Identifying Model Weaknesses Using Image System Degradations

Background

Z-Score

The z-score is a statistical measure that indicates how far a given value deviates from the mean of a distribution and is measured in units of standard deviation. The z-score tells us how many standard deviations a value is from the mean. A z-score of 0 indicates that the value is equal to the mean, while positive and negative z-scores indicate that the value is above or below the mean, respectively. Z-scores are useful for identifying outliers and understanding how unusual a given observation is relative to the overall data distribution. The z-score for an observation $o$ is calculated as: $z=\frac{o-\mu }{\sigma }$ Where:

• $o$ is the observed value,
• $\mu$ is the mean of the distribution, and
• $\sigma$ is the standard deviation of the distribution.

Methods

Using Z-Score to Narrow Down the Most Affected Classes

To identify which classes are most affected by a degradation, we utilized z-score to quantify the degree of systematic confusion at the class level.

For each class, we measure the change in the top-1 class prediction probability for each image before and after applying degradation. The drop in the top-1 class probability is calculated as: ${\text{drop}}_i=p_{\text{original}}-p_{\text{degraded}}$ Where $p_{\text{original}}$ is the probability of the top-1 prediction before degradation, and $p_{\text{degraded}}$ is the probability after degradation. We calculate this drop for the 10 images per class and compute the mean and standard deviation of these probability drops.

Using these statistics, we compute the z-score for each image's probability drop as: $z_i=\frac{{\text{drop}}_i-\mu }{\sigma }$ To calculate the confusion for the entire class, we compute the mean of the z-scores across all 10 images. Classes with mean z-scores close to zero exhibit consistent confusion, meaning the degradation affects the classification probabilities for all images in a similar way. Classes with higher mean z-scores exhibit more random effects as the degradation causes larger and more inconsistent changes in prediction probabilities across the 10 images. Ultimately, this method allows us to pinpoint the classes that are most sensitive to specific degradations.

Using AUC Scores to Quantify Uncertainty

After identifying the classes most affected by the degradation using the class average z-score method, we used AUC scores to quantify the level of uncertainty introduced by the degradation for specific classes.

To do this, we analyzed how the model's top-1 prediction changed after the degradation was applied. We focused on cases where the model's new top-1 prediction differed from its original top-1 prediction. The newly predicted class after degradation was treated as the "ground truth" for AUC analysis. For each image in the affected classes, we recorded the model's predicted probabilities for this "new ground truth" label and computed an ROC curve to assess how well the model ranked this label compared to other classes.

For example, images of fiddler crabs were frequently misclassified as hermit crabs after applying the pixel size degradation. To quantify this confusion, we treated the hermit crab as the "ground truth" label and calculated the AUC score using the model’s predicted probabilities for the hermit crab across images from both the fiddler crab class and the hermit crab class. This approach allows us to measure how well the model distinguishes the two classes under the influence of degradation.

Figure showing the relationship between the level of degradation (x-axis) and the AUC scores (y-axis) for the hermit crab as the ground truth class, with fiddler crab as the comparison class. The AUC scores quantify the model's ability to distinguish between hermit crab and fiddler crab predictions as the degradation increases, highlighting the impact of degradation on model uncertainty.

Low AUC scores indicated... Specifically, the TPR and FPR values indicate that...Thus, comparing the results with the komodor and the tiger

INSERT PICTURE OF KOMODOR DOG and tiger confused picture INSERT PICTURE of roc/auc curve for komodor and tiger

Appendix

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