Error Slice Discovery via Manifold Compactness

Authors: Han Yu, Jiashuo Liu, Hao Zou, Renzhe Xu, Yue He, Xingxuan Zhang, Peng Cui
Primary area: interpretability and explainable AI
Keywords: Error Slice Discovery, Manifold Compactness, Model Evaluation

Abstract:
Despite the great performance of deep learning models in many areas, they still make mistakes and underperform on certain subsets of data, i.e. error slices. Given a trained model, it is important to identify its semantically coherent error slices that are easy to interpret, which is referred to as the error slice discovery problem. However, there is no proper metric of slice coherence without relying on extra information like predefined slice labels. The current evaluation of slice coherence requires access to predefined slices formulated by metadata like attributes or subclasses. Its validity heavily relies on the quality and abundance of metadata, where some possible patterns could be ignored. Besides, current algorithms cannot directly incorporate the constraint of coherence into their optimization objective due to the absence of an explicit coherence metric, which could potentially hinder their effectiveness. In this paper, we propose manifold compactness, a coherence metric without reliance on extra information by incorporating the data geometry property into its design, and experiments on typical datasets empirically validate the rationality of the metric. Then we develop Manifold Compactness based error Slice Discovery (MCSD), a novel algorithm that directly treats risk and coherence as the optimization objective, and is flexible to be applied to models of various tasks. Extensive experiments on the current benchmark and case studies on other typical datasets demonstrate the effectiveness of our algorithm.

Decision: reject
Reviewer scores: 6, 8, 5, 5

Reviews and discussion:
<thread>
creation date:
1730086440347

thread_type:
official_review

<thread_object>
creator: reviewer_dag2

<content>
summary:
The paper identifies error slices within data subsets using manifold compactness and measures the similarity of certain features in the error samples based on the level of manifold compactness. This approach focuses on detecting error slices that have both high risk (high error rate) and high coherence, making these slices easier to interpret and understand.

strengths:
1. It provides a different perspective for measuring error slices, and this metric does not require predefined slice label information.
2. An algorithm called MCSD is proposed, which directly uses model risk and coherence as optimization objectives.
3. The experimental data is thorough and demonstrates the effectiveness of the proposed method across multiple datasets.

weaknesses:
The further explanation of the experiments is missing. More information pls see Questions.

questions:
1. In the first paragraph of the problem definition on page 2: Does $\mathcal{Y} \times \mathcal{Y}$ represent the Cartesian product of two sets? If so, one should represent the predicted label, and the other should represent the true label. Why are both symbols $\mathcal{Y}$?

2. The method proposed by the authors provides greater interpretability and feature similarity consistency when identifying error subsets, as shown in the visualization results of the CELEBA dataset in Figure 4. However, why does the ACC of the error slices identified by MCSD outperform the SOTA methods by such a large margin? Besides this specific similar feature, what other factors could lead to poor performance of the sliced subsets?

3. Why does Table 4 only compare the MCSD method with the Spotlight method?

4. I have some concerns about the metric proposed by the authors. The expected trend in the experimental data is that as ACC increases, the Comp result should also increase. Why do Tables 2, 3, and 5 not follow this trend? Perhaps I am missing something—do the authors provide any further explanation?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730208339035

thread_type:
official_review

<thread_object>
creator: reviewer_jvfs

<content>
summary:
In this paper, authors propose manifold compactness, a coherence metric that does not depend on additional information, by incorporating data geometric properties into its design. And experiments are conducted on typical datasets to empirically validate the reasonableness of the metric. Authors then propose an method (MCSD), which directly considers risk and coherence as optimization objectives.

strengths:
The authors show the results of many experiments.

weaknesses:
There are a number of problems that the author needs to address, as detailed in the Questions section.

questions:
1. The example given by the author on page 4 is not convincing. The author claims that monotonicity can be used as a criterion for determining whether a measure of the semantics of slices is good, yet I do not think this is sufficient. Suppose I propose a measure that uses the difference between the number of elements in the cluster and the total number of elements as the measure, in which case the slices, as shown in Figure 3, would result in a positive increase in the value of the measure for each further slice, with a consistent trend with the measure proposed by the authors. Clearly, this arbitrarily proposed measure is not superior. Therefore, the authors need to further clarify the example.
(e.g. Provide step-by-step details on how Figure 2c is generated, or clarify the relationship between the optimization variables w and g and how they relate to generating a new space)

2. Some key details are missing. The variables involved in the optimization objective appear to be w and the binary classifier g; how does this generate an new space? How do you generate the picture that the authors show in Figure 2c? If my understanding is wrong, please let me have further information.


3. The author mentions in line 273 that the w obtained by solving Eq. 2 is used to train the slice function g. Are the training samples obtained using w already the desired samples? Does this result in a meaningless slice function g?
(e.g. Clarify the purpose of training g if w already identifies the desired samples)


4. Does the slicing function obtained by the authors give the same output results from the same input data in each slicing? If so, does multiple slices require re-solving Eq. 2 and re-training the slice function g? I think the desired slicing result can already be obtained before training the slicing function g, does this mean that training the slicing function is meaningless? Can the authors clarify this?

5. What is the difference between Eq. 2 and a clustering method? Equation 2 seems to be a clustering method as well. 
(e.g. Discuss how the proposed method specifically addresses the goals of error slice discovery in ways that clustering alone may not )

6. In line 71, the authors describe the coherence method of past methods as only indirectly joining the optimization process. However, the authors' method also seems to be a two-step optimization process: i.e., first optimize the clustering and then optimize the slicing function g. If I have misunderstood, please clarify further.

7. The authors need to clarify further in the Section 1 what is the reason for proposing this method. The current motivation of the authors for proposing the method seems to be somewhat weak.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730223608769

thread_type:
official_review

<thread_object>
creator: reviewer_q2dt

<content>
summary:
The paper focuses on error slice discovery, where error slices refer to specific data subsets on which the model underperforms. It first proposes a new evaluation metric, manifold compactness, which does not rely on external information such as predefined slices or metadata attributes. Furthermore, the paper leverages manifold compactness to design a new error slice discovery algorithm, which can be flexibly applied across various task models.

strengths:
1. This is a relatively new and interesting field that merits further exploration.
2. The organization and writing of this paper are reader-friendly.
3. Extensive case studies support the authors' views, accompanied by new metrics and algorithms.

weaknesses:
1. Although extensive case studies support the authors' viewpoints, the lack of theoretical analysis is regrettable.
2. There is no analysis of time and space complexity. For a dataset of size $n$, constructing a graph requires at least $O(n^2) $ and solving Equation 2 takes $O(n^3)$. In fact, as seen in Table 8, efficiency is indeed a drawback. The authors might consider explaining why this efficiency loss is worthwhile.
3. The paper suggests that Euclidean distance is inferior to manifold, but this may be misleading. In fact, constructing the k-nearest neighbors graph still depends on Euclidean distance. Additionally, because distance variance lacks bounds, it is more sensitive to samples, especially if the sample features are not normalized. Therefore, the superiority of manifold compactness over variance may not be fully convincing. Consider adding a new distance-based measure. Different manifold constructions and distance calculations are also anticipated.
4. The algorithm is divided into multiple parts, and an end-to-end model would be more desirable.

questions:
See Weaknesses.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730555294071

thread_type:
official_review

<thread_object>
creator: reviewer_gugx

<content>
summary:
This paper studies ERROR SLICE DISCOVERY issue. In the paper, the authors mainly proposed the concept of manifold compactness and a coherence metric. The proposed optimization objective can be applied to models of various tasks. The authors also conduct many experiments to demonstrate the effectiveness of the method.

strengths:
The authors mainly proposed the concept of manifold compactness and a coherence metric.

weaknesses:
The paper is difficult to understand and follow as the source code is not provided.

questions:
1. The dimensions of all variables are not provided clearly, making the paper difficult to understand.
2. What’s the physical meaning of the second term in (2)? What’s the optimization solution for (2)?
3. There are not enough comparison methods. 
4. What are the main advantages of the proposed method compared with the existing works?
</content>
</thread_object>

</thread>
<thread>
creation date:
1732293170213

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Common Response

comment:
We thank all reviewers for their valuable comments. In this common response, we will list all the changes we have made in the revised version of paper according to the reviews. The changes are also marked in blue on page 1, 5-6, 16, and 34-36. 

1. On page 1, we modify Section 1 to better illustrate the motivation of error slice discovery in the first paragraph. 
2. On page 5-6, we remove the training of the slicing function from the algorithm procedure and put it into the section of experiments as part of the experimental details, since we designed this component mainly for fair comparisons with previous methods that output a slicing function and it is not a necessary component of our algorithm. We also add a new subsection of Appendix A.11 on page 36 to illustrate that our method is still effective without the additionally trained slicing function. 
3. On page 16, in Appendix A.1.2, we add comparisons with three other metrics that are directly calculated in the Euclidean space: Mean Absolute Deviation, Median Absolute Deviation, and Interquartile Range, so that the superiority of our proposed metric can be better demonstrated. 
4. On page 34-35, we add a new subsection of Appendix A.10, where we conduct some theoretical analyses on Equation 2, the optimization objective of our method. We theoretically prove that our optimization objective not only explicitly considers the manifold compactness inside the identified slice, but also implicitly considers the separability between samples in and out of the identified slice. Meanwhile, we theoretically prove that our optimization objective is equivalent to the discrete version of sample selection with proper assumptions, which confirms the validity of transforming the sample selection problem into the continuous version for the convenience of optimization. 

We sincerely hope that these modifications could help address reviewers' concerns, and that reviewers might kindly take these improvements into account when evaluating our contributions after rebuttal. Thanks again for your time and efforts in reviewing our work!
</content>
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</thread>


Metareview:
metareview:
I have read all the materials of this paper including the manuscript, appendix, comments, and response. Based on collected information from all reviewers and my personal judgment, I can make the recommendation on this paper, reject. No objection from reviewers who participated in the internal discussion was raised against the reject recommendation.

**Research Questions**

This paper considers error slice discovery problem that identifies several semantically coherent and incorrectly predicted subsets. 

**Challenge Analysis**

The authors argue that the existing methods employ the predefined metadata and do not consider the coherence. 

**Philosophy**

The authors aim to solve the research problem purely from the data and take the coherence into consideration.

**Technique**

Based on the above philosophy, the authors formulate an optimization. The technique is straightforward but suffers from high computational cost. Moreover, the authors do not consider the case with multiple error slice.

**Experiment**

The experiments are not solid, which do not well address the research problem. (1) The authors fail to demonstrate the identified subset is semantically coherent. The trivial solution that returns all the wrongly prediction samples as a set can achieve high performance in terms of the metrics used in this paper. (2) Parameter analysis and corresponding experiment setup is missing.