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 pinpointing specific classes that the degradation affected the most using the class average z-score method, we used AUC scores as a way to quantify the amount of uncertainty the degradation introduced to specific classes.

Specifically, we looked at the new top-2 labels that the model was predicting after we applied the image degradations. The new high probability label was set as the ground truth label, and the ROC/AUC is calculated by using the model's probabilities associated with that label for each image in the dataset of each class. As an example, tigers were regularly confused with different species of dog, thus, we produced an AUC curve where the ground truth label was the komodor dog, and we supplied the probabilities associated with that class from each of the ten images in the komodor and tiger class.

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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