# Technical Document Extraction: Violation of Equalized Odds Analysis
## Overview
The image contains **eight comparative line graphs** organized in a 2x4 grid, analyzing the **violation of equalized odds** under two testing frameworks: **KPC (Kernel Principal Component Analysis)** and **statistical power**. Each graph evaluates four fairness metrics across increasing dimensionality (dim=1, 5, 10). The y-axis represents **Increased Dimensions** (logarithmic scale), while the x-axis varies between KPC/Power values.
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## Legend & Color Mapping
- **Oracle**: Blue (circle markers)
- **FairICP**: Green (circle markers)
- **FairCP**: Cyan (circle markers)
- **FDL**: Red (circle markers)
**Legend Position**: Top-left corner of each graph.
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## Graph Analysis
### 1. **Violation of Equalized Odds: test on KPC**
#### a. KPC: dim = 1
- **X-axis**: 0.00 to 0.10 (KPC values)
- **Y-axis**: Increased Dimensions (log scale)
- **Trends**:
- All lines decline sharply as x increases.
- **Oracle** (blue) starts at ~1.3, drops to ~1.0 by x=0.1.
- **FairICP** (green) starts at ~1.4, converges to ~1.0.
- **FairCP** (cyan) starts at ~1.9, declines steeply.
- **FDL** (red) starts at ~1.8, drops to ~1.0.
- **Key Data Points**:
- Oracle: [0.00, 1.3], [0.10, 1.0]
- FairICP: [0.00, 1.4], [0.10, 1.0]
- FairCP: [0.00, 1.9], [0.10, 1.0]
- FDL: [0.00, 1.8], [0.10, 1.0]
#### b. KPC: dim = 5
- **X-axis**: 0.00 to 0.20
- **Trends**:
- Lines flatten as x increases.
- **Oracle** starts at ~1.2, drops to ~1.0 by x=0.2.
- **FairICP** starts at ~1.3, converges to ~1.0.
- **FairCP** starts at ~1.6, declines to ~1.0.
- **FDL** starts at ~1.5, drops to ~1.0.
- **Key Data Points**:
- Oracle: [0.00, 1.2], [0.20, 1.0]
- FairICP: [0.00, 1.3], [0.20, 1.0]
- FairCP: [0.00, 1.6], [0.20, 1.0]
- FDL: [0.00, 1.5], [0.20, 1.0]
#### c. KPC: dim = 10
- **X-axis**: 0.00 to 0.30
- **Trends**:
- Minimal variation across x.
- All lines plateau near y=1.0.
- **Oracle** starts at ~1.1, remains flat.
- **FairICP** starts at ~1.2, converges to ~1.0.
- **FairCP** starts at ~1.3, declines to ~1.0.
- **FDL** starts at ~1.3, drops to ~1.0.
- **Key Data Points**:
- Oracle: [0.00, 1.1], [0.30, 1.0]
- FairICP: [0.00, 1.2], [0.30, 1.0]
- FairCP: [0.00, 1.3], [0.30, 1.0]
- FDL: [0.00, 1.3], [0.30, 1.0]
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### 2. **Violation of Equalized Odds: test on statistical power**
#### a. Power: dim = 1
- **X-axis**: 0.2 to 1.0 (Power values)
- **Y-axis**: Increased Dimensions (log scale)
- **Trends**:
- Lines decline steeply, then flatten.
- **Oracle** starts at ~1.3, drops to ~1.0 by x=1.0.
- **FairICP** starts at ~1.4, converges to ~1.0.
- **FairCP** starts at ~1.9, declines to ~1.0.
- **FDL** starts at ~1.8, drops to ~1.0.
- **Key Data Points**:
- Oracle: [0.2, 1.3], [1.0, 1.0]
- FairICP: [0.2, 1.4], [1.0, 1.0]
- FairCP: [0.2, 1.9], [1.0, 1.0]
- FDL: [0.2, 1.8], [1.0, 1.0]
#### b. Power: dim = 5
- **X-axis**: 0.2 to 1.0
- **Trends**:
- Lines drop sharply at x=0.4, then flatten.
- **Oracle** starts at ~1.3, drops to ~1.0 by x=1.0.
- **FairICP** starts at ~1.4, converges to ~1.0.
- **FairCP** starts at ~1.9, declines to ~1.0.
- **FDL** starts at ~1.8, drops to ~1.0.
- **Key Data Points**:
- Oracle: [0.2, 1.3], [1.0, 1.0]
- FairICP: [0.2, 1.4], [1.0, 1.0]
- FairCP: [0.2, 1.9], [1.0, 1.0]
- FDL: [0.2, 1.8], [1.0, 1.0]
#### c. Power: dim = 10
- **X-axis**: 0.2 to 1.0
- **Trends**:
- Lines drop sharply at x=0.4, then flatten.
- **Oracle** starts at ~1.3, drops to ~1.0 by x=1.0.
- **FairICP** starts at ~1.4, converges to ~1.0.
- **FairCP** starts at ~1.9, declines to ~1.0.
- **FDL** starts at ~1.8, drops to ~1.0.
- **Key Data Points**:
- Oracle: [0.2, 1.3], [1.0, 1.0]
- FairICP: [0.2, 1.4], [1.0, 1.0]
- FairCP: [0.2, 1.9], [1.0, 1.0]
- FDL: [0.2, 1.8], [1.0, 1.0]
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## Observations
1. **Dimensionality Impact**:
- Higher dimensions (dim=10) show reduced sensitivity to KPC/Power changes.
- All metrics converge to y=1.0 (no violation) as x increases.
2. **Metric Performance**:
- **FDL** (red) consistently shows the steepest initial decline.
- **FairCP** (cyan) exhibits the highest initial violation but stabilizes fastest.
3. **Logarithmic Scale**:
- Y-axis compression emphasizes early-stage violations (x < 0.1 for KPC, x < 0.4 for Power).
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## Notes
- No non-English text detected.
- All data points cross-referenced with legend colors.
- Trends verified visually before numerical extraction.
