## Bar Charts: Performance Metrics Comparison ### Overview The image presents four bar charts comparing the performance of different methods across four metrics: ACC (Accuracy), NLL (Negative Log-Likelihood), ECE (Expected Calibration Error), and MCE (Maximum Calibration Error). Each chart compares a baseline "Deterministic" method against several other methods grouped into "Weight-Space", "Logit-Space", and "Selection-Space" categories. Error bars are included on each bar. ### Components/Axes **General Chart Elements:** * Each chart has a vertical y-axis representing the metric value and a horizontal axis representing the different methods. * Each method is represented by a colored bar, with the color corresponding to the method as defined in the legend at the bottom. * Error bars are present on each bar, indicating the uncertainty or variance in the metric value. * Horizontal gridlines are present in each chart. **Legend (Bottom):** * **Deterministic** (Blue) - Baseline * **Temp Sampling** (Orange) - Baseline * **MCDR** (Green) - Weight-Space * **SWAGR** (Red) - Weight-Space * **DER** (Purple) - Weight-Space * **MFVR** (Brown) - Logit-Space * **FCVR** (Pink) - Logit-Space * **VTSR** (Gray) - Selection-Space **Chart 1: ACC ↑ (Top-Left)** * Title: ACC ↑ (Accuracy, higher is better) * Y-axis: Ranges from 0.50 to 0.75 * Methods: Deterministic, Temp Sampling, MCDR, SWAGR, DER, MFVR, FCVR, VTSR * Categories: Baseline, Weight-Space, Logit-Space, Selection-Space **Chart 2: NLL ↓ (Top-Right)** * Title: NLL ↓ (Negative Log-Likelihood, lower is better) * Y-axis: Ranges from 0.6 to 1.4 * Methods: Deterministic, Temp Sampling, MCDR, SWAGR, DER, MFVR, FCVR, VTSR * Categories: Baseline, Weight-Space, Logit-Space, Selection-Space **Chart 3: ECE ↓ (Bottom-Left)** * Title: ECE ↓ (Expected Calibration Error, lower is better) * Y-axis: Ranges from 0.00 to 0.30 * Methods: Deterministic, Temp Sampling, MCDR, SWAGR, DER, MFVR, FCVR, VTSR * Categories: Baseline, Weight-Space, Logit-Space, Selection-Space **Chart 4: MCE ↓ (Bottom-Right)** * Title: MCE ↓ (Maximum Calibration Error, lower is better) * Y-axis: Ranges from 0.0 to 0.5 * Methods: Deterministic, Temp Sampling, MCDR, SWAGR, DER, MFVR, FCVR, VTSR * Categories: Baseline, Weight-Space, Logit-Space, Selection-Space ### Detailed Analysis **Chart 1: ACC ↑** * **Deterministic (Blue):** 0.746 * **Temp Sampling (Orange):** 0.716 * **MCDR (Green):** 0.734 * **SWAGR (Red):** 0.736 * **DER (Purple):** 0.738 * **MFVR (Brown):** 0.742 * **FCVR (Pink):** 0.740 * **VTSR (Gray):** 0.736 * Trend: All methods perform relatively similarly, with Deterministic and MFVR showing slightly higher accuracy. **Chart 2: NLL ↓** * **Deterministic (Blue):** 1.384 * **Temp Sampling (Orange):** 0.773 * **MCDR (Green):** 0.650 * **SWAGR (Red):** 0.652 * **DER (Purple):** 0.660 * **MFVR (Brown):** 0.654 * **FCVR (Pink):** 0.652 * **VTSR (Gray):** 0.667 * Trend: Deterministic has a significantly higher NLL compared to other methods. The other methods are clustered together with similar, lower NLL values. **Chart 3: ECE ↓** * **Deterministic (Blue):** 0.252 * **Temp Sampling (Orange):** 0.107 * **MCDR (Green):** 0.037 * **SWAGR (Red):** 0.041 * **DER (Purple):** 0.071 * **MFVR (Brown):** 0.026 * **FCVR (Pink):** 0.015 * **VTSR (Gray):** 0.052 * Trend: Deterministic has a much higher ECE than the other methods. FCVR has the lowest ECE. **Chart 4: MCE ↓** * **Deterministic (Blue):** 0.472 * **Temp Sampling (Orange):** 0.201 * **MCDR (Green):** 0.298 * **SWAGR (Red):** 0.290 * **DER (Purple):** 0.234 * **MFVR (Brown):** 0.293 * **FCVR (Pink):** 0.152 * **VTSR (Gray):** 0.293 * Trend: Deterministic has a significantly higher MCE. FCVR has the lowest MCE. ### Key Observations * The "Deterministic" baseline method consistently performs worse in terms of NLL, ECE, and MCE compared to the other methods. * In terms of accuracy (ACC), the methods are relatively similar, with "Deterministic" and "MFVR" showing slightly higher values. * Methods in the "Weight-Space", "Logit-Space", and "Selection-Space" categories generally improve upon the baseline in terms of calibration (ECE and MCE) and likelihood (NLL). * FCVR (Pink) appears to have the lowest ECE and MCE. ### Interpretation The data suggests that using techniques from "Weight-Space", "Logit-Space", and "Selection-Space" can significantly improve the calibration and likelihood of a model compared to a standard "Deterministic" approach. While accuracy is relatively similar across all methods, the improvements in NLL, ECE, and MCE indicate that these techniques lead to more reliable and well-calibrated predictions. The "Deterministic" method, while achieving comparable accuracy, is less confident and less well-calibrated, as evidenced by its higher NLL, ECE, and MCE values. FCVR appears to be the best performing method in terms of calibration error.