## Scatter Plot: Multiple Protected Attributes ### Overview The image contains two components: a causal diagram on the left and a scatter plot on the right. The scatter plot visualizes the relationship between **Causal Effect (ATE)** and **Error (1 - AUC)** for two groups: "Unfair" (pink circles) and "FairPFN" (blue stars). The diagram illustrates relationships between protected attributes, variables, and error terms. --- ### Components/Axes #### Left Diagram (Causal Model) - **Nodes**: - **A₀** (blue circle): Protected attribute 0 - **A₁** (blue circle): Protected attribute 1 - **X_b** (purple circle): Intermediate variable - **Y_b** (orange circle): Outcome variable - **X_f** (yellow circle): Feature variable - **ε_Xb** (green circle): Error term for X_b - **ε_Yb** (green circle): Error term for Y_b - **Connections**: - A₀ → X_b - A₁ → X_b - X_b → Y_b - X_f → Y_b - ε_Xb → X_b - ε_Yb → Y_b #### Right Scatter Plot - **Axes**: - **X-axis**: Causal Effect (ATE) (0.00 to 1.00) - **Y-axis**: Error (1 - AUC) (0.00 to 0.80) - **Legend**: - **Pink circles**: Unfair - **Blue stars**: FairPFN --- ### Detailed Analysis #### Left Diagram - **Flow**: - Protected attributes **A₀** and **A₁** directly influence **X_b**. - **X_b** propagates its effect to **Y_b**, with **X_f** also contributing to **Y_b**. - Error terms **ε_Xb** and **ε_Yb** are connected to **X_b** and **Y_b**, respectively, suggesting noise or unobserved factors. #### Right Scatter Plot - **Data Distribution**: - **Unfair (pink circles)**: - Clustered in the **lower-right quadrant** (high ATE, low error). - Some outliers extend toward higher error values (e.g., ATE ~0.2, error ~0.6). - **FairPFN (blue stars)**: - Concentrated in the **upper-left quadrant** (low ATE, high error). - A few points overlap with Unfair in the lower-right quadrant. - **Trends**: - Both groups show a **negative correlation** between ATE and error (as ATE increases, error decreases). - **FairPFN** consistently exhibits **lower error** than Unfair for equivalent ATE values. --- ### Key Observations 1. **FairPFN Advantage**: FairPFN achieves lower error (1 - AUC) across most ATE values, indicating better performance. 2. **Unfair Outliers**: A subset of Unfair data points (e.g., ATE ~0.2, error ~0.6) deviates from the general trend, suggesting potential misclassification or edge cases. 3. **Causal Diagram Complexity**: The diagram implies that protected attributes (A₀, A₁) and features (X_f) jointly determine outcomes (Y_b), with error terms introducing variability. --- ### Interpretation - **Fairness vs. Performance**: The scatter plot highlights a trade-off between fairness (FairPFN) and error rates. FairPFN reduces bias (lower error) but may sacrifice some predictive power (higher ATE in some cases). - **Causal Relationships**: The diagram suggests that protected attributes (A₀, A₁) and features (X_f) are critical drivers of outcomes (Y_b), with error terms (ε_Xb, ε_Yb) representing external noise or model limitations. - **Practical Implications**: The Unfair group’s outliers may indicate scenarios where fairness interventions (e.g., FairPFN) fail to generalize, warranting further investigation into model robustness. --- ### Notes on Data Extraction - **No explicit numerical values** are provided for individual data points; trends are inferred from spatial distribution. - **Legend alignment**: Pink circles (Unfair) and blue stars (FairPFN) are consistently matched to their respective data clusters.