Class-Context-Aware Phantom Uncertainty Modeling

I find the text itself pretty raw, and I think a revision should be done.

• There are misprints:

1. In Eq. 1: The representation g: f(x) -> Y where Y is a set of labels {1,..., K} suggests that g should extract the argmax from the softmax output. However, in Eq. (1), g is depicted as the last FC layer. Thus, g should represent a mapping from R^d -> R^K. Otherwise, under Softmax, you have class labels, not logits.
2. In Eq. 9: It seems $\hat{\sigma}^2$ should be changed to $\hat{\sigma}^{-2}$, as in Eq. (8).

• Not accurate statements:

1. Page 3: "Epistemic uncertainty ... is incurred by a lack of knowledge, usually due to insufficient training data". It is partially true, but also epistemic uncertainty is related to model misspecification (see for example [1]).
2. Page 3: On the other hand, our focus is more on aleatoric uncertainty ... which mainly comes from ... OOD outliers and unknown domain shifts". Can you please elaborate on what you mean by saying OOD outliers influence aleatoric uncertainty?

• Method

1. The method itself is based on the intuition that embeddings are well separated and there is no so-called "feature collapse" (see for example [2, 3, 4]). But this might not hold in practice. Thus, some special treatments, like spectral normalization or gradient penalty, may help. In any case, the discussion is required
2. It is not mentioned what norm was used to compute eq. 5. In any case, the geometry might be too complicated, and standard p-norms could be suboptimal.
3. On page 5: "2) the negative class context $x^{-}$, visually similar to $x$". Again, if there is a collapse of features, these intuitions that "close in image space -> close in embedding space" do not hold anymore.
4. I think there is a missing opportunity to visualize these $x^{-}$ and $x^{+}$ samples.

• Experiments:

1. It is not clear what Table 3 (which is referred to as Table 4.2 in the text) represents. Is it Accuracy? ROC-AUC?
2. Page 9: "... improving the overall improvement"
3. I think it is worth discussing baselines more in detail. At least in the appendix.
4. The section in the Appendix with computation overhead seems to be never referenced.

[1] Lahlou, Salem, et al. "Deup: Direct epistemic uncertainty prediction." arXiv preprint arXiv:2102.08501 (2021).

[2] Van Amersfoort, Joost, et al. "Uncertainty estimation using a single deep deterministic neural network." International conference on machine learning. PMLR, 2020.

[3] Mukhoti, Jishnu, et al. "Deep deterministic uncertainty for semantic segmentation." arXiv preprint arXiv:2111.00079 (2021).

[4] Kotelevskii, Nikita, et al. "Nonparametric Uncertainty Quantification for Single Deterministic Neural Network." Advances in Neural Information Processing Systems 35 (2022): 36308-36323.

There are unclear points in the derivation of the equations, as mentioned in the question. Moreover, as the variational inference, the proposed method involves numerous approximations rather than relying on the Evidence Lower Bound (ELBO), it is not trivial that the proposed objective function is "proper" or "appropriate" objective function, yet this issue is not discussed in the paper.

Another concern is about creating phantoms in Equation 5 using a mini-batch. While mini-batching is computationally efficient, I am not sure whether it provides sufficient boundary information about ambiguous class labels within a selected minibatch. This raises doubts about the method's effectiveness being heavily dependent on mini-batch selection.

The paper also mentions using self-paced learning in experiments, yet it lacks a thorough discussion on its critical necessity for the proposed method. This aspect needs further exploration and clarification to strengthen the paper’s validity.

I believe there are some shortcomings in the paper's experimental approach. Firstly, it's somewhat unclear why aleatoric uncertainty would be beneficial in detecting and filtering out Out-of-Distribution (OOD) data. Secondly, the proposed method doesn't seem to exhibit substantial improvements when compared with existing methods. Moreover, the absence of confidence intervals for the results is notable, and this is crucial, especially considering the closely matched performances of various methods.

In the concluding paragraph of Section 2, the authors point out that a key issue associated with Variational Inference (VI) is the potential for VI to result in posterior collapse and subsequently lead to an underestimation of variance. They assert that their proposed method does not suffer from this limitation. In the same paragraph, authors state that "variance linked to these phantoms establishes a minimum threshold for estimating the actual variance of interest." This statement appears to carry a potential contradiction. We kindly request the authors to provide additional clarification to reconcile this seeming discrepancy.

It is not clear if and why modeling distribution in phantom space can tackle the variance underestimation problem of VI. It would be useful if authors can provide some insights regrading this.

Based on Equation 5, it looks like the proposed method is highly susceptible to label noise, as x^+ and x^- are highly susceptible to noise. In most practical settings, label noise might be unavoidable. Would it be better if the authors actually used percentile methods (ex: datapoint which is say 99 percentile away) to make this more robust.

Above Eq 7, an independence assumption about z, z^+, and z^- was made. It would be better to make this assumption more explicit. More importantly, it is not clear why z, z^+, z^- being conditionally independent of each other given x, x^+, x^- can lead to q(z|x, x^+, x^-) = q(z|x). Can authors explain this in more detail?

• The paper is motivated by "mean-field VI underestimates the variance". The motivation is sensible however the paper did not provide any evidence verifying this motivation.

• The method does show performance improvement but I am worried that the performance could be sensitive to the setting of the three hyper-parameters. It is also not clear how one should set these hyper-parameters.

• The paper does not mention the "complexity" of the proposed method, e.g. does the method require extra training time, hyper-parameter tuning effort, memory cost, etc. compared with baseline approaches?

• It would be good if the paper could have more uncertainty-related results, the current version does not have any direct results demonstrating the uncertainty acquired through the method. A simple example would be to show the decision boundary on two moons dataset or XOR dataset.