Binary Classification with Confidence Difference

Recently, learning with soft labels has been shown to achieve better performance than learning with hard labels in terms of model generalization, calibration, and robustness. However, collecting pointwise labeling confidence for all training examples can be challenging and time-consuming in real-world scenarios. This paper delves into a novel weakly supervised binary classification problem called confidence-difference (ConfDiff) classification. Instead of pointwise labeling confidence, we are given only unlabeled data pairs with confidence difference that specifies the difference in the probabilities of being positive. We propose a risk-consistent approach to tackle this problem and show that the estimation error bound achieves the optimal convergence rate. We also introduce a risk correction approach to mitigate overfitting problems, whose consistency and convergence rate are also proven. Extensive experiments on benchmark data sets and a real-world recommender system data set validate the effectiveness of our proposed approaches in exploiting the supervision information of the confidence difference.

Paper

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Peer review

Reviewer G7aZ9/10 · confidence 3/52023-07-06

Summary

This paper studies binary classification problems. A new data type is introduced, where each observation consists of two input instances, together with the "confidence difference," defined as the difference of the conditional probabilities (output=1|input) of the two input instances. New loss functions are introduced and the excess risk bound is derived with probability. To extend the research, the author(s) also studied the case when the confidence difference is contaminated by noise, and the idea of rectifying the empirical loss function by dropping the negative summands. Empirical tests are done on benchmark datasets where the proposed algorithm consistently outperforms the competitors.

Strengths

To my knowledge, the proposed data type (based on confidence difference) is new. The presented research is original. The high quality of the research is guaranteed by solid theoretical analysis, and the definition of a new class of classification data that captures more possible application scenarios. This paper is written clearly and is easy to follow. The broad application scenarios support the significance of the research.

Weaknesses

I have no major concerns about this work. Some minor issues are listed in the "Questions" section below, for the author(s) to clarify.

Questions

1. Table 2 has a structure similar to Table 1 in [11]. In particular, the methods Pcomp-*** have different values from those reported in Table 1 in [11]. Would it be possible for the author(s) to take a look at Table 1 in [11] and briefly explain the difference in experiment design or other conditions that leads to such a difference in the values in these two tables? Same question for Table 2 of this manuscript, and Table 3 in [11]. 2. It seems that the density (or probability mass function?) tilde-p defined in Eq. (4) is not used elsewhere. Is that true? Is there any insight into this density? 3. Since x and x' are drawn from the same probability distribution, what is the relation between x_i and x_i'? Is the sample in Line 137 just n independent copies? Would the analysis still work if n=m^2 is the square of some integer, so that x_i and x_i's are obtained by the full combination of some sample points u_1,...,u_m? 4. Is the definition (6) and (8) newly introduced, or cited from the literature? It would be better if the author(s) could specify the facts around these equations.

Rating

9: Very Strong Accept: Technically flawless paper with groundbreaking impact on at least one area of AI/ML and excellent impact on multiple areas of AI/ML, with flawless evaluation, resources, and reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

4 excellent

Presentation

4 excellent

Contribution

4 excellent

Limitations

This is theoretical research, and I have not identified any limitations.

Reviewer XYQ66/10 · confidence 3/52023-07-06

Summary

The paper discusses weak supervised learning for binary classification, specially in the setting where labeled data is not available. Based on pairwise-comparison (Pcomp) confidence, where we are given data pair $(x_1, x_2)$ and binary label {+1, -1} of $x_1$ being more or less probable of being positive compared to $x_2$, this paper suggests the novel problem setting of ConfDiff, where we are given $((x_1, x_2), P(y = 1 | x_2) - P(y = 1 | x_1))$. The paper then proceeds to provide risk estimators and error bounds for this new problem setting. Experimental results on curated benchmarks and one real benchmark shows the usefulness of the paper’s theoretical results and motivated algorithm.

Strengths

1. The paper is well written and organized. 2. The theoretical results in the paper are non-trivial and well done. 3. Good experiments and ablation studies.

Weaknesses

My main complain with the paper is that the problem setting does not feel well justified. Since the main goal of the paper is to suggest a novel problem setting, this is a big weakness. For example, in line 39, the paper makes the claim that $P(y = 1 | x_2) - P(y = 1 | x_1)$ values might be less biased than individual $P(y = 1 | x_2)$ and $P(y = 1 | x_1)$ estimates by human labelers. I do not think this claim is well justified. Similarly, line 51 claims that section 4 will give a real world case study of this problem. While section 4 does present a real world problem where the paper’s algorithm works better, it is not clear that this is due to the problem setup being more useful/ideal. More study would need to establish that this problem setup has indeed lower bias then the case of pointwise confidence value, possibly with collecting a large scale dataset with human annotators. Finally, if someone is unconvinced of the problem setting, the paper seems **tautological**, i.e., defining a custom problem where a modified risk estimator works (which, while the proof being involved, is not hard to see).

Questions

1. Based on the weakness mentioned, are there prior works that suggests this problem setup is more meaningful? 2. Line 233, “Since the data sets were originally designed for multi-class classification, we manually partitioned them into binary classes.”, how is this manual partitioning done for each dataset? Referencing to the appendix would be fine here.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

4 excellent

Contribution

2 fair

Limitations

N/A

Reviewer DX8U6/10 · confidence 3/52023-07-06

Summary

- This work proposes a confidence label based training approach called _ConfDiff_ for binary classification models as an improvement over traditional hard labels. Specifically, authors argue that obtaining hard labels for traditional supervised learning paradigm, or confidence metrics around positive labels for weakly supervised learning paradigm is expensive and at times infeasible process. Therefore, they propose training such classification models on pairwise comparisons between confidence in positive labeling of training data example. - Authors prove error bounds, and demonstrate the robustness of the proposed approach theoretically. - Authors evaluate the proposed approach on benchmark classification datasets and a real world recommender system.

Strengths

**Motivation** Authors make a strong technical as well as intuitive case in support of their approach, _ConfDiff_, in comparison to prevalent approaches in the related work such as _Pconf_. Similar to traditional supervised learning paradigm where approaches such as _soft labeling_, _pairwise loss_, etc. have provided benefits over pointwise models utilizing hard labels in the form of increased robustness and robustness, it is intuitive that pairwise confidence differences should outperform methods like _Pconf_, as demonstrated by the paper. **Technical Presentation** The work is very well presented and easy to digest. The Preliminaries section sets up the reader very well equipped to compare/contrast the proposed approach with existing classification approaches. Specifically, the authors do a great job at using formal notations with perfect granularity required to compare different approaches, without being overwhelming to the reader. **Experiments** Authors evaluate their proposed approach on multiple benchmark datasets as well one real world recommender system dataset. All the details as well as source code required for reproducibility are available in the Appendix section of the work. The observed evaluation metrics clearly favors the proposed approach against the baseline comparisons. Authors further analyze the sample efficiency and robustness of the proposed approach and provide empirical evidence supporting the theoretical analysis in the prior sections.

Weaknesses

**Choice of comparative baselines** While the authors clearly position their work as an improvement over the existing approaches in weakly supervised learning domain, they make a case throughout the introductory as well as technical sections regarding benefits over traditional hard label supervised learning. Given that _ConfDiff_ was evaluated using backbones such as ResNet-34, I believe it would help the work to include inside Table 1 the metrics corresponding to vanilla ResNet-34 or logistic regressions. **Generalizability of proposed approach** Theoretical contributions not withstanding, it is not entirely clear how generalizable the proposed approach is in terms of obtaining confidence difference values. Authors present the real world evaluation on KauiRec dataset where _watching ratio_ i.e., ratio of watching time of short video and total length of short video, has an intuitive relationship with $p(y=1|x)$. > We clipped the watching ratio above 2 and regarded the examples with watching ratio greater than 2 as positive examples. Following the experimental protocol of [8], we regarded the latest positive example for each user as the positive testing data, and sampled 49 negative testing data to form the testing set for each user. As I understand, based on the above text in the Appendix, even in this example, the authors had to resort to assigning hard labels to training data using a heuristic based approach. I am not sure what would be a similar intuitive approach to compute $c(x, x^{\prime})$ in a more common user-item recommender system where purchase labels/click labels are by nature hard labels, and the priors are heavily biased by the fact that only limited number of recommendations can be shown to a user?

Questions

- Could you address the weakness/include discussions about the same in the manuscript?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

In the Appendix section, authors have addressed limitations of the approach being currently limited to binary classification and potential negative societal impact in terms of loss of annotation work.

Reviewer Qs9H6/10 · confidence 4/52023-07-07

Summary

The paper proposes to solve a classification problem using weakly supervised learning problem called confidence-difference (ConfDiff) classification, where unlabeled data pairs are equipped with confidence difference specifying the difference in the probabilities of being positive. The authors further develop a risk-consistent approach to tackle this problem and show that the estimation error bound achieves the optimal convergence rate. They provide additional analysis for noisy labels. The authors empirically show the effectiveness of their suggested technique on several classification benchmarks such as MNIST, CIFAR-10 and FASHION datasets (TABLE 1), where they show that they approach performs better compared to PComp methods. They further show effectiveness of their method in leveraging the supervision information of the confidence difference on a real-world recommender system data set.

Strengths

The paper is relatively clear and presents an interesting take on classification approach. Instead of an exact label the paper proposes to use relative confidence and provides theory to establish the performance bounds. The paper further validates the effectiveness on a real world recommender dataset, surpassing PComp teacher. The authors also investigate what happens when the volume of the labeled data is reduced and show that the suggested approach achieves superior or comparable performance even when only 10% of training data are used. It elucidates that leveraging confidence difference may be more effective than increasing the number of training examples.

Weaknesses

My main concern is that there is no comparison to a performance based on regular labels. Such comparison can at least show the gap in case regular classification performs better (and labels can be provided). Also the authors mention medical application in motivation, however they do not provide experiments with similar data.

Questions

Please add performance of regular classification for your experiments if such is possible to benchmark. Are there any other methods applicable for the Recommendation systems you can compare against? Providing more comparisons will help to strengthen your experimental section.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

I feel there are not so many applications that will have relative comparison between two samples. The two applications provided in the motivation are well-suited for such approach, but unfortunately the method is only benchmarked on one application. The authors might want to benchmark against additional application that benefits from relative comparison.

Reviewer XYQ62023-08-11

Follow-up question: **The claim that the confidence difference has a lower bias is not well justified.** Based on the authors' answer, do all the data points $((x, x'), c(x, x'))$ get collected from the same expert/confidence estimation system? The medical use-case example the authors provided works if the confidence estimate of two doctors, let them be $c_1(x)$ and $c_2(x)$, vary by a constant, i.e, there exists $A$ such that $c_1(x) = c_2(x) + A$ for all $x$. Then for any $x, x'$, we have $c_1(x) - c_1(x') = c_2(x) - c_2(x')$. However, it is quite possible that this is not the case. In the extreme case, the confidence difference estimated by two doctors on the very same data pair can be different. In the less extreme case, similar data point pair can get different confidence difference estimate by two doctors. It is quite likely that any such large scale dataset would contain annotations by multiple experts, thereby bringing the same bias. Would the authors have any intuitive or theoretical explanation for why confidence difference would have a lower bias in this case?

Authorsrebuttal2023-08-12

Response to the Further Question

First of all, we would like to express our sincere gratitude for your valuable comments and insights. Based on your valuable question, both pointwise confidence and pairwise confidence difference can be biased in many cases. Then, we conducted more theoretical analysis and found that our setting would have a lower bias. We assume that the output of the confidence estimation system is given by a deterministic function. Let $x$ denote the ground-truth pointwise confidence value and $y$ denote the output confidence value given by the estimation system. For a pair of examples, the ground-truth confidence values are $(x_1, x_2)$. The outputs of the confidence estimation system are $(y_1, y_2)$. If we use the pointwise confidence value directly, the total bias is $$E_{point}=|y_1-x_1|+|y_2-x_2|.$$ If we consider the confidence difference, then the total bias is $$ \begin{align} E_{pair}&=|(y_1-y_2)-(x_1-x_2)| \\\\ &=|(y_1-x_1)-(y_2-x_2)|. \end{align} $$ Based on the absolute value inequality that $|A-B|\leq |A|+|B|$, we have $E_{pair} \leq E_{point}$. The implication is that the pairwise confidence difference can have a lower bias than the pointwise confidence for a given estimation system. The conclusion can also be extended to the existence of multiple estimation systems (doctors). Therefore, the confidence difference would have a lower bias in this case. I hope this rebuttal addresses your concerns. If you have any further concerns or questions, please do not hesitate to raise them. Thank you again for your time and effort in reviewing our submission.

Reviewer DX8U2023-08-14

I thank the authors for addressing some of my concerns mentioned in the review and their acknowledgement of a potential limitation of the proposed approach. Considering the additional information, my overall rating of the work remains unchanged.

Reviewer G7aZ2023-08-16

notation not used elsewhere may be removed

We appreciate the comprehensive information. For Q2, we think that a notation not used elsewhere may be removed.

Authorsrebuttal2023-08-16

Thank you for your suggestion. We will remove the unused notation in the final version of our paper.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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