combines MSE and MAE. Configurable outlier threshold δ. |
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| [LOGCOSH](lib/errors/logcosh/LogCosh.md) | Log-Cosh Loss | ✅ | Smooth approximation to MAE. Twice-differentiable. |
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| [MAE](lib/errors/mae/Mae.md) | Mean Absolute Error | ✅ | Average of absolute differences. Robust baseline. |
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| [MAAPE](lib/errors/maape/Maape.md) | Mean Arctangent APE | ✅ | Bounded percentage error using arctangent. Range: 0 to π/2. |
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| [MAPD](lib/errors/mapd/Mapd.md) | Mean Absolute % Deviation | ✅ | Percentage error relative to mean of actual and predicted. |
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| [MAPE](lib/errors/mape/Mape.md) | Mean Absolute % Error | ✅ | Percentage error relative to actual. Unbounded when actual≈0. |
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| [MASE](lib/errors/mase/Mase.md) | Mean Absolute Scaled Error | ✅ | Scale-free. Uses naive forecast as baseline. |
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| [MDAE](lib/errors/mdae/Mdae.md) | Median Absolute Error | ✅ | Median of absolute differences. Outlier-robust. O(n log n). |
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| [MDAPE](lib/errors/mdape/Mdape.md) | Median Absolute % Error | ✅ | Median percentage error. Outlier-robust. O(n log n). |
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| [ME](lib/errors/me/Me.md) | Mean Error | ✅ | Signed average. Detects systematic bias. |
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| [MPE](lib/errors/mpe/Mpe.md) | Mean Percentage Error | ✅ | Signed percentage. Shows directional bias. |
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| [MRAE](lib/errors/mrae/Mrae.md) | Mean Relative Absolute Error | ✅ | Error relative to naive forecast. |
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| [MSE](lib/errors/mse/Mse.md) | Mean Squared Error | ✅ | Squared differences. Penalizes large errors heavily. |
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| [MSLE](lib/errors/msle/Msle.md) | Mean Squared Log Error | ✅ | MSE on log-transformed values. For multiplicative errors. |
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| [PSEUDOHUBER](lib/errors/pseudohuber/PseudoHuber.md) | Pseudo-Huber Loss | ✅ | Smooth Huber approximation. Fully differentiable. |
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| [QUANTILE](lib/errors/quantile/QuantileLoss.md) | Quantile Loss | ✅ | Asymmetric loss for quantile regression. Pinball loss. |
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| [RAE](lib/errors/rae/Rae.md) | Relative Absolute Error | ✅ | Absolute error relative to mean predictor. |
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| [RMSE](lib/errors/rmse/Rmse.md) | Root Mean Squared Error | ✅ | √MSE. Same units as input. Penalizes outliers. |
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| [RMSLE](lib/errors/rmsle/Rmsle.md) | Root Mean Squared Log Error | ✅ | √MSLE. For multiplicative error structures. |
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| [RSE](lib/errors/rse/Rse.md) | Relative Squared Error | ✅ | Squared error relative to mean predictor. |
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| [RSQUARED](lib/errors/rsquared/Rsquared.md) | R² (Coefficient of Determination) | ✅ | Variance explained. 1 = perfect. Can be negative. |
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| [SMAPE](lib/errors/smape/Smape.md) | Symmetric MAPE | ✅ | Bounded 0-200%. Symmetric around zero. |
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| [THEILU](lib/errors/theilu/TheilU.md) | Theil's U Statistic | ✅ | Forecast vs naive. <1 beats naive. >1 worse than naive. |
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| [TUKEY](lib/errors/tukey/TukeyBiweight.md) | Tukey Biweight Loss | ✅ | Hard-rejects outliers beyond threshold. Redescending. |
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| [WMAPE](lib/errors/wmape/Wmape.md) | Weighted MAPE | ✅ | Volume-weighted percentage error. For heterogeneous data. |
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| [WRMSE](lib/errors/wrmse/Wrmse.md) | Weighted RMSE | ✅ | Weighted root mean squared error. Custom observation weighting. |
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**Status Key:** ✅ Implemented | 📋 Planned
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## Choosing an Error Metric
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### By Use Case
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| Use Case | Recommended Metrics |
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| :--- | :--- |
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| General accuracy | MAE, RMSE |
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| Outlier-robust | MAE, Huber, MASE, MDAE, Tukey |
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| Percentage interpretation | MAPE, SMAPE, MAPD, MAAPE |
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| Bias detection | ME, MPE |
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| Scale-free comparison | MASE, RAE, RSE, MRAE, TheilU |
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| Model quality score | R², RSE |
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| Log-scale data | MSLE, RMSLE |
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| Gradient optimization | LogCosh, PseudoHuber |
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| Quantile forecasting | Quantile Loss |
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| Volume-weighted | WMAPE |
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### By Properties
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| Metric | Scale | Outlier Sensitivity | Complexity |
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| :--- | :--- | :--- | :--- |
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| MAE | Original units | Low | O(1) |
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| MSE | Squared units | High | O(1) |
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| RMSE | Original units | High | O(1) |
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| MAPE | Percentage | Medium | O(1) |
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| SMAPE | 0-200% | Medium | O(1) |
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| Huber | Original units | Low (configurable) | O(1) |
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| R² | 0-1 (for good models) | High | O(1) |
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| MDAE | Original units | Very Low | O(n log n) |
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| MDAPE | Percentage | Very Low | O(n log n) |
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| LogCosh | Original units | Low | O(1) |
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| PseudoHuber | Original units | Low | O(1) |
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| Tukey | Original units | Very Low | O(1) | |