Robust Learning with Progressive Data Expansion Against Spurious Correlation

While deep learning models have shown remarkable performance in various tasks, they are susceptible to learning non-generalizable spurious features rather than the core features that are genuinely correlated to the true label. In this paper, beyond existing analyses of linear models, we theoretically examine the learning process of a two-layer nonlinear convolutional neural network in the presence of spurious features. Our analysis suggests that imbalanced data groups and easily learnable spurious features can lead to the dominance of spurious features during the learning process. In light of this, we propose a new training algorithm called PDE that efficiently enhances the model's robustness for a better worst-group performance. PDE begins with a group-balanced subset of training data and progressively expands it to facilitate the learning of the core features. Experiments on synthetic and real-world benchmark datasets confirm the superior performance of our method on models such as ResNets and Transformers. On average, our method achieves a 2.8% improvement in worst-group accuracy compared with the state-of-the-art method, while enjoying up to 10x faster training efficiency. Codes are available at https://github.com/uclaml/PDE.

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Peer review

Reviewer uURe6/10 · confidence 4/52023-06-29

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.

Soundness

3 good

Presentation

3 good

Contribution

3 good

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

Reviewer YdZz5/10 · confidence 4/52023-07-05

Summary

In this paper, the author propose a learning framework for improving the performance of classifiers on the worst group in the presence of spurious features. The authors focus on a two-layer convolutional neural network. They first show that imbalanced data and easy-to-learn spurious features can lead to bias in the classifier. Then, they propose a learning procedure that focuses on balanced data and gradually progresses how the model learns from core features to all features. The new method is evaluated on several datasets demonstrating that the new approach is fast and can improve accuracy on worst groups.

Strengths

The paper is mostly well-written and easy to follow, and the idea makes sense. The proposed approach is motivated theoretically using a two-layer CNN model. The method is simple and relies on a two-stage training procedure, therefore can be easily implemented and adapted to other algorithms. The proposed method improves the performance of the worst group in all evaluated examples; in some cases, it leads to significant improvements.

Weaknesses

The theoretical analysis in the paper is focused on binary classification. The method requires tuning several hyperparameters. While the worst group performance is improved in most cases the overall accuracy degradation is non negligible. The method is only evaluated on a small number of datasets.

Questions

How is the method applied to non-binary data? The analysis focuses on the activation z^3. Can this be replaced with more commonly used activations? Why is there a significant drop in average accuracy in some examples? Some parts are not well explained; for example, the caption in Figure 1 is unclear.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

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.

Soundness

3 good

Presentation

2 fair

Contribution

2 fair

Limitations

Limitations are discussed in the last section of the paper. Addressing some of the limitations presented by the authors is indeed important to increase the usability of the proposed approach.

Reviewer 6r1Q8/10 · confidence 3/52023-07-06

Summary

The paper works on understanding and mitigating the impacts on spurious features. Specifically, the authors provide theoretical analysis on the learning process of a non-linear two-layer CNN, under spurious features. Theoretical insights reveal the need to start with balanced data, and progressively expand the train set. The proposed PDE is right based on such insights, and is demonstrated to be efficient and effective on certain datasets.

Strengths

* (1) The authors provide theoretical insights on the learning process of a two-layer non-linear CNN under spurious features, which aligns with empirical observations. * (2) The proposed method starts with group-balanced training set and then gradually injects more data samples to capture the core features. And its effectiveness and efficiency are demonstrated on several popular datasets when compared with exiting methods. * (3) The paper is clearly presented and well organized, and insights/motivations are easy to follow.

Weaknesses

Although the proposed PDE is super efficient by referring to existing learning/training based approaches, it would be better to mention/discuss the efficiency of some fine-tuning or post-hoc approaches during the related work section, for example, fine-tune the last layer is sufficient to spurious features [R1], post-hoc adjustment on model prediction improves robustness to spurious features [R2]. References: R1: Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations. [ICLR'23] R2: Distributionally Robust Post-hoc Classifiers under Prior Shifts. [ICLR'23]

Questions

* (1) The results on the synthetic data is a bit confusing: in table 1, the performance of ERM on worst-group is 0%; besides, PDE has a better worst-group performance than the overall one, which is kind of conterintuitive. * (2) It would be much better if authors could add more discussions on the role and selection/suggestions of certain parameters, i.e., the number of times for dataset expansion and the number of data to be added in each expansion.

Rating

8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

4 excellent

Presentation

3 good

Contribution

4 excellent

Limitations

The authors clearly stated their limitations at the end of paper, * The theoretical analysis rely on simplified model; * Certain hyper-parameters might be crucial in model training: i.e., the number of warmup epochs, the number of times for dataset expansion and the number of data to be added in each expansion.

Reviewer vLux4/10 · confidence 5/52023-07-07

Summary

The authors propose a new method called PDE to address spurious features and improve generalization. Building on the existing literature, the authors consider an imbalanced binary classification problem where two types of features coexist: core features and spurious features. The core features can lead to good generalization performance but a classification model may pick up spurious features. To avoid that, the proposed method (1) starts with a downsampled balanced classification as a warm-up, which will not pick up the spurious features, and (2) then gradually increase the imbalance ratio until the full dataset is used for training. The main justification for this two-stage algorithm is that gradient descent with momentum can benefit from the warm-up stage where no spurious features are picked up. Numerous experiments on synthetic data and real data are used to support the proposed method.

Strengths

Classification with spurious features is a very practical and relevant problem. The proposed method is easy to implement and new to my knowledge. The experiments result show promising performance compared with alternatives. Overall, the warm-up stage in optimization seems to be an interesting idea. It starts with an "easy" downsampled dataset without data imbalance---which is known to be the culprit of picking up spurious features. Then, in the second stage, we hope to use the full datasets without picking up spurious features by using momentum. The presentation of this paper is clear and theoretical/experimental results are easy to follow.

Weaknesses

In my opinion, this paper misses a crucial element in classification with spurious features---that is, the effect of overparametrization. It is known, for example in [1], that there is a very important difference between underparameterization and overparametrization when spurious features are present. It is, therefore, expected to have analyses on the inductive bias of the proposed method and how it may select a superior solution compared with ERM and recent alternatives. Unfortunately, the effect of overparametrization is absent in the analyses, as the number of neurons $J$ does not play a role in the analysis. Besides, while the two-stage optimization idea looks interesting, the analysis is a bit handwaving, so it is unconvincing to me why momentum method is able to keep avoiding spurious features in the second stage. An investigation of inductive bias would make this paper much stronger; perhaps even some in-depth experiments on synthetic datasets would shed lights on the behavior of momentum in terms on avoiding spurious features. Lastly, I think the experimental results look fine, but I am not convinced that the proposed method is better than the recent alternatives. For example, in Table 2, while PDE achieves better accuracy on worst classes, it usually incurs a worse accuracy on average. Since there is a clear tradeoff between majority and minority classes in binary classification, better accuracy for the minority class can be often trivially improved by shifting the decision boundary. It would be more convincing if empirical results show improvements for *all* classes. [1] Sagawa, S., Raghunathan, A., Koh, P. W., and Liang, P. An investigation of why overparameterization exacerbates spurious correlations. In International Conference on Machine Learning, pp. 8346– 8356. PMLR, 2020.

Questions

See the weaknesses section.

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.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

NA

Reviewer YdZz2023-08-15

Response to authors

I thank the authors for the hard work spent on this rebuttal. I have some comments about the response: Q1) These were stated as weaknesses, and they indeed are; despite appearing in the limitations, these are some of the disadvantages of the method and therefore should be mentioned in this bullet. I truly appreciate that the authors mentioned these and gave them positive credit. Q2) I understand this tradeoff and the importance of improving worst-case performance. Still, DFR offers a better tradeoff based on your reported results. Nonetheless, I see the value of improving performance on the worst case but suggest that this issue be discussed in the paper. Q3) Following the papers mentioned by the authors I see additional datasets including MultiNLI, CMNIST, and Adult-Confounded. Q4) Noted; better to mention this. To conclude, the authors have addressed most of my concerns and I decided to raise my score.

Authorsrebuttal2023-08-16

Thank you!

Thank you for your positive feedback and increasing the score! We'll be sure to incorporate all the suggested changes into our final version. Regarding the additional datasets, we will add experiments on the CMNIST and MultiNLI datasets in our upcoming revision. We'll update the experimental results here if time allows.

Reviewer vLux2023-08-20

I have read the replies by the authors and other reviewers. I appreciate the detailed explanations and references. While I feel a bit surprised by the general positivity from other reviewers, I do respect the consensus here and so I increased the score by 1.

Reviewer uURe2023-08-21

Thank you for the rebuttal!

Dear authors, thank you for the rebuttal! I appreciate the new results on the robustness of performance with respect to the expansion period training length, and other clarifications.

Reviewer 6r1Q2023-08-21

Thanks authors for the detailed responses and ablation studies, which have addressed most of my concerns. After reading the author's rebuttal and the other reviewers' comments, I would like to keep my original score (8: Strong Accept).

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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