## Bar Chart: ECE and AUROC Comparison ### Overview The image presents a bar chart comparing three categories: "Incorrect", "Sampled", and "Probe" across two metrics: ECE (Expected Calibration Error) and AUROC (Area Under the Receiver Operating Characteristic curve). The chart displays the mean values for each category with error bars indicating variability. ### Components/Axes * **Y-axis (Left):** * Top Chart: ECE, labeled vertically. Scale ranges from 0% to 20% in increments of 10%. * Bottom Chart: AUROC, labeled vertically. Scale ranges from 30% to 70% in increments of 20%. * **X-axis:** Implicitly represents the three categories: "Probe", "Incorrect", and "Sampled". * **Legend (Top):** Located at the top of the image. * Light Blue: "Incorrect" * Dark Blue: "Sampled" * Orange: "Probe" ### Detailed Analysis **Top Chart: ECE** * **Probe (Orange):** ECE value is approximately 12% with an error bar extending from about 8% to 16%. * **Incorrect (Light Blue):** ECE value is approximately 16% with an error bar extending from about 12% to 20%. * **Sampled (Dark Blue):** ECE value is approximately 9% with an error bar extending from about 5% to 13%. **Bottom Chart: AUROC** * **Probe (Orange):** AUROC value is approximately 62% with an error bar extending from about 58% to 66%. * **Incorrect (Light Blue):** AUROC value is approximately 64% with an error bar extending from about 60% to 68%. * **Sampled (Dark Blue):** AUROC value is approximately 71% with an error bar extending from about 67% to 75%. ### Key Observations * For ECE, "Sampled" has the lowest value, while "Incorrect" has the highest. * For AUROC, "Sampled" has the highest value, while "Probe" has the lowest. * The error bars indicate the variability within each category. ### Interpretation The chart suggests that the "Sampled" category performs best in terms of calibration (lower ECE) and discrimination (higher AUROC). The "Incorrect" category has the worst calibration (highest ECE) but performs comparably to "Sampled" in terms of discrimination (AUROC). The "Probe" category has the worst discrimination (lowest AUROC). The error bars provide an indication of the uncertainty associated with each estimate.

\n ## Bar Charts: Performance Metrics Comparison ### Overview The image presents two bar charts comparing performance metrics across three conditions: "Probe", "Incorrect", and "Sampled". The metrics being compared are "ECE" (Expected Calibration Error) and "AUROC" (Area Under the Receiver Operating Characteristic curve). Each bar represents the mean value of the metric for a given condition, with error bars indicating the variability. ### Components/Axes * **Legend:** Located at the top-center of the image. * Light Blue: "Incorrect" * Dark Blue: "Sampled" * Orange: "Probe" * **Y-axis (Top Chart):** "ECE" (Expected Calibration Error), ranging from 0% to 20%. * **Y-axis (Bottom Chart):** "AUROC" (Area Under the Receiver Operating Characteristic curve), ranging from 30% to 70%. * **X-axis (Both Charts):** Categories: "Probe", "Incorrect", "Sampled". * **Error Bars:** Black vertical lines extending from the top of each bar, representing the standard error or confidence interval. ### Detailed Analysis or Content Details **Top Chart: ECE** * **Probe (Orange):** The bar is approximately at 11%. The error bar extends from roughly 8% to 14%. * **Incorrect (Light Blue):** The bar is approximately at 13%. The error bar extends from roughly 10% to 16%. * **Sampled (Dark Blue):** The bar is approximately at 9%. The error bar extends from roughly 6% to 12%. **Bottom Chart: AUROC** * **Probe (Orange):** The bar is approximately at 62%. The error bar extends from roughly 58% to 66%. * **Incorrect (Light Blue):** The bar is approximately at 57%. The error bar extends from roughly 53% to 61%. * **Sampled (Dark Blue):** The bar is approximately at 68%. The error bar extends from roughly 64% to 72%. ### Key Observations * For ECE, the "Incorrect" condition has the highest mean value, while the "Sampled" condition has the lowest. The "Probe" condition falls in between. * For AUROC, the "Sampled" condition has the highest mean value, while the "Incorrect" condition has the lowest. The "Probe" condition falls in between. * The error bars suggest that the differences between the conditions for ECE are not statistically significant, as they overlap considerably. The error bars for AUROC show less overlap, suggesting potentially significant differences. ### Interpretation The data suggests that the "Sampled" condition performs best in terms of discrimination (AUROC), but may have a higher calibration error (ECE) compared to the other conditions. The "Incorrect" condition performs worst in terms of discrimination and has a relatively high calibration error. The "Probe" condition represents a middle ground between the two. The higher AUROC for "Sampled" indicates that it is better at distinguishing between true positives and false positives. The higher ECE for "Incorrect" suggests that the confidence scores produced by this condition are less well-calibrated, meaning that a prediction with a confidence of 80% is not actually correct 80% of the time. The overlapping error bars for ECE suggest that the observed differences may be due to random chance. Further statistical analysis would be needed to confirm whether these differences are statistically significant. The data implies a trade-off between calibration and discrimination, where improving one may come at the expense of the other.

## Bar Chart: Model Performance Metrics (ECE and AUROC) ### Overview The image displays a comparative bar chart with two vertically stacked subplots, evaluating three different methods ("Incorrect", "Sampled", "Probe") across two performance metrics: Expected Calibration Error (ECE) and Area Under the ROC Curve (AUROC). The chart includes a legend and error bars on each bar, indicating variability or uncertainty in the measurements. ### Components/Axes * **Legend:** Positioned at the top center of the image. It contains three entries: * A light blue square labeled "Incorrect". * A dark blue square labeled "Sampled". * An orange square labeled "Probe". * **Subplot 1 (Top):** * **Y-Axis Label:** "ECE" (Expected Calibration Error). * **Y-Axis Scale:** Percentage, ranging from 0% to 20%, with tick marks at 0%, 10%, and 20%. * **Bars:** Three bars corresponding to the legend categories. * **Subplot 2 (Bottom):** * **Y-Axis Label:** "AUROC" (Area Under the Receiver Operating Characteristic Curve). * **Y-Axis Scale:** Percentage, ranging from 30% to 70%, with tick marks at 30%, 50%, and 70%. * **Bars:** Three bars corresponding to the legend categories. * **X-Axis:** No explicit categorical labels are present on the x-axis. The bars are grouped by the three methods defined in the legend. ### Detailed Analysis **ECE Subplot (Top):** * **Trend Verification:** The "Incorrect" (light blue) bar is the tallest, indicating the highest ECE. The "Probe" (orange) and "Sampled" (dark blue) bars are shorter and of similar height. * **Data Points (Approximate):** * **Incorrect (Light Blue):** ~15% ECE. Error bar extends from approximately 12% to 18%. * **Probe (Orange):** ~10% ECE. Error bar extends from approximately 8% to 12%. * **Sampled (Dark Blue):** ~10% ECE. Error bar extends from approximately 7% to 13%. **AUROC Subplot (Bottom):** * **Trend Verification:** The "Sampled" (dark blue) bar is the tallest, indicating the highest AUROC. The "Incorrect" (light blue) and "Probe" (orange) bars are shorter and of similar height. * **Data Points (Approximate):** * **Incorrect (Light Blue):** ~50% AUROC. Error bar extends from approximately 48% to 52%. * **Probe (Orange):** ~50% AUROC. Error bar extends from approximately 45% to 55%. * **Sampled (Dark Blue):** ~65% AUROC. Error bar extends from approximately 60% to 70%. ### Key Observations 1. **Inverse Relationship:** There is an inverse relationship between the performance of the "Incorrect" method and the "Sampled" method across the two metrics. "Incorrect" has the worst (highest) ECE but ties for the lowest AUROC. "Sampled" has a low ECE (tied with "Probe") and the best (highest) AUROC. 2. **"Probe" Method Consistency:** The "Probe" method shows consistent, moderate performance. It matches the "Sampled" method on the calibration metric (ECE) but performs similarly to the "Incorrect" method on the discrimination metric (AUROC). 3. **Variability:** The error bars suggest the most uncertainty (widest range) is associated with the "Probe" method's AUROC measurement and the "Sampled" method's ECE measurement. The "Incorrect" method's AUROC appears to have the least variability. ### Interpretation This chart likely compares different strategies for handling or sampling data in a machine learning context, possibly related to model calibration or uncertainty estimation. * **What the data suggests:** The "Sampled" method appears to be the most effective overall, achieving strong discrimination (high AUROC) while maintaining good calibration (low ECE). The "Incorrect" method, which may represent a baseline or a flawed approach, is poorly calibrated (high ECE) and has poor discriminative ability. The "Probe" method offers a middle ground; it is well-calibrated but does not improve discrimination over the flawed baseline. * **How elements relate:** The two subplots together provide a more complete picture of model performance than either metric alone. A model can be well-calibrated (low ECE) but have poor discriminative power (low AUROC), or vice-versa. The ideal model minimizes ECE while maximizing AUROC, a position occupied here by the "Sampled" method. * **Notable anomalies:** The near-identical ECE for "Probe" and "Sampled" is notable, suggesting these two methods are equally effective at reducing calibration error compared to the "Incorrect" baseline. The significant jump in AUROC for "Sampled" is the most striking result, indicating it provides a substantial benefit in classification performance.

## Bar Chart: Performance Metrics Comparison ### Overview The chart compares three methods (Probe, Incorrect, Sampled) across two performance metrics: ECE (Expected Calibration Error) and AUROC (Area Under the Receiver Operating Characteristic curve). Values are represented as percentages. ### Components/Axes - **X-axis**: Categories labeled "ECE" and "AUROC". - **Y-axis**: Percentage scale from 0% to 70% in 10% increments. - **Legend**: Located at the top-left, mapping colors to methods: - Orange: Probe - Light Blue: Incorrect - Dark Blue: Sampled ### Detailed Analysis #### ECE Section - **Probe (Orange)**: ~10% - **Incorrect (Light Blue)**: ~15% - **Sampled (Dark Blue)**: ~5% - **Trend**: Probe and Incorrect show moderate error, while Sampled has the lowest error. #### AUROC Section - **Probe (Orange)**: ~50% - **Incorrect (Light Blue)**: ~55% - **Sampled (Dark Blue)**: ~65% - **Trend**: All methods improve performance, with Sampled achieving the highest AUROC. ### Key Observations 1. **ECE**: - Probe underperforms compared to Incorrect and Sampled. - Sampled achieves the best calibration (lowest error). 2. **AUROC**: - All methods show improvement, but Sampled outperforms others significantly. - Probe has the lowest AUROC, suggesting weaker discriminative ability. ### Interpretation - The **Probe** method appears to be a baseline or naive approach, as it performs poorly in both metrics. - The **Incorrect** method slightly improves ECE but lags in AUROC, indicating inconsistent gains. - The **Sampled** method demonstrates the strongest performance, excelling in both calibration (ECE) and discriminative power (AUROC). - The stark contrast in AUROC values (50–65%) suggests that sampling strategies significantly impact model reliability. - The **Incorrect** method’s higher ECE than Probe implies it introduces more calibration errors despite its name, possibly due to overconfidence or misalignment. This analysis highlights the importance of sampling techniques in balancing calibration and discriminative accuracy, with "Sampled" emerging as the optimal approach.