Hyper Evidential Deep Learning to Quantify Composite Classification Uncertainty

Thank you for your constructive feedback and for recognizing the novel aspects of our work. We appreciate the opportunity to address your concerns regarding the empirical evaluation of our framework.

Are all the composite labels used in the empirical evaluations synthetically generated? Could you provide more concrete examples in these synthetic datasets? I am curious how realistic these generated composite labels are. is it possible to run evaluations on real-world composite set labels?

The composite labels used in our empirical evaluations were indeed synthetically generated. One concrete example could be found in Fig.1(right). A blurring image which is difficult to distinguish between {husk} and {wolf}. We admit that the datasets with Gaussian blurring are semi-synthetic. From a sizable pool of applicants, we selected 23 students from our department and tasked them with annotating images in the CIFAR10 dataset, categorizing each as either a singleton class or a composite set. This effort successfully resulted in a real-world dataset enriched with human-annotated singleton and composite labels. Our method, along with various baseline approaches, was applied to this dataset. The comparative results were in line with those obtained from the synthetic datasets. Additionally, we plan to publicly release the dataset and the labels. The following table results are also represented in the Table 15 in the rebuttal revision. We also show AUROC curves in Figure 7 in the revision, which indicates that vagueness is still the best among different uncertainties to distinguish composite examples from singleton examples.

Backbone: ResNet18

Backbone: EfficientNet-b3

Please kindly let us know if you have any concerns you find not fully addressed. We are more than happy to have a further discussion regarding it. Thank you so much for your time!

Specific Q10: It is unclear exactly how superclasses are extracted for Living17 and Nonliving26 datasets.

The extraction of superclass and class hierarchy for these two datsaets are explored by Santurkar et al. (2021). We add one sentence in the Datasets&Preprocessing (Section 5.1):

“Their superclasses and hierarchy information have been extracted by Santurkar et al. (2021) based on visual similarities.”

We also introduce more detail in Appendix E.1 to explain why the Living17 and Nonliving26 are considered:

"Additionally, distinguishing between different classes can often be challenging due to their similar visual features. Unlike WordNet, which organizes its hierarchy based on semantic relationships between words, the class hierarchies of Living17 and Nonliving26 are constructed considering both visual and semantic similarities. These two subsets, part of the broader ImageNet dataset (Deng et al., 2009), consist of images with a resolution of 224×224 pixels. For detailed information about these subsets, please refer to Tables 5 and 6 in the original paper."

Specific Q11: The full list of data augmentations is required for reproducibility.

Data augmentation has been included in Appendix E.2 actually. To make this more clear, we add more sentences to explain what data augmentation we used at the end of Appendix E.2:

“We used 2 methods for data augmentation following a typical computer vision setting. First, each image is applied to a random horizontal flip with the flipping probability of 0.5. After that, a random corp is introduced for each image with a size of 32×32 and padding of 4.”

Specific Q12: Up until the last paragraph in page 26 in Appendix, it is not clear how the process of duplicating samples with composite labels is working (there is no reference to this paragraph in the earlier text).

We add detailed process to explain this in Appendix E.3 Implementation:

DNN and ENN are typically designed to process examples with singleton labels and cannot deal with composite class labels during training. Given that our training dataset includes vague images with composite class labels, we have devised a strategy to enable these baseline models to handle such examples without eliminating training data. This involves duplicating composite examples and assigning them singleton labels derived from their composite set labels, ensuring that all class labels during training remain exclusive. For instance, if there is an image x with a composite label A, B during training, we create two duplicates of x – one labeled as singleton A and the other as singleton B – and use these as inputs for model training.

Specific Q13: Section F.4 There are SinglJS, SingleAcc and Acc mentioned in different places. What is the correct one?

We united these terms to Acc in F.4. Basically it means the top-1 accuracy for singleton label prediction.

Quality: The code is provided which should elevate this weakness, but based on the text not all implementation details are provided sufficiently to reproduce the results. See details below. Different types of image corruption would be interesting to see in the experiments, in addition to the Gaussian blur.

We have added more detail which is necessary to reproduce the results according to the above questions. In addition, we also wrote a README file in our code repo to explain how to use our code.

For different type of image corruption in addition to Gaussian blur, use another data corruption method: bicubic interpolation, which is popular in the super-resolution research community. For example, in paper [1], the low resolution (LR) input is generated based on the high resolution images. Also, the same method is also used in paper [2]: “The LR counterparts are downsampled using bicubic interpolation”. The first column is LR image after Bicubic interpolation in the following figure (figure 6 from paper [1]):

we conduct experiments on Living17dataset. The results are shown below and also represented in Appendix Section F.6.3. It indicates the consistence with results using Gaussian Blur.

Reference:

• [1] Image Super-Resolution via Iterative Refinement, TPAMI 2022
• [2] Super-Resolution Neural Operator, CVPR 2023

Other Minor issues

We have updated them.

Please kindly let us know if you have any concerns you find not fully addressed. We are more than happy to have a further discussion regarding it. Thank you so much for your time!

We appreciate your thorough review of our paper and the opportunity to address your concerns, particularly regarding the motivation and practical implications of our work.

The question of motivation of the problem setup. I.e. how important is the problem of having composite labels during training and why do we need to also output composite labels by a NN?

We added two more examples in the first paragraph of the Introduction section to motivate the problem setup.

“In various applications, particularly those dependent on data from low-quality sensors or high-quality data with insufficiently distinct features to separate some individual classes, the resulting data often exhibits significant vagueness and ambiguity (Allison, 2001; Ng et al., 2011). For example, in security surveillance, grainy images from store cameras may not provide clear enough resolution to accurately distinguish between different individuals or activities, necessitating the use of composite class labels to address this uncertainty (Allison, 2001). Similarly, in the field of medical imaging, a radiograph displaying features suggestive of multiple possible diagnoses may require composite labels to capture this uncertainty (Allison, 2001) effectively.”

The area of research devoted to multiclass classification is missing in the related works (e.g., Augustin, A.; Venanzi, M.; Hare, J.; Rogers, A.; and Jennings, N. 2017. Bayesian aggregation of categorical distributions with applications in crowdsourcing. AAAI Press/International Joint Conferences on Artificial Intelligence, but there are lots of others).

The AAAI paper by Augustin et al. considers the problem of aggregating judgments (labels) of proportions from crowdsourcing annotators that are skewed and may provide judgments randomly (i.e., they are spammers). This is different from our work. We are concerned with images collected in challenging environments where weather, poor lighting, smoke, fires, poor focusing, etc., lead to less-than-ideal images. Clean images lead to precise annotations, and degraded images lead to vague annotations. We expect the classifier to make the best classification effort and provide a composite label when the image is degraded to the point that a human cannot discern a singleton. In short, we are concerned with composite and precise labels for possibly poor-quality images. The classifier needs to make a best-effort prediction for the degraded images as opposed to a bad singleton prediction.

the experiments with the composite labels in training, which is not well motivated how often in practice we would have these labels for training. To this end, I think a small experiment, showing that the proposed framework still works with traditional setup of single labels for training only, would be beneficial.

We added extra experiments on singleton class only datasets and evaluated the performance on traditional classification tasks with Accuracy for ENN and our HENN. Please refer to the result shown in Appendix F6.4. Tab.18 presents the accuracy results from the ENN and HENN methods trained and evaluated on CIFAR100 with only singleton class data (without Gaussian blurring and label replacement) across 5 trials each. The mean accuracy and the standard deviation are reported. Under a traditional singleton classification setting, HENN still shows comparable performance in terms of accuracy compared to ENN model. A notable advantage of HENN is its ability to quantify an additional type of uncertainty compared to ENN with minimal performance degradation observed even if the training data consists of exclusive singleton ones.

Moreover, performance seems to heavily depend on regularization hyperparameter, which is selected in an ad-hoc manner. Is this a pitfall for method's robustness over different datasets?

We proposed a KL-based regularization term in Equation (14) to address the limitations of the UPCE loss function analyzed in our Propositions 1 and 2, discussed in Section 4.1. The best hyperparameter ($\lambda$) of this regularization term was selected based on a grid search on the validation set for each dataset, a standard procedure for hyperparameter selection. We observed consistent performance results across our datasets, so our method is robust over different datasets. We also analyzed other variants of the regularization term, and the results are reported in Table 3 shown in Section 5.2. The results demonstrate that the HENN learned based on the KL-based regularization term or its variants consistently outperforms other baselines in different settings, indicating its robustness.

We note that the traditional ENN incorporates a different KL regularization term primarily to increase the vacuity for samples likely to be misclassified. This term can be considered a special instance of our proposed KL-based regularization term in Equation (14) when the prediction is Dirichlet distribution for singleton classes instead of hyperDirichlet distribution for singleton class or composite set labels. We will discuss this relation in our revised version. To summarize, our proposed HENN does not have more hyperparameters than ENN, but the regularization term is designed differently to address the limitations of UPCE for hyper-dirichlet predictions.

Please kindly let us know if you have any concerns you find not fully addressed. We are more than happy to have a further discussion regarding it. Thank you so much for your time!

We thank you for your insightful review and the opportunity to address the concerns raised regarding our work on our work!

The dataset used in the paper is a rather specific synthetically generated experiment, which can not justify the significance of the results over real-world applications. would it be possible to apply the method in real-world applications involving composite labels?

We employed synthetic datasets generated through Gaussian blurring (as per Richard Webster et al. 2018), due to the absence of public benchmarking datasets with composite set labels from annotators. Annotators of commonly used benchmarking datasets, such as CIFAR100 and TinyImageNet, are typically restricted to providing only singleton class labels, lacking the option for composite class labeling. As a result, these datasets do not include any composite class labels. Gaussian blurring is commonly used to simulate images collected from low-quality sensors (e.g., security and surveillance cameras) (add references) that human annotators will more likely label as composite sets of classes, as these images lack fine details annotators can spot to label singleton classes. However, we admit that the datasets with Gaussian blurring are semi-synthetic. From a sizable pool of applicants, we selected 23 students from our department and tasked them with annotating images in the CIFAR10 dataset, categorizing each as either a singleton class or a composite set. This effort successfully resulted in a real-world dataset enriched with human-annotated singleton and composite labels. Our method, along with various baseline approaches, was applied to this dataset. The comparative results were in line with those obtained from the synthetic datasets. Additionally, we plan to publicly release the dataset and the labels. The following table results are also represented in the Table 15 in the rebuttal revision. We also show AUROC curves in Figure 7 in the revision, which indicates that vagueness is still the best among different uncertainties to distinguish composite examples from singleton examples.

Backbone: ResNet18

Backbone: EfficientNet-b3

References: RichardWebster, Brandon, Samuel E. Anthony, and Walter J. Scheirer. "Psyphy: A psychophysics driven evaluation framework for visual recognition." IEEE transactions on pattern analysis and machine intelligence 41.9 (2018): 2280-2286.

did you perform experiments on more relevant benchmark datasets, like NABirds

As the NABirds dataset does not have composite class labels from annotators, similar to the datasets that we used, we degraded the images in NABirds synthetically based on Gaussian blurring in the same way used in our other synthetic datasets and compared our proposed HENN and other baselines. The results are shown below. It indicates that HENN outperforms DNN and ENN for a large margin in terms of CompJS. And HENN also performs better in terms of OverJS and Acc, which is consistent with previous experiments on reported four datasets in the paper.

However, we admit that the datasets with Gaussian blurring are semi-synthetic. From a sizable pool of applicants, we selected 23 students from our department and tasked them with annotating images in the CIFAR10 dataset, categorizing each as either a singleton class or a composite set. This effort successfully resulted in a real-world dataset enriched with human-annotated singleton and composite labels. Our method, along with various baseline approaches, was applied to this dataset. The comparative results were in line with those obtained from the synthetic datasets. Additionally, we plan to publicly release the dataset and the labels. The following table results are also represented in the Table 15 in the rebuttal revision. We also show AUROC curves in Figure 7 in the revision, which indicates that vagueness is still the best among different uncertainties to distinguish composite examples from singleton examples.

Backbone: ResNet18

Backbone: EfficientNet-b3

the selected datasets are not suitable to demonstrate a (at least for me) complex theory behind uncertainty and how to include it into deep learning loss functions and regularization. For example, I am not sure what Gaussian blurring will make with tiny-images, i.e. what remains as information after blurring.

Gaussian blurring is commonly used to simulate images collected from low-quality sensors (e.g., security and surveillance cameras) (Richard Webster et al. 2018) that human annotators will more likely label as composite sets of classes, as these images lack fine details annotators can spot to label singleton classes. Although the blurred images may not have edges and fine details, the annotators can still rule out some classes based on the shapes and other features of the objects within the images (e.g., horses can be easily distinguished from cats and dogs in their traits).

We have generated synthetic datasets based on four base datasets, including CIFAR100, TinyImagenet, living-17 and non-living-26. Now all the datasets are tiny images. The first two datasets are small in image sizes (32 x 32). The images in living-17 and non-living-26 are greater than 224 x 224, but we rescaled them to 224 x 224.

As detailed in our response to the preceding item 2, we also conducted the empirical comparison on a real-world dataset CIFAR10 enriched with human-annotated singleton and composite labels. The results are consistent with the results on the five synthetic datasets.

References: RichardWebster, Brandon, Samuel E. Anthony, and Walter J. Scheirer. "Psyphy: A psychophysics driven evaluation framework for visual recognition." IEEE transactions on pattern analysis and machine intelligence 41.9 (2018): 2280-2286.

The authors suggest DST for solving this issue, which I did not see before for DNN. If the theoretical analysis (Sec. 4.1) can be confirmed to be correct and relevant in practice (which I could not!), I would see a relevant contribution by this work, at least to inspire others to look into hyper-opinions.

In essence, our proposed HENN is the GDD extension of evidential deep learning (Ulmer et al. (2023)) (which was based upon Dirichlet distributions). As demonstrated in the detailed proofs in Sections C.2 and C.3 in Appendix, the two propositions are correct and demonstrate the need for the KL term so that only the evidence for the ground truth class tends to infinity. The issues of the UPCE identified by our two proposition 1 are also empirically verified by our case study on CIFAR100 in Appendix F.7: (1) the HENN learned based on UPCE and a training set consisting of only singleton class labels predicts non-zero evidence on composite set labels for 14.4% of the training samples even that the training set does not have evidence of composite class labels to accumulate, and (2) the HENN learned based on UPCE and a training set consisting of only composite class labels predicts non-zero evidence on singleton class labels for 100.0% of the training samples even that the training set does not have evidence of singleton class labels to accumulate. Our proposed regularization can avoid these unexpected behaviors.

References: Dennis Thomas Ulmer, Christian Hardmeier, and Jes Frellsen. Prior and posterior networks: A survey on evidential deep learning methods for uncertainty estimation. Transactions on Machine Learning Research, 2023.

I am also not happy with the theoretical part of the paper, although I have to admit that I am not that familiar with DST, and this hindered me from diving deeper into the derivations done in Sec. 4.1 The notation and style of presentation is probably only proper for an expert in this area.

In our updated submission, we revised Section 4.1 to explain the proposed regularization term in more detail. We added a paragraph at the end of this section to discuss the motivations and limitations of our theoretical analysis. An ablation study is discussed at the end of Section5.2 to empirically demonstrate the need for the regularization term. We also added more explanations in the proofs of the propositions in Appendix C.2 to make the proofs more self-contained.

Please kindly let us know if you have any concerns you find not fully addressed. We are more than happy to have a further discussion regarding it. Thank you so much for your time!

We appreciate your insightful feedback and the opportunity to clarify aspects of our work. Your comments have given us a chance to articulate the novelty and strengths of our approach more clearly.

Do you see any relation to Brust et al.: Making Every Label Count: Handling Semantic Imprecision by Integrating Domain Knowledge. ICPR 2020 and which concepts of this work is related to yours?

The problem setting of the work by Brust et al. is stated in Section III of the ICPR 2020 paper: “We require the classifier to predict only precise labels from $Y$. At the same time, it needs to be able to learn from training data with labels from both $Y$ and $Y^+$, which we refer to as semantically imprecise data”. Here, the authors refer to “precise labels” as singleton labels. The Experimental Section V only evaluates the accuracies of the proposed method, named CHILLAX, and baselines on this problem setting. It is unclear if this method can be effectively adapted to predict composite set labels.

In our proposed work, we are training a classifier to perform on par with human annotators where the training data is annotated by humans, so there is no ground truth. With that said, we expect to be concerned with images collected in challenging environments where weather, poor lighting, smoke, fires, poor focusing, etc., lead to less-than-ideal images. Clean images lead to precise annotations, and degraded images lead to vague annotations. We expect the classifier to make the best classification effort and provide a composite label when the image is degraded to the point that a human cannot discern a singleton. In short, we are concerned with composite and precise labels for possibly poor-quality images. The classifier needs to make a best-effort prediction for the degraded images as opposed to a bad singleton prediction. This differs from CHILLAX, which assumes pristine images, but subsets of annotators do not have the expertise to provide singleton labels.

Based on the above motivation, our proposed HENN model is designed to quantify a new type of uncertainty, called 'vagueness', for each singleton or composite prediction. This vagueness measure refers to the degree of predictive uncertainty caused by evidence in training samples with composite labels. This offers useful insights for decision-making in safety-critical applications, such as medical disease classifications.

To explain vagueness, suppose we have two singleton classes: 'cat' and 'dog'. Suppose the evidence supporting a prediction for an input image includes 6 training images labeled as 'cat' (a singleton class) and 4 images labeled as the composite set {cat, dog}. HENN compares these quantities (6 > 4) and predicts the singleton class {cat}. However, it also assigns a non-zero vagueness score 0.33, reflecting the presence of evidence from the training samples with composite labels. Let “c” and “d” denote cat and dog, respectively. The evidence of cat $e_c = 6$ and $e_{c,d} = 4$. According to Equations (2) and (5), the vagueness $vag = b_{c,d} =4/(e_c + e_{c,d} + K) = 4/12=0.33$, where $K = 2$ refers to the number of singleton classes. This vagueness score is important as it informs the user that the prediction is partly supported by training samples with composite set labels (e.g., {dog, cat}) while the ground truth is a singleton class (e.g., {cat} or {dog}).