Paper: Confidence-Based Model Selection: When to Take Shortcuts in Spurious Settings (ICLR-2024)

Reviewer comment (Theory):
The algorithm's design lacks interpretability. The analysis did not take into account the relationship between the algorithm's design and the use of shortcut and invariant features, nor did it explain why different classifiers can use various combinations of these two features instead of relying on the same shortcut features.

Author response:
The intuition behind why our method utilizes both shortcut and invariant features is described in Section 4.1. In summary, the inference problem can be formulated as smoothed entropy minimization, which motivates our use of confidence in choosing which classifier to use. Shortcut and invariant features naturally have different confidences on different inputs as a result of how they are trained and this is also reflected in how they have different accuracies on different groups of inputs (as shown in Table 1). Thus, by leveraging these different confidences, our method is able to utilize different combinations of both shortcut and invariant features.

Reviewer comment (Experiments):
Another drawback related to numerous base classifiers is the need to train multiple base classifiers, each with potentially different architectures or training backbones. This increases the complexity and computational cost of the training process, as each base classifier must be trained and calibrated individually. Managing and optimizing multiple training pipelines can be difficult, particularly when working with large-scale datasets or complex models. In comparison to many existing methods that only require one base encoder (e.g., see [1, 2] and benchmarking methods in [3]), COSMOS displays increased training complexity.

Author response:
We do use different base classifiers, which may require additional compute over training a single model, but we find that this is worth it for the additional improvement in performance that we get from maintaining high majority and minority group accuracies. Furthermore, other methods like Ensembling do also train and use multiple models and we find in our experiments that we are able to leverage the models more effectively for better performance.

Reviewer comment (Experiments):
As the paper focuses exclusively on spurious correlations as a type of subpopulation shift, it neglects the wider variety of subpopulation shift types found in the literature. According to [3], subpopulation shifts can take many forms, such as attribute imbalance and class imbalance. Real-world datasets often exhibit multiple types of shifts at the same time, and the paper does not discuss how COSMOS would perform in these situations. As a result, the paper's limited scope undermines its generalizability and applicability to real-world datasets that may display different types of subpopulation shifts.

Author response:
We focus on datasets with spurious correlations because our aim is to highlight the benefits of leveraging the strengths of both shortcut and debiased classifiers, which are commonly trained for datasets with spurious correlations. Our method is designed to benefit particularly when given shifts in the frequencies of data subpopulations, as different classifiers often perform better on different subpopulations in this setting. However, the method can also be used to generalize to novel data subpopulations that were not observed during training and does so in the MetaShift evaluation.

Reviewer comment (Experiments):
The paper does not offer a comprehensive comparison with current state-of-the-art methods, making it challenging to evaluate COSMOS' relative performance and advantages compared to other techniques.

Author response:
We compare to state-of-the-art classifiers and methods that use multiple classifiers (e.g. ensembling variants). If you have any recommendations for other specific methods that would be informative to compare against, we would be happy to consider including them.

Reviewer comment (Experiments):
The ablation experiment is insufficient. The authors did not examine whether this advantage is due to the presence of TS. Moreover, if random selection or other selection methods are used among K classifiers, it is unclear whether the results will differ. It remains uncertain whether the advantage of the results is due to the integration of multiple classifiers.

Author response:
Temperature scaling is a part of COSMOS and is key to ensuring that the classifiers are similarly calibrated. Our main results, shown in Table 2, show that on all four domains, using COSMOS achieves significantly higher accuracy and lower regret than any of the individual classifiers, demonstrating how multiple classifiers can be used to obtain performance gains on a wide range of potential subpopulations.

Below, we include an additional comparison to random selection among K classifiers. We see that COSMOS significantly outperforms this baseline on our 4 datasets on both average accuracy and average regret metrics, showing the benefits of our selection method. 

|                   | Waterbirds |          | CelebA   |          | MultiNLI |          | MetaShift |          |
|:-----------------:|:----------:|:--------:|:-------:|:--------:|:--------:|:--------:|:---------:|:--------:|
|                   |   Avg Acc  | Avg Regret | Avg Acc | Avg Regret | Avg Acc  | Avg Regret | Avg Acc   | Avg Regret |
|       Random      |    88.35   |    -4.02   |  84.47  |    -9.72   |   80.9   |    -1.42   |   79.39   |    -3.4    |
| COSMOS (clusters) |    91.72   |    -0.74   |  90.96  |    -1.5    |   81.62  |    -0.58   |   83.78   |    -1.49   |

Reviewer comment (Theory):
There exists gap between the formal intuition and practical approach. Some assumptions are strict to stand in practice. The rationality of theories and the gap between theories and methods need to be addressed. Otherwise, we have no way of knowing the scope of the method.

Author response:
We apologize for any potential confusion here. Can you explain what you find to be the gap between our theory and method so that we can clarify this?

Reviewer comment (Experiments):
More methods, as well as some SOTA, should be considered in experiment.

Author response:
We already compare to state-of-the-art classifiers and methods that use multiple classifiers (e.g. ensembling variants). If you have any recommendations for other specific methods that would be informative to compare against, we would be happy to consider including them.

Reviewer comment (Novelty):
I believe that the solution presented in the paper relates also to the problem of dynamic or instance-wise classifier selection, where the goal is to select the best classifier to use during testing for each test example. The related work section does not seem to include any relevant work in this area. Some example references follow: (1) R. M. Cruz, R. Sabourin, and G. D. Cavalcanti, Dynamic classifier selection: Recent advances and perspectives, Information Fusion, vol. 41, pp. 195–216, 2018. (2) M. Sellmann and T. Shah, Cost-sensitive hierarchical clustering for dynamic classifier selection, arXiv preprint arXiv:2012.09608, 2020. (3) R. M. O. Cruz, L. G. Hafemann, R. Sabourin, and G. D. C. Cavalcanti, Deslib: A dynamic ensemble selection library in python, Journal of Machine Learning Research, vol. 21, no. 8, pp. 1–5, 2020. (4) S. P. Ekanayake, D. Zois and C. Chelmis, Sequential Datum-Wise Joint Feature Selection and Classification in the Presence of External Classifier, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Rhodes Island, Greece, 2023, pp. 1-5, doi: 10.1109/ICASSP49357.2023.10097057.

Author response:
Thank you for bringing this up and the links to references. We have added these and some discussion to the related work section accordingly. Our method is an example of dynamic selection (DS) from multiple classifiers; we propose a distinct selection criteria, combining both clustering and confidence strategies in order to enhance performance on subpopulation shifts.

Reviewer comment (Novelty):
It would be great if the authors discuss how the proposed method differs from the problem of dynamic or instance-wise classifier selection, and depending on the relevance, they will consider extending their related work section accordingly.

Author response:
Thank you for bringing this up and the links to references. We have added these and some discussion to the related work section accordingly. Our method is an example of dynamic selection (DS) from multiple classifiers; we propose a distinct selection criteria, combining both clustering and confidence strategies in order to enhance performance on subpopulation shifts.

Reviewer comment (Writing):
I am a little bit confused about the relationship between the index variable of the subpopulation and the label. Initially, I thought that the test set could be split into subpopulations based on the possible values of the labels. However, as I continued reading, it seems that subpopulations are not necessarily constructed based on the possible values of the labels. In this case, what is the meaning of subgroups and how do you justify this?

Author response:
Thanks for bringing this point up, and we apologize for any confusion. In subpopulation shifts that occur as a result of spurious correlations, we follow prior literature, e.g. Group DRO, JTT, etc., and consider different combinations of (spurious attribute, label) as a group. For example, for the Waterbirds dataset, where background type spuriously correlates with the label of bird type, we consider 4 groups total, 2 of them majority: (land background, landbird), (water background, waterbird), and 2 of them minority (water background, landbird), (land background, waterbird).

Reviewer comment (Theory):
Can you explain what is the meaning of the invariance assumptions in Sec. 3?

Author response:
We apologize for any confusion here. The invariance assumptions simply define the scope of the distribution shifts that we consider. We are specifically interested in subpopulation shifts where the main difference between the source distribution and target distributions is the proportion of subpopulations and other aspects between the distributions remain the same.

Reviewer comment (Writing):
I believe there is a small typo in notation. Namely, shouldn't p_{T_i} be p_{T^i} in Sec. 3 or am I confused?

Author response:
Thank you for your careful reading of our paper. We have fixed these points in the revised pdf.

Reviewer comment (Writing):
In pg. 5, dist(.) should be properly defined as a divergence measure.

Author response:
Thank you for your careful reading of our paper. We have fixed these points in the revised pdf.

Reviewer comment (Experiments):
The statistics of the datasets (e.g., number of instances, features, etc) are not reported.

Author response:
Thank you for your careful reading of our paper. We have fixed these points in the revised pdf.