Complementary-label learning for arbitrary losses and models
In contrast to the standard classification paradigm where the true (or possibly noisy) class is given to each training pattern, complementary-label learning only uses training patterns each equipped with a complementary label. This only specifies one of the classes that the pattern does not belong to. The seminal paper on complementary-label learning proposed an unbiased estimator of the classification risk that can be computed only from complementarily labeled data. How- ever, it required a restrictive condition on the loss functions, making it impossible to use popular losses such as the softmax cross-entropy loss. Recently, another formulation with the softmax cross-entropy loss was proposed with consistency guarantee. However, this formulation does not explicitly involve a risk estimator. Thus model/hyper-parameter selection is not possible by cross-validation— we may need additional ordinarily labeled data for validation purposes, which is not available in the current setup. In this paper, we give a novel general framework of complementary-label learning, and derive an unbiased risk estimator for arbitrary losses and models. We further improve the risk estimator by non-negative correction and demonstrate its superiority through experiments.
 Pros: - The authors consider an interesting problem of learning from complementary labels - They propose an approach that, assuming that the complementary label is selected uniformly at random, provides an unbiased estimate for any loss function, which is an improvement over the previous work. - Experiments show promising results for modifications of the proposed estimate Cons: - Having an unbiased estimate doesn*t imply that its minimisation is a successful learning strategy. Indeed, the authors show that minimising their original estimate for the cross-entropy loss leads to overfitting. While the authors attribute this behaviour to the fact that the estimate can be negative, I believe the loss being negative is not problem per se (for example, substituting 0/1 loss with -100/-99 loss would not change the learning; similarly, this is not a problem for the losses considered in [Ishida*17]). I would rather attribute the problem to the fact that the proposed estimate is unbounded from below and there are no generalisation guarantees for it. Indeed, assuming there exists a training example that appears in the training set only once, with one complementary label, estimate (8) can be made arbitrary small by just training to predict probability 0 for the provided complementary label on that example ( and any non-zero probability for other classes). - to cope with the above mentioned problem, the authors propose two heuristic-based modifications of the estimate, which are potentially biased. This weakens the initial motivation for finding an unbiased estimate and shifts the focus towards the experimental evaluation - one of the mentioned motivations for unbiased estimates - being able to perform model selection on complementary labeled validation set - is not illustrated in the experiments Questions: - I believe 1/(K-1) normalisation factor in (5) is not needed - there seems to be a mistake in (9) (and its modifications later on) - I would expect either the subscript of the probability distribution in the last summand to be exchanged with in the loss, or a factor added - also, I think there are some mistakes in subscripts in (11) - what loss is the method from [Ishida*17] optimising in the experiments?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Complementary-label learning for arbitrary losses and models
In contrast to the standard classification paradigm where the true (or possibly noisy) class is given to each training pattern, complementary-label learning only uses training patterns each equipped with a complementary label. This only specifies one of the classes that the pattern does not belong to. The seminal paper on complementary-label learning proposed an unbiased estimator of the classification risk that can be computed only from complementarily labeled data. How- ever, it required a restrictive condition on the loss functions, making it impossible to use popular losses such as the softmax cross-entropy loss. Recently, another formulation with the softmax cross-entropy loss was proposed with consistency guarantee. However, this formulation does not explicitly involve a risk estimator. Thus model/hyper-parameter selection is not possible by cross-validation— we may need additional ordinarily labeled data for validation purposes, which is not available in the current setup. In this paper, we give a novel general framework of complementary-label learning, and derive an unbiased risk estimator for arbitrary losses and models. We further improve the risk estimator by non-negative correction and demonstrate its superiority through experiments.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 Pros: - The authors consider an interesting problem of learning from complementary labels - They propose an approach that, assuming that the complementary label is selected uniformly at random, provides an unbiased estimate for any loss function, which is an improvement over the previous work. - Experiments show promising results for modifications of the proposed estimate Cons: - Having an unbiased estimate doesn*t imply that its minimisation is a successful learning strategy. Indeed, the authors show that minimising their original estimate for the cross-entropy loss leads to overfitting. While the authors attribute this behaviour to the fact that the estimate can be negative, I believe the loss being negative is not problem per se (for example, substituting 0/1 loss with -100/-99 loss would not change the learning; similarly, this is not a problem for the losses considered in [Ishida*17]). I would rather attribute the problem to the fact that the proposed estimate is unbounded from below and there are no generalisation guarantees for it. Indeed, assuming there exists a training example that appears in the training set only once, with one complementary label, estimate (8) can be made arbitrary small by just training to predict probability 0 for the provided complementary label on that example ( and any non-zero probability for other classes). - to cope with the above mentioned problem, the authors propose two heuristic-based modifications of the estimate, which are potentially biased. This weakens the initial motivation for finding an unbiased estimate and shifts the focus towards the experimental evaluation - one of the mentioned motivations for unbiased estimates - being able to perform model selection on complementary labeled validation set - is not illustrated in the experiments Questions: - I believe 1/(K-1) normalisation factor in (5) is not needed - there seems to be a mistake in (9) (and its modifications later on) - I would expect either the subscript of the probability distribution in the last summand to be exchanged with in the loss, or a factor added - also, I think there are some mistakes in subscripts in (11) - what loss is the method from [Ishida*17] optimising in the experiments?
assistant
 Pros: - The authors consider an interesting problem of learning from complementary labels - They propose an approach that, assuming that the complementary label is selected uniformly at random, provides an unbiased estimate for any loss function, which is an improvement over the previous work. - Experiments show promising results for modifications of the proposed estimate Cons: - Having an unbiased estimate doesn*t imply that its minimisation is a successful learning strategy. Indeed, the authors show that minimising their original estimate for the cross-entropy loss leads to overfitting. While the authors attribute this behaviour to the fact that the estimate can be negative, I believe the loss being negative is not problem per se (for example, substituting 0/1 loss with -100/-99 loss would not change the learning; similarly, this is not a problem for the losses considered in [Ishida*17]). I would rather attribute the problem to the fact that the proposed estimate is unbounded from below and there are no generalisation guarantees for it. Indeed, assuming there exists a training example that appears in the training set only once, with one complementary label, estimate (8) can be made arbitrary small by just training to predict probability 0 for the provided complementary label on that example ( and any non-zero probability for other classes). - to cope with the above mentioned problem, the authors propose two heuristic-based modifications of the estimate, which are potentially biased. This weakens the initial motivation for finding an unbiased estimate and shifts the focus towards the experimental evaluation - one of the mentioned motivations for unbiased estimates - being able to perform model selection on complementary labeled validation set - is not illustrated in the experiments Questions: - I believe 1/(K-1) normalisation factor in (5) is not needed - there seems to be a mistake in (9) (and its modifications later on) - I would expect either the subscript of the probability distribution in the last summand to be exchanged with in the loss, or a factor added - also, I think there are some mistakes in subscripts in (11) - what loss is the method from [Ishida*17] optimising in the experiments?