Venue: UAI 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate to high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations. 
review_content: Q1 Summary and contributions: This paper analyzes the Monotonicity Regularization.
It adds noise and interpolation to populate the space and enforce the penalty in a larger region so that the monotonicity property can be guaranteed if space shifts. 
For the applications of Monotonicity Regularization: 1. it could help to control the generation process and produce outputs with smooth transitions in VAE. 2. propose Group Monotonicity, the corresponding classification models could provide explanations and detect anomalous data.
Q3 Main strengths: 1. The applications of monotonicity regularization are helpful in terms of generation, interpretation, robustness, and anomaly detection. 
2. The experiments are comprehensive, and the example is straightforward. 
3. The monotonicity regularization is a general concept that can be adapted to other application domains and it is compatible with a variety of neural network structures without hurting the predictive performance. 
Q4 Main weakness: 1. The related work section focuses on different approaches to achieving monotonicity, but does not discuss the previous application of monotonicity regularization. The novelty in terms of the applications of monotonicity regularization should be further justified. 
2. It is not clear about the requirement of the monotonicity, such that in section 3 it is required to control over the volume of the input space while it is not a requirement in section 4.  
3. The mechanism why the group monotonicity can help the anomaly detection is not clearly described. 
Q5 Detailed comments to the authors: 1.In section 4.2.1, you use activations a_w(x) while in 4.2.2 p_k(x) is applied. Could you please tell the intuition of the different choices? 

Q2(4) Quality of experiments (Optional): 3: Good: The experimental evaluation is adequate, and the results convincingly support the main claims.
Q7 Justification for your score: Monotonicity Regularization is applicable to different tasks and model structures, to help with generation, interpretation, robustness, and anomaly detection. 
The writing and reproducibility need to be improved.
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final_score: rating: 6: Weak Accept: Technically solid, moderate to high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations. 
review_content: Q1 Summary and contributions: This paper explores monotonicity regularization in the context of risk minimization using deep function approximators. 
Q3 Main strengths: The paper is well motivated from a practical perspective.
The contributions of the paper are clearly presented and distinguished from previous work
The quantitative and qualitative results provide improvements in the desired metrics compared to appropriately chosen baseline models
Cohesive story and interesting applications
Q4 Main weakness: The main weakness of this paper is the rather incremental technical contribution. 
Q5 Detailed comments to the authors: First, the authors argue that existing approaches enforce the monotonicity property in inappropriate parts of the input space that fail to capture the underlying data distribution. To address this conundrum, they propose to include mixtures of training instances (and random noise) for computing the regularization term, the benefit of which the authors empirically demonstrate. Second, they show how monotonicity in regularization can impose structure on the learned representations in deep generative models and convolutional neural networks without negatively affecting their original performance.

This is basically a solid paper with almost no shortcomings apart from being somewhat straight forward (in a positive sense of meaning).
Q2(4) Quality of experiments (Optional): 3: Good: The experimental evaluation is adequate, and the results convincingly support the main claims.
Q7 Justification for your score: I consider the paper in terms of contributions or novelities to be rather incremental. However, it is a solid work that combines/modifies existing techniques and adresses previous shortcomings. The paper should therefore be considered for acceptance.
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final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., lack of novelty, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: Q1 Summary and contributions: The paper deals with learning models whose output is monotonic w.r.t to some specified coordinates, by incorporating suitable regularization terms. The main contributions are an application of mixup to enforce monotonicity on a larger space, and the application of monotonicity regularizers to several problems. Specifically, to enforce monotonicity in disentangled factors of generative models, for classification and anomaly detection.
Q3 Main strengths: The paper shows some nice applications of regularizing toward monotonicity.
It is easy to follow and some of the suggested methods may be useful in practice.
Q4 Main weakness: There is a large disconnect between the different parts of the paper, especially between section 3 and section 4.
While section 3 studies the generalization of the monotonicity property beyond training data, section 4 has contributions that are completely distinct and have little to do with the method proposed in section 3.

Another weakness of the paper, in my opinion, is section 3. I failed to see how the method or motivation is specifically interesting in the case of enforcing monotonicity. It seems like a straightforward matter of generalization: monotonicity generalizes to data that is drawn from the same distribution as the training distribution. Then mixup is just a form of data augmentation that helps us enforce monotonicity in other regions of the input space. Yet monotonicity could have been replaced with any other property in this story, hence I do not see a major novelty in the paper's proposal.
Q5 Detailed comments to the authors: To expand on the point regarding the disconnect between sections 3 and 4: Generally, it would've been easier to read and appreciate the paper if it focused on applications of monotonicity regularization. Even a thorough study that includes many datasets, on just one of the applications presented in section 4, could make a nice contribution.

As for section 3, another small point that made me doubt the novelty and motivation of the paper, is that the empirical evaluation shows that the standard regularization on training data does quite well in generalizing to test data (i.e. the proposed mixup method is not required). To the average reader of an ML paper, generalization to test data would be the desirable benchmark, and it seems peculiar to expect generalization to other parts of the input space. Then again there is nothing surprising about failure on uniformly distributed inputs. While I see how enforcing a property on a larger input region is desirable for things like safety concerns etc., I still don't see how to proposed method offers any novelty beyond what is offered by standard mixup. This might be because I'm not very familiar with the literature on monotonicity regularizers, but I think that for most of the UAI crowd such an evaluation can look somewhat confusing.

Finally, I think that section 4 has some nice contributions, especially in the applications to enforcing the monotonicity of disentangled latent factors. Yet these need to be expanded and fleshed out in a more thorough study on diverse datasets.
Q2(4) Quality of experiments (Optional): 3: Good: The experimental evaluation is adequate, and the results convincingly support the main claims.
Q7 Justification for your score: As described in the previous parts of the review, I think that the paper is not coherent enough and presents some ideas that are linked but do not make up a solid work with clear contributions. Therefore, I believe that the weaknesses outweigh the merits of this paper.
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final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area of AI or moderate to high impact on more than one area of AI, with good to excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations. 
review_content: Q1 Summary and contributions: The authors present an intuitive solution based on mixup to regularising for monotonicity in neural networks which shows good improvements on existing sampling methods. They then apply this to disentangled representation learning to give interpretable disentangled representations as well as anomaly detection for K-way classifiers. 
Q3 Main strengths: The solution presented is very intuitive and easy to follow. Furthermore upon giving a good the mixup based solution the authors then give two very original applications of their method, both of which are very compelling and show good results. 
Q4 Main weakness: My main critique is just the reproducibility of some of the results. It seems surprising to me that the mixup method would improve over uniform random sampling when assessed for monotonicity on a uniform random sample, however the authors find it does in every case. Furthermore it seems odd to me that for so many mixup runs the authors did not find mixup to have even 0.01% points not satisfying monotonicity. As the authors attach no code or further detail or experiment results it is hard to understand what is going on here.
Q5 Detailed comments to the authors: - Following on from the concerns about the authors having such a low proportion of non monotonicity on mixup, I wonder if having an interval of 0.00% +/- 0.00 is the best way to report these results. This makes it hard to understand on what scale mixup achieves monotonicity. If it is the case that mixup guarantees such impressive results the authors should still give insight into how many non monotone points mixup finds, whereas in its current state these results don't seem to demonstrate this.
Q2(4) Quality of experiments (Optional): 3: Good: The experimental evaluation is adequate, and the results convincingly support the main claims.
Q7 Justification for your score: Overall this seems to be a very good paper which derives a clear workable method and then gives two original applications of it. My only concern is with the presentation of some of the results, however I believe this can be remedied. I believe this would make a good addition to UAI.
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Meta-review: Meta Review: The reviewers overall found this to be a solid paper, with somewhat modest technical novelty. 
However, the experimental results overall are useful and strong, which in the bottom line justifies acceptance. The paper's clarity is generally good, with one major issue being the disconnect between sections 3 and 4. I suggest the authors take the reviewers suggestions into account while preparing the finalized version of the paper. 
Decision: Accept (Poster)