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Refactor documentation for various filters and indicators to enhance clarity and consistency
- Updated Bessel, Bilateral, Blma, Butter, Conv, Ema, Kama, LSMA, MAMA, MGDI, SSF, USF, ATR, ADL, and ADOSC documentation to use bullet points for key concepts and features. - Added a new Qodana configuration file for code analysis. - Removed coverage configuration from Quantower.Tests.csproj to streamline testing setup.
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@@ -14,10 +14,10 @@ The biweight function is a smooth, bell-shaped curve that rises from 0, peaks at
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### Properties
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- **Redescending**: Large errors contribute zero loss (complete outlier rejection)
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- **Smooth**: Continuously differentiable everywhere
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- **Bounded**: Maximum loss is c²/6, regardless of error magnitude
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- **Tunable**: Parameter c controls the outlier threshold
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* **Redescending**: Large errors contribute zero loss (complete outlier rejection)
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* **Smooth**: Continuously differentiable everywhere
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* **Bounded**: Maximum loss is c²/6, regardless of error magnitude
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* **Tunable**: Parameter c controls the outlier threshold
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## Mathematical Foundation
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@@ -31,8 +31,8 @@ $$\rho(e) = \begin{cases}
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\end{cases}$$
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Where:
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- $e = y - \hat{y}$ = prediction error
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- $c$ = tuning constant (threshold)
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* $e = y - \hat{y}$ = prediction error
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* $c$ = tuning constant (threshold)
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### 2. Alternative Form
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@@ -44,9 +44,9 @@ where $u = e/c$
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### 3. Key Values
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- At $e = 0$: $\rho(0) = 0$
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- At $e = c$: $\rho(c) = c^2/6$ (maximum)
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- For $|e| > c$: $\rho(e) = c^2/6$ (constant, flat)
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* At $e = 0$: $\rho(0) = 0$
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* At $e = c$: $\rho(c) = c^2/6$ (maximum)
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* For $|e| > c$: $\rho(e) = c^2/6$ (constant, flat)
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### 4. Running Update (O(1))
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@@ -133,15 +133,15 @@ Tukey's biweight is the only loss function that completely stops penalizing erro
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## Edge Cases
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- **Perfect Predictions**: Returns exactly 0
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- **All Outliers**: Returns c²/6 (maximum bounded loss)
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- **NaN Handling**: Uses last valid value substitution
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- **Single Input**: Not supported (requires two series)
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- **c = 0**: Invalid (division issues)
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- **Errors exactly at c**: Smooth transition (differentiable)
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* **Perfect Predictions**: Returns exactly 0
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* **All Outliers**: Returns c²/6 (maximum bounded loss)
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* **NaN Handling**: Uses last valid value substitution
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* **Single Input**: Not supported (requires two series)
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* **c = 0**: Invalid (division issues)
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* **Errors exactly at c**: Smooth transition (differentiable)
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## Related Indicators
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- [Huber](../huber/Huber.md) - Huber Loss (linear, not redescending)
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- [MdAE](../mdae/Mdae.md) - Median Absolute Error (robust via median)
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- [LogCosh](../logcosh/LogCosh.md) - Log-Cosh Loss (smooth L1/L2 hybrid)
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* [Huber](../huber/Huber.md) - Huber Loss (linear, not redescending)
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* [MdAE](../mdae/Mdae.md) - Median Absolute Error (robust via median)
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* [LogCosh](../logcosh/LogCosh.md) - Log-Cosh Loss (smooth L1/L2 hybrid)
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