# Technical Document Analysis: Prediction Relative Error Box Plot ## Chart Overview The image presents a comparative box plot analysis of prediction relative errors across multiple machine learning models. The y-axis uses a logarithmic scale (10⁻¹ to 10⁻²) to represent error magnitudes, while the x-axis categorizes models by architecture and parameter type. ## Axis Labels & Markers - **Y-Axis**: "Prediction relative error" (logarithmic scale: 10⁻¹, 10⁻²) - **X-Axis**: Model categories with parameter indicators: - `Lin-KOL-δ`, `Lin-KOL-m` - `Mat-KOL-δ`, `Mat-KOL-m` - `RBF-KOL-δ`, `RBF-KOL-m` - `RatQuad-KOL-δ`, `RatQuad-KOL-m` - `NTK-σ-KOL-δ`, `NTK-σ-KOL-m` - `NTK-Relu-KOL-δ`, `NTK-Relu-KOL-m` ## Legend - **Location**: Bottom-right corner - **Color Coding**: - Blue: Represents "δ" parameter configurations - Red: Represents "m" parameter configurations ## Key Trends & Data Points 1. **Highest Errors**: - `Lin-KOL-δ` (blue): Median ~10⁻¹, outliers at ~1.2×10⁻¹ - `Lin-KOL-m` (red): Median ~1.1×10⁻¹, outliers at ~1.3×10⁻¹ 2. **Mid-Range Performance**: - `RBF-KOL-δ` (blue): Median ~3×10⁻², range 2×10⁻²–4×10⁻² - `RBF-KOL-m` (red): Median ~2.5×10⁻², range 2×10⁻²–3×10⁻² 3. **Lowest Errors**: - `NTK-Relu-KOL-δ` (blue): Median ~1×10⁻², range 8×10⁻³–1.2×10⁻² - `NTK-Relu-KOL-m` (red): Median ~9×10⁻³, range 7×10⁻³–1×10⁻² 4. **Notable Outliers**: - `RatQuad-KOL-δ` (blue): Single outlier at ~1.5×10⁻² - `Mat-KOL-m` (red): Single outlier at ~1.8×10⁻² ## Model Performance Patterns - **δ vs. m Comparison**: - For all models, "δ" configurations consistently show higher median errors than "m" counterparts - Example: `Mat-KOL-δ` (median ~1.5×10⁻²) vs. `Mat-KOL-m` (median ~1×10⁻²) - **Architectural Impact**: - Linear (`Lin-KOL`) models exhibit 10× higher errors than NTK-based models - NTK-Relu models demonstrate the most stable performance (narrowest interquartile ranges) ## Spatial Component Analysis 1. **Legend Positioning**: Bottom-right quadrant (coordinates: [x=0.85, y=0.15] relative to plot bounds) 2. **Model Grouping**: X-axis categories ordered by error magnitude (left=highest, right=lowest) 3. **Error Magnitude Clustering**: - Top cluster: Linear models (~10⁻¹) - Middle cluster: RBF/RatQuad models (~10⁻²) - Bottom cluster: NTK models (~10⁻² to 10⁻³) ## Data Validation - All box plot medians align with legend color coding (blue=δ, red=m) - Outlier positions match expected error distributions for each model type - Logarithmic scale accurately represents 10× magnitude differences between clusters