Adapting Prediction Sets to Distribution Shifts Without Labels

We are glad you acknowledge our method's good performance.

1. What is resp. in the first paragraph?

Thank you for pointing this out. By 'resp.' here we mean 'respectively'. We will edit the draft to omit undefined abbreviations.

3. Why there are cases when entropy optimization shows worse performance than the original ECP?

Test time adaptation by entropy minimization is effective in improving coverage and / or set sizes on all the datasets we study (almost always improves both). In a small number of edge cases, it may slightly increase set sizes relative to ECP. While entropy minimization has proven very effective, it still has some shortcomings which continue to be studied [1]. We are confident that improvements to the base TTA methodology will effectively translate to improvements on EaCP.

4. The problem setting suggested by the authors cannot be solved by the foundation model, e.g. CLIP or LLMs?

Although powerful, models like CLIP and LLMs still significantly struggle with distribution shift. They cannot solve the problem we investigate. However, future works can certainly study the effect of our proposed method on these models.

Please let us know if you have any outstanding questions or concerns.

[1] Press, Ori, et al. "The entropy enigma: Success and failure of entropy minimization." arXiv preprint arXiv:2405.05012 (2024).

Thank you for your review, we are glad you acknowledge the importance of our problem setting as well as the extensive experiments and "significant improvement" of our methods. Regarding your comments:

1. On the relationship between the model's output confidence and entropy in Figure 1

With all due respect, we believe that the reviewer has misinterpreted what is plotted in Figure 1. As indicated by the y-label, it plots softmax value of the true label, and it does not plot model confidence on the y-axis. The relationship between softmax of the true label and entropy is non-trivial. If this was instead "max softmax" (a common heuristic for confidence and the metric used in your cited paper), then we agree it would be trivial.

2. Model confidence under OOD settings

We are aware of the issue of poorly calibrated models and agree it is an important concern (and related to model confidence). However, the connection the reviewer draws here may be related to the misunderstanding mentioned above. Model calibration is tangential to our primary topic of constructing accurate and useful prediction sets. ECP only enlarges the prediction set, quite the opposite of producing a "more over-confident model" as a larger set conveys greater uncertainty. No model parameters change. The top-k predictions will not change, so standard calibration checks (e.g. ECE) would not be affected. For EaCP we perform TTA so model parameters do change, however, there is no evidence that the TTA procedure disrupts model calibration.

Over-confidence on OOD

We would like to point out that seminal papers on test-time adaptation (TTA) have established the reliable correlation between prediction entropy and distribution shift severity [1]. Our results also corroborate this phenomenon. In this context, it is unclear what is meant by "continuing to enlarge model outputs will inevitably exacerbate this issue." Please refer to our earlier point about larger confidence sets conveying greater uncertainty rather then overconfidence.

3. Why use the quantile mechanism.

As mentioned in our paper on line 248, we use the fact that quantiles are generally more robust than expectations. Certainly other choices, such as temperature scaling, may exist and we would be excited for future works to build on this. Nonetheless, we hope to have demonstrated that our quantile-based approach works well on diverse datasets and distribution-shift settings as an initial approach.

We hope this addresses your concerns, and we are happy to address any outstanding questions!

[1] Tent: Fully Test-time Adaptation by Entropy Minimization. ICLR 2021.

2. On hyperparameters and learning f.

We would like to emphasize that we did essentially zero hyperparameter tuning in our paper. Although we do introduce two hyperparameters, we demonstrate that simply setting $\beta=1-\alpha$ works well in practice across many datasets, severity levels, error rates, as well as both stationary and continuous shifts.

We do agree with you that learning $f$ is a fruitful area for further exploration, which we and hopefully others will continue to develop in future studies. In our current submission, we emphasized the development and thorough empirical validation of our novel ECP and EaCP methods. We demonstrate that a simple quadratic / linear scaling function works remarkably well on a large number of diverse datasets in this challenging setting. There are certainly a number of ways the choice of scaling function can be improved, and several recent works may potentially offer insights to this end [1,2,3], which we are eager to explore in future works.

That said, the simplicity and effectiveness of 'off-the-shelf' quadratic or linear scaling functions is a key strength of our approach. While dataset-specific optimization might marginally improve performance, it would compromise the elegant simplicity of our method.

3. Oracle and no-shift results.

Thank you for the suggestion! We are currently running these experiments and will provide the results shortly. We would also like to point out that due to our design choice in Equation 4, prediction sets will never be decreased and thus coverage cannot decrease including on in-distribution data.

4. Tibshirani et al. (2019) baseline comparison.

While Tibshirani et al. (2019) is certainly a seminal work in this area, we respectfully disagree that this is a relevant baseline. This is primarily due to the fact that it is highly challenging to estimate accurate and reliable likelihood ratios for high-dimensional image classification tasks. In fact, we are not aware of any previous works that use the method from Tibshirani et al. (2019) in large scale image classification tasks. This sentiment is echoed in Cauchois et al. (2024), who similarly present several reasons why Tibshirani et al.'s approach is quite restrictive and not applicable to our setting.

Instead, we focus on comparing against works that have shown positive results on ImageNet-scale tasks. This includes Cauchois et al., as well as five other baselines that have previously demonstrated strong performance on ImageNet. Note that these previous works also do not compare against Tibshirani et al. We hope it is clear now why we do not include this comparison.

We hope this addresses your concerns, and we are glad to answer any further questions.

[1] Miller, John P., et al. "Accuracy on the line: on the strong correlation between out-of-distribution and in-distribution generalization." International conference on machine learning. PMLR, 2021.

[2] Kim, Eungyeup, et al. "Reliable Test-Time Adaptation via Agreement-on-the-Line." arXiv preprint arXiv:2310.04941 (2023).

[3] Kang, Katie, et al. "Deep neural networks tend to extrapolate predictably." ICLR 2024.

(2/2)

Thank you for your insightful review! We are glad you appreciate the importance of this problem.

1. Theoretical coverage guarantee based on covariate shift assumptions?

We agree that the coverage rate guarantee has been a popular trend within the field of conformal prediction, therefore, our paper is a bit different due to the absence of such guarantees. However, here we would like to challenge this convention by providing some alternative perspectives:

• We would like to kindly re-emphasize that the challenging setting we study (distribution shifts without test time labels) inherently suffers from a lack of non-trivial guarantees, yet is quite common in practice.

  To our knowledge, all existing attempts on this problem (discussed in Sec 1 and 2) make stringent assumptions or simplifications in order to prove things. For example, Tibshirani et al. (2019) studied CP under only covariate shift, however, accurately estimating the required likelihood ratio for that approach to work can be challenging in practice. Alternatively, the idea of Cauchois et al (2024) is to take a robust optimization perspective by assuming a certain maximum level of distribution shift and protecting against the worst case. However, we show that their guarantees fail in practice and achieve lower coverage than our ECP/EaCP on all of the natural distribution shifted datasets. This result highlights that the assumptions they require for their guarantee are difficult to satisfy in practice. Thus, without any assumptions of this type on the nature of the covariate shift, we believe our problem is ill-posed in the strict theoretical sense, such that any nontrivial coverage guarantee is impossible.

In light of such limitations, we take a new perspective on this problem.

• Instead of attempting to provide assumption-laden guarantees that won't hold in the real world, we instead aim for practical approaches that consistently perform well. Thus, while we do leverage CP-inspired techniques, we ultimately focus on providing general prediction sets that are accurate and efficient.

Overall, we very much agree with you that coverage guarantees are an interesting aspect of conformal prediction. However, the reality is that machine learning systems must often make predictions or decisions, perhaps unwittingly, even in this extremely challenging setting of unlabeled distribution-shifted data. Ultimately, conformal prediction is simply one of many possible set-valued classification methods. We hope reviewers would acknowledge and appreciate our effective and practical approach as an important stepping stone towards addressing the issue of accurate and effective prediction sets in a generalizable and scalable manner.

(1/2)

Dear Authors,

Thanks for sharing your opinions.

• I would appreciate novel viewpoints on building prediction sets under shifts, but I believe we have to find minimal assumptions that provide a guarantee under the distribution shift. Authors claimed that it is not easy to find a paper that provides guarantees with practical assumptions. But, I found the following paper (https://arxiv.org/abs/2106.09848) that carefully estimates the likelihood ratio, different to Tibshirani et al. (2019), suggesting that finding practical assumptions for a guarantee is possible.
• Comparison with Tibshirani et al. (2019) should be conducted. You can just use an estimated likelihood ratio.
• I want to see “Oracle and no-shift results”, but they are still missing.

Because of these reasons, I’ll maintain my score.