Venue: NeurIPS 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: summary: By assuming a beta distribution on the softmax probabilities of a Bayesian classification network, the authors derive the marginalized joint entropy of a datapoint x and use it in a new acquisition function (balanced entropy learning acquisition) for active learning.
strengths_and_weaknesses: **Strength**
- The paper is well organized. The authors explained their assumptions carefully and also the method.
- Theorem 4.1 motivates the reciprocal of BalEnt well. Note that I haven't checked the proof in detail.

**Weakness and Question**
- I wonder how the assumption about the beta distribution of the softmax probabilities holds in practice. It would be beneficial to test this, for the dropout network, and for other types of Bayesian variational approximation methods.

- The authors didn't seem to discuss the limitations of the work clearly. 
questions: Please see above
limitations: The authors didn't seem to discuss the limitations of the work although they claimed to have done that in the checklist (my apologies if I missed it somewhere).
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: The context is Bayesian active learning, using MC dropout-based models. The paper places Beta distributions over the class marginals (ie one for each $p(y=i|x, w)$). The paper states that BALD as it is usually computed cannot be computed as such and instead proposes a different formulation, which it upper-bounds using what the paper calls a *marginalized joint entropy (MJEnt)* based on the entropy of the Beta distribution approximations. It then introduces a balanced entropy as the ratio between the MJEnt and the regular prediction entropy. Finally, it uses either this value or the reciprocal as the acquisition score (depending on the sign). The paper tries to motivate all this as principled and reports encouraging experimental results.

strengths_and_weaknesses: The paper presents a few interesting perspectives on BALD. The experiments show good performance on CIFAR-100 and superior performance on CIFAR-100x3 and TinyImageNet.

I was aware of the papers "BABA: Beta Approximation for Bayesian Active Learning" and "Analytic Mutual Information in Bayesian Neural
Networks" (Anonymous, 2021 &2022), but not the authors. Comparing the text of these papers, there might seem to be a case of self-plagiarism. While the former only exists as a preprint, the latter is to be published in ISIT 2022 (as also noted in this paper). I'm flagging this for the AC to decide and take a look at. The portions in question are not restricted to the Background section of this paper.

In regards to the content of the paper:

1. It is not clear why the Beta approximation makes sense. Indeed, only the marginals $p(y=i | x)$ could be motivated to follow a Beta distribution, similar to the central limit theorem, as these are marginalized over $w$. The $p(y=i|x, w)$ as r.v. of $w$ however, need not follow such a distribution. This is a well-known criticism of e.g. prior networks (Malinin et al, 2018), which fit Dirichlet distributions.

2. The paper states in (4) and (5) that the common formulation of BALD is equal to the more complex formulation using $\Phi$. It then finds an upper bound to this formulation (MJEnt). This is similar to how the predictive entropy (Ent) upper-bounds normal BALD. In (10), the paper states that MJEnt = Ent + some additional term ("Posterior Uncertainty") = Epistemic Uncertainty + Aleatoric Uncertainty + Posterior Uncertainty, and that it thus decomposes three different uncertainties. This is wrong: it actually confounds these three terms (as it takes a sum/is a function of them)! 

    The citation right before (4) and (5) is actually wrong. Gal et al, 2017, do not motivate the statement that follows.

3. Section 3.3 is not novel and only restates what is known from Houlsby et al, 2011, Gal et al, 2017, and Kirsch et al, 2019: entropy acquisition is over-confident compared to BALD because it adds in aleatoric (irreducible) uncertainty (Ent =  Epistemic Uncertainty (BALD) + Aleatoric Uncertainty), which will not be learnt away.

4. BalEnt falls out of nowhere as a ratio and is not actually motivated.
questions: 1. How does BalEntAcq compare to BABA?

2. Appendix A.12.2 contains ablations. Could you provide an ablation for P4 = BalEnt[x]^-1.

It would seem that BalEntAcq's second case (for negative scores) does not matter as long as there are sufficient positive scorers. This raises the question: it is needed at all even for the experiments provided in the main paper?
limitations: --
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: This paper proposes a new uncertainty measure, called BalEntAcq (Balanced Entropy Acquisition), that aims to correct the potential "bias" of existing active learning schemes based on information-theoretic uncertainty measures, such as the popular BALD (Bayesian active learning by disagreement).
The paper shows that the proposed BalEntAcq captures the "information balance" between the uncertainty of the underlying softmax probability and the label, thereby outperforming other active learning schemes based on similar entropy-based principles.
Based on popular benchmarks, the authors demonstrate the potential advantages of active learning based on BalEntAcq compared to other alternatives.


strengths_and_weaknesses: STRENGTHS

1. The proposed uncertainty measure "BalEntAcq", which aims to effectively capture information balance between the uncertainty of the underlying softmax probability and the label variable, has been shown to result in well-diversified data point selection near the decision boundary, consistently outperforming other information-theoretic uncertainty measures often utilized for active learning.

2. The closed-form expression of the proposed BalEntAcq leads to a computationally efficient active learning scheme, which nevertheless may improve the learning outcomes compared to other existing alternatives.


WEAKNESSES

1. The overall presentation - both literary and technical - requires improvement. For example, the authors do not clearly explain nor define what type of "bias" this study is focusing on, although this is crucial for understanding the main motivation of the proposed scheme as well as the major contributions in this work. Furthermore, many acronyms should be clearly defined before using them.

2. Literature review on existing relevant schemes is too short and shallow. For example, although the authors present a brief summary of existing active learning schemes in Sec. 2.3, the treatment and review of other schemes is not comprehensive and fairly sketchy to be informative for the readers.

3. While BalEntAcq has been shown to result in improved performance over some alternatives, a more comprehensive evaluation is needed to clearly demonstrate the advantage of the proposed scheme. For example, how does it compare to various active learning schemes based on ELR (expected loss reduction) strategy, which focuses on maximally reducing the expected error, and thereby focus on acquiring data points that can maximize the uncertainty directly impacting the predictive performance?

4. Current results show that the proposed BalEntAcq may have potential benefits over other alternatives in terms of efficiency (through closed-form expression of the acquisition function) and performance gain (as reflected in Figure 3 and Table 1). However, the uncertainty measure BalEntAcq is defined in a somewhat heuristic manner, and it is unclear whether it would provide meaningful advantages over recently proposed Bayesian active learning schemes - in terms of performance, robustness, and convergence properties.

For example, the following papers propose Bayesian active learning schemes based on ELR strategies, which have shown to effectively reduce model uncertainty that directly affect the predictive performance of the learned model. 

Zhao et al. "Uncertainty-aware Active Learning for Optimal Bayesian Classifier", ICLR 2021.

Tan et al. "Diversity Enhanced Active Learning with Strictly Proper Scoring Rules", NeurIPS 2021.

Both papers provide theoretical convergence guarantees to the optimal model as well as consistent performance improvements compared to other existing schemes, including BALD, the main method to which BalEntAcq is compared in this study. It would be helpful if the authors could compare their scheme to the above methods or other recent Bayesian active learning schemes and discuss what would be the main benefits of the proposed scheme.

5. Based on Figure 3, it is unclear whether BalEntAcq would provide meaningful advantages over other alternatives in the small-data regime, which would be of special interest when studying active learning schemes.



questions: 1. How does the performance of BalEntAcq compare to the popular ELR strategy, which directly focuses on reducing model uncertainty via active learning so as to improve the predictive performance?

2. How does the proposed active learning scheme perform, in comparison with other existing schemes, in a small-data regime, where the role of active learning would be most important?

3. Does BalEntAcq provide any convergence guarantee - either theoretically or empirically? What would be its main advantages over recently proposed Bayesian active learning schemes?

limitations: The authors do not explicitly discuss the limitations of the proposed work. The authors note there are no specific "negative societal impacts" relevant to the proposed method.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper proposes a new acquisition function BalEntAcq for Al in BNN. It captures the information balance between the uncertainty of underlying softmax probability and the label variable. It facilitates parallelization over all classes (by estimating distribution parameters in marginal distribution). It is a purely standalone measure that could reduce relational computation like BatchBALD, CoreSet, and BADGE. Nevertheless, the paper shows that BalEntAcq captures a well-diversified selection near the decision boundary. The authors also demonstrate the new principle can outperforms other well-known Bayesian active learning algorithms. 
strengths_and_weaknesses: Strengths:
1) The new acquisition function is novel. It facilitates the parallelization both over classes and batch selection (there is no relational computation within data points inside a batch). It captures both informativeness (uncertainty) and diversity.

Weaknesses:
1) Baselines are limited. (a) The paper mentioned BatchBALD. The computational cost for selecting a batch is proportional to the batch size. It is still tolerable. As shown in the paper, it is superior to BALD in many settings. This paper can compare its method with BatchBALD with a small batch size, e.g., batch size <= 40. (2) Variation-Ratio [1] is also a potential baseline that have shown competitive performance. (3) Non-Bayesian AL algorithms can be applied to BNN. For example, in order to apply CoreSet to BNN, we can take the average last-layer representations with N MC dropouts or simply one representation with MC dropout, which is also the case for any DNN with dropout layers. Similarly, we can also apply BADGE to BNN. For all the examples, we can still maintain the expressiveness of the BNNs.
2) The authors only tried their method on MC dropout. There are many other BNNs, e.g., [2] and [3], that need to be considered since the paper focus on AL in BNNs.
3) Datasets are limited. The datasets considered in the paper should cover different aspects of AL, e.g., batch size, data format, and dataset size. The authors can compare their method with BatchBALD and [4] on MNIST and Repeated-MNIST with small batch size, i.e., <= 10. The author can also consider some small UCI datasets and some larger batch sizes for datasets like CIFAR10 and SVHN. If the new method does not work well in these settings, the authors should discuss it in the limitation or conclusion section.

References:
[1] Kirsch, Andreas, Joost Van Amersfoort, and Yarin Gal. "Batchbald: Efficient and diverse batch acquisition for deep Bayesian active learning." Advances in neural information processing systems 32 (2019).
[2] Lakshminarayanan, Balaji, Alexander Pritzel, and Charles Blundell. "Simple and scalable predictive uncertainty estimation using deep ensembles." Advances in neural information processing systems 30 (2017).
[3] Kingma, Durk P., Tim Salimans, and Max Welling. "Variational dropout and the local reparameterization trick." Advances in neural information processing systems 28 (2015).
[4] Kirsch, Andreas, Tom Rainforth, and Yarin Gal. "Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers." arXiv preprint arXiv:2106.11719 (2021).
questions: 1) Discuss computational complexity and compare it with other AL algorithms.
2) Can the authors explain why we can not apply non-Baysian AL algorithms to BNNs?
limitations: See 3 weaknesses.
review_title: null

Meta-review: metareview: The majority of reviewers found this paper to be confusing in its presentation, lacking novelty (e.g. Section 3), and not well motivated (e.g. BalEntAcq), with 3 out of 4 recommending rejection.  I find that the paper particularly falters in its explanation of the point process entropy and derivation of the ultimate acquisition function.  As the author-review discussion makes clear, the deviation from Shannon / differential entropy to point process entropy is at the core of the paper, but this is lost in the current draft.  Due to this and moderate-to-minor issues such as the validity of the Beta approximation, the use of only MC dropout, and relationship to ELR schemes, I recommend rejection at this time.
confidence: Certain
Decision: Reject