Summary
The paper describes Progressive Data Expansion (PDE), a new method for training models which are robust to spurious features. The idea of the method is to split the training into two phases: warmup and expansion. In the warmup stage, the dataset is balanced, and the model learns a classifier that ignores the spurious feature. In the expansion stage, the remaining data is used to finetune. The authors also provide a theoretical argument about feature learning, and show strong empirical performance on benchmark datasets.
**W** — weakness, **S** — strength, **Q** — question.
Strengths
**S1.** The authors provide a theoretical analysis, that provides some intuition for the method
**S2.** The proposed method is simple and computationally cheap
**S3.** The authors achieve strong empirical performance across three benchmark datasets
Weaknesses
**Q1/W1. Relationship to DFR**
The works [1, 2] advocated for an approach that is almost opposite to PDE: they train a model with standard ERM, and then retrain only the last layer on a group-balanced dataset. PDE on the other hand pretrains the model on a group-balanced dataset, and then finetunes with standard ERM. The methods achieve similar performance, if we consider DFR^Val, which is the main method in [1] (the authors argue that DFR^Val uses the validation data, but I believe PDE also uses the same amount of validation data to tune the hyper-parameters?). In fact, PDE achieves better performance on CelebA and CivilComments, while DFR achieves better performance on waterbirds.
However, conceptually [1, 2] argue that in fact standard ERM learns the core features as well as GroupDRO on the standard benchmarks, and once the last layer is retrained we can recover the performance of GroupDRO. This intuition is quite the opposite of the intuition presented in this paper, which is that ERM does not learn the core features without intervention. I think it would be good if the authors could comment on this distinction.
My intuition is that the pretraining in the warmup stage prevents the model from learning the spurious feature, and makes it harder for the model to use the spurious features in the expansion stage. Alternatively, it could be that the model still represents the spurious features, but because of the momentum, it is unable to switch to using this feature in the expansion phase. It would be interesting to explore more deeply which of these options is happening.
Lastly, in line 287 you mention that the method is more efficient than DFR, because it does not train the model twice. However, DFR only retrains the last layer of a pretrained ERM model, which is computationally cheap, so I don't believe this statement is correct.
**Q2/W2. Robustness to the choice of hyper-parameters**
It is important to understand how sensitive the method is to the choice of hyper-parameters. In particular, I would be interested in the impact of
- Length of the expansion training phase
- Learning rate in the expansion phase
My intuition is that the method continues going in a good direction for some time during the expansion phase, but then eventually it should converge to an optimal solution on the full data distribution, i.e. maximize the average accuracy and not the worst group accuracy. However, due to early stopping, the authors are able to achieve good performance, before the optimization learns to use the spurious feature. Is this intuition correct?
**W3. Theoretical analysis**
The theoretical analysis is quite toy. The authors use a model which is basically a bag of features, i.e. the result is a sum of cubed dot-products of features and "filters". This model is not very non-linear. However, it is understandable, given that theoretical analysis of non-linear models is challenging.
Questions
**Q3. Expansion phase:** In line 225 you mention that during the expansion phase you try to sample data uniformly across groups. What do you do exactly in this phase? Isn't all of the minority data used in the warmup phase?
**Q4. Intuition for expansion phase:** Related to Q3, why is performance on the training data distribution go down in Fig 4 (b), even when you reset the momentum variables? Is the training loss going up then? Why would this happen? Or is the data not just sampled from the training distribution early in the expansion phase?
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Limitations
**References**
[1] [_Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations_](https://openreview.net/forum?id=Zb6c8A-Fghk);
P. Kirichenko, P. Izmailov, A. G. Wilson;
ICLR 2023
[2] [_On Feature Learning in the Presence of Spurious Correlations_](https://proceedings.neurips.cc/paper_files/paper/2022/hash/fb64a552feda3d981dbe43527a80a07e-Abstract-Conference.html);
P. Izmailov, P. Kirichenko, N. Gruver, A. G. Wilson;
NeurIPS 2022