## Box Plot Series: Causal Effect (ATE) Across Six Fairness Scenarios ### Overview The image displays a 2x3 grid of six box plots, each visualizing the distribution of "Causal Effect (ATE)" for four different methods under distinct experimental conditions. The plots are titled to indicate the scenario being tested. A shared legend at the bottom identifies the four methods and provides a summary performance metric. ### Components/Axes * **Chart Type:** Box and whisker plots with overlaid data points (jitter). * **Y-Axis (All Plots):** Labeled **"Causal Effect (ATE)"**. The scale ranges from -0.5 to 0.75, with major gridlines at intervals of 0.25 (-0.5, -0.25, 0, 0.25, 0.5, 0.75). * **X-Axis (All Plots):** Represents four categorical methods. The categories are not labeled on the axis but are defined by color in the legend. * **Legend (Bottom Center):** Contains the title **"Avg. Rank (ATE)"** and defines the four methods with associated colors and a numerical rank (lower is better): * **Pink:** `FairPFN: 1.88/4` * **Purple:** `EGR: 2.11/4` * **Orange:** `Unaware: 2.16/4` * **Blue:** `Unfair: 3.42/4` * **Subplot Titles (Top of each plot):** 1. **Biased** (Top Left) 2. **Direct-Effect** (Top Center) 3. **Indirect-Effect** (Top Right) 4. **Fair Observable** (Bottom Left) 5. **Fair Unobservable** (Bottom Center) 6. **Fair Additive Noise** (Bottom Right) ### Detailed Analysis **General Structure per Plot:** Each subplot contains four box plots, one for each method (Blue, Orange, Purple, Pink from left to right). The box represents the interquartile range (IQR), the line inside is the median, whiskers extend to 1.5*IQR, and circles represent individual data points/outliers. **Plot-by-Plot Analysis:** 1. **Biased:** * **Unfair (Blue):** Highest median (~0.05), largest IQR (box from ~0 to ~0.2), and widest overall range (whiskers from ~-0.15 to ~0.45). Many high-value outliers up to ~0.75. * **Unaware (Orange):** Median near 0, smaller IQR than Blue, range ~-0.05 to ~0.3. * **EGR (Purple):** Median slightly below 0, IQR similar to Orange, but with notable low-value outliers down to ~-0.5. * **FairPFN (Pink):** Median at 0, very compact IQR, range ~-0.1 to ~0.1. Tightest distribution. 2. **Direct-Effect:** * **Unfair (Blue):** Dominates the plot. Median ~0.15, large IQR (box from ~0.05 to ~0.35), whiskers from ~-0.1 to ~0.65. * **Unaware (Orange), EGR (Purple), FairPFN (Pink):** All are extremely compressed around 0. Their boxes are nearly flat lines, indicating near-zero variance and median. Minor outliers exist within ±0.1. 3. **Indirect-Effect:** * **Unfair (Blue):** Similar pattern to "Biased" plot. Median ~0.05, IQR ~0 to ~0.2, outliers up to ~0.75. * **Unaware (Orange):** Median ~0, IQR ~0 to ~0.1. * **EGR (Purple):** Median ~0, IQR ~0 to ~0.1, with low outliers to ~-0.4. * **FairPFN (Pink):** Very tight distribution around 0. 4. **Fair Observable:** * **Unfair (Blue):** Median ~0.15, IQR ~0.05 to ~0.3. * **Unaware (Orange):** Median ~0, very compact. * **EGR (Purple):** Median ~0, compact but with low outliers to ~-0.4. * **FairPFN (Pink):** Extremely tight around 0. 5. **Fair Unobservable:** * **Unfair (Blue):** Median ~0.2, IQR ~0.05 to ~0.35, whiskers to ~0.7. * **Unaware (Orange):** Median ~0.05, small IQR. * **EGR (Purple):** Median ~0, small IQR, low outliers. * **FairPFN (Pink):** Tight around 0. 6. **Fair Additive Noise:** * **Unfair (Blue):** Median ~0.15, IQR ~0.05 to ~0.3. * **Unaware (Orange):** Median ~0, small IQR. * **EGR (Purple):** Median ~0, small IQR, low outliers. * **FairPFN (Pink):** Tight around 0. ### Key Observations 1. **Consistent Hierarchy:** Across all six scenarios, the **Unfair (Blue)** method consistently shows the highest median causal effect (ATE) and the greatest variance (widest box and whiskers). **FairPFN (Pink)** consistently shows a median at or very near zero with the smallest variance. 2. **Scenario Impact:** The "Direct-Effect" scenario shows the most dramatic suppression of effect for the three fair/unaware methods (Orange, Purple, Pink), compressing them to near-zero variance. The "Biased" and "Indirect-Effect" scenarios show the most pronounced high-value outliers for the Unfair method. 3. **Method Comparison:** The **Unaware (Orange)** and **EGR (Purple)** methods generally perform similarly, with medians near zero. EGR exhibits a recurring pattern of negative outliers (low ATE values) in several plots (Biased, Indirect-Effect, Fair Observable). 4. **Legend Rank Correlation:** The visual performance aligns with the "Avg. Rank" in the legend. FairPFN (rank 1.88) is visually the best (lowest, tightest ATE). Unfair (rank 3.42) is visually the worst (highest, most variable ATE). Unaware and EGR are in the middle and close in rank (2.16 vs. 2.11), reflecting their similar visual performance. ### Interpretation This figure evaluates how different algorithmic approaches (FairPFN, EGR, Unaware) perform in estimating or mitigating **causal effects** (specifically, Average Treatment Effect - ATE) compared to an **Unfair** baseline, across various data-generating scenarios related to fairness. * **What the data suggests:** The "Unfair" method, which likely does not account for fairness constraints, results in substantial and variable estimated causal effects. In contrast, the methods designed for fairness (FairPFN, EGR) or that are simply unaware of sensitive attributes (Unaware) successfully drive the estimated ATE towards zero. This implies these methods are effective at removing or neutralizing the measured causal influence of a treatment, which in a fairness context often corresponds to a sensitive attribute like race or gender. * **How elements relate:** The six scenarios (Biased, Direct/Indirect Effect, Fair Observable/Unobservable/Noise) test the robustness of the methods under different assumptions about how bias or fairness is embedded in the data. The consistent pattern across plots indicates the core finding is robust: fairness-aware methods suppress the measured causal effect. * **Notable patterns/anomalies:** * The extreme compression in the "Direct-Effect" plot suggests that when the causal pathway is direct, the fairness interventions (and even the unaware method) are exceptionally effective at nullifying the measured effect. * The negative outliers for EGR are an anomaly, suggesting that in some runs, this method may over-correct, leading to a negative estimated ATE. * The high-value outliers for the Unfair method in "Biased" and "Indirect-Effect" scenarios indicate that under those data conditions, the lack of fairness constraints can lead to very large estimated causal disparities. **In summary, the visualization provides strong evidence that the FairPFN method (and to a lesser extent EGR and Unaware) consistently and effectively minimizes the estimated average causal effect of a treatment across a variety of fairness-related data scenarios, outperforming an unfair baseline.**