Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes a novel model perturbation-based method for the source-free domain adaptation (SFDA) problem. Under the mild assumption, the authors connected their variational model perturbation with the bayesian neural network and proposed a perturbation parameters update method for source-free adaptation, avoiding changing the source domain model’s weight severely while improving the model’s generalizability. The experimental results on several domain adaptation benchmarks under three different settings(offline SFDA, Generalized SFDA, and continual SFDA) verify the effectiveness of the proposed method.
strengths_and_weaknesses: Strengths

1. As far as I am aware, this is the first time that the probabilistic model approach is introduced in the source-free domain adaptation. The proposed method is technically sound and novel in the SFDA problem. The intuition behind the variational model perturbation method in this paper fits well the SFDA setting, which can bring some novel insights to the community.
2. The proposed method is efficient and can be combined with other SFDA methods.
3. The experiments cover three different SFDA scenarios, and the results generally look promising. The analysis in section 4.3 is comprehensive and addresses some of my concerns during reviewing.

Weaknesses

1. The Methodology section lacks some necessary description of the proposed method and generated algorithm, which results in unclarity and ambiguity. For example: 
    1. What is the form of the specific objective function? （Under the assumption of prior and posterior distribution mentioned in the paper）Could the author further clarify the expression of the regularization term?
    2. Is the main parameter \sigma calculated and updated (if any) directly by the neural network？
2. Some descriptions of the experimental section are confusing.
    1. For example, in lines 218-225, while describing the offline SFDA, the paper utilizes the “training phase” represents the target training process; however, it is written “the model is first trained using 80% source data and then tested using the rest of the source data and all the target data” for Generalized SFDA setting. Then, in lines 245-247, it mentions only the training phase and the test phase. I suppose these two phrases are both noted for target training. Could the authors harmonize “source training” or “target training” to avoid ambiguity? Besides, could the source model generation process be introduced to make the experimental description more complete? Considering the particular setting of SFDA, I look forward to a clearer elaboration of the experimental details.
3. The experimental results only mention the accuracy but do not include the variance part. As the proposed model perturbation method only optimized the perturbation’s variance and did not update the source model’s weight, I am curious about the stability of the proposed method.
4. There are some unclear mathematical expressions. For example, in line 110-111, “Here we assume that we adopt the same prior, i.e., $p(w_t)=p(\Delta w)$”, does it means that these two random variables have the same variance?
5. In line 91, this paper directly assumes the zero-mean isotropic Gaussian distribution as the posterior distribution family. Could the authors explain more about such choices and assumptions?

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Thanks for the effort from the authors, and the rebuttal has well addressed my concerns mentioned above. I would like to raise my score to 7.
questions: Please refer to the questions in Weaknesses.
limitations: The authors discussed the limitations in section 2.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The challenge of source-free domain adaptation (SFDA) is that the source data is inaccessible after the source model is trained. Two prevalent approaches to address the problem is fine-tuning the source model on target domain and incorporate the adapters into the source model and learn it with target data. However the fine-tuned model usually has poor generalization of the model since it tends to be biased to a specific target domain. The adapter/modulating method is unable to handle large domain shifts as all the convolutional layers and fully-connected layers are frozen. 

To alleviate these problems, in this work, the authors proposed to perturb the parameters of the source model to achieve adaptation to target domain. The model perturbation approach learn domain-specific knowledge through variational Bayesian inference, allowing the model to generalize to relevant domains. This model-agnostic framework can efficiently adapt to target domain while largely preserving the discriminative ability of the source model. The method has been validated in various datasets and experiment settings.
strengths_and_weaknesses: Strengths:
- The work is well-motivated, the writing is easy to follow, and the framework is general and flexible
- Provided a novel probabilistic framework for SFDA
- Demonstrated the theoretical connection between their probabilistic framework and the Bayesian neural network
- The theoretical analysis of the method is clear and sound 
- The empirical and comprehensive experiments validated the method in various settings

Weaknesses:
- To make it self-contain, a more detailed description of the model training or a pseudocode of the training algorithm is expected. For instance, in line 227 and 237, the authors only mentioned that the expected likelihood adopted the same losses used in reference papers. It would be better to include the loss function as supplementary. 
- Since the authors adopted the local reparameterization trick in line 247, it would be better to briefly explain how to optimize the objective function in eq(3) so that help the general audience understand why and how to apply the trick. In turns, it also help the audience get a better understanding of the training workflow.

questions: I only have some minor questions regrading the experiment details
- For a fair comparison, the authors adopted the same network architecture and even the same hyper-parameters (if I am wrong, please correct me) with baseline methods. Did you consider/try to tune the hyper-parameters to fully release the power of the proposed method. It would be interesting to show the best performance after tuning. 
- Could you please elaborate more about why the perturbation method is able to preserve discriminative power of the source model? For instance, when the testing example comes from the source domain, how the model would perturb the model? 
- In Table 2, there are 6 tasks in total, why the total winers are 10? is it because the tie existing in some tasks?
- In Table 3, the bold number in "source" column has special meaning?
limitations: I would recommend to add a pseudocode of the training algorithm in the main body or supplementary such that to help the readers to get a clear view of the model training workflow.
review_title: null

final_score: 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.
review_content: summary: In this paper, the authors propose to solve the source-free domain adaptation problem by perturbing the source model to adapt it to the target domain. The perturbations for the source model are learned through variational Bayesian inference. The authors provide a parameter sharing strategy to significantly reduce the number of learnable perturbations. Therefore, the proposed method is a flexible and lightweight framework and can be integrated with existing methods. Extensive experiments on 5 datasets under 3 different SFDA settings demonstrate the superior performance of variational model perturbations.
strengths_and_weaknesses: 1. A flexible and lightweight framework, easy to be integrated with previous methods.
2. Very few learnable parameters.
3. It decouples the process of domain adaptation into the invariant part (the static source model) and varying part (the learnble perturbations).
4. The authors connected variational model perturbation with Bayesian neural networks, which provides a theoretical guarantee for the generalization performance of model perturbation.
5. Most experimental details required for reproducing the results were given. Code was submitted as well, which is noteworthy.
6. The performance is competitive. Variational model perturbation can achieve the best results in almost settings against the compared baselines.
7. The experiments take into account both SFDA and test time adaptation settings, which seem very sufficient. Note that previous methods solved SFDA and test time adaptation independently, e.g., SHOT[1] (SFDA), NRC[2] (SFDA), HCL[3] (SFDA), TENT[4] (test-time adaptation), BACS[5] (test-time adaptation), CoTTA [6] (test-time adaptation). This paper essentially unifies the two settings into one framework.
questions: 1. My major concern is why variational model perturbation is effective? Even though the learnable parameters are very few? Clear and detailed explanations are needed.
2. In Fig. 1, using the classification accuracy as an indicator of domain shifts may be not appropriate. According to Ben-David's domain adaptation theory [7][8], it is better to use the A-distance as a proxy of the domain shifts.
3. Does model perturbation depend on a specific architecture? In addition to CNNs, the effectiveness of model perturbation on other architectures, e.g., ViT, is of interest.
4. The proposed method works under the assumption that the source data are not provided. Though I acknowledge the importance of this setting, in real-world applications it is possible to make use of some of the source data. In my opinion, model perturbation can be applied to the setting of standard source-needed domain adaptation, so could you provide results of other implementations based on the standard domain adaptation setting? (e.g., CDAN).
5. Is it safe to adopt assumption of same prior p(wt) = p(Δw) in Eq. 7?
6. I don't see the results of other implementations of model perturbations. Although these results appear in the supplementary material, I still suggest that these results are included in the main text.
7. How does the number of sample points (size of the datasets) affect performance? How many target data points are sufficient for adaptation? Does the performance advantage relative to the baseline methods vary with the size of the datasets?


References (including the reference from above section):
[1] Liang J, Hu D, Feng J. Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation[C]//International Conference on Machine Learning. PMLR, 2020: 6028-6039.
[2] Yang S, van de Weijer J, Herranz L, et al. Exploiting the intrinsic neighborhood structure for source-free domain adaptation[J]. Advances in Neural Information Processing Systems, 2021, 34: 29393-29405.
[3] Huang J, Guan D, Xiao A, et al. Model adaptation: Historical contrastive learning for unsupervised domain adaptation without source data[J]. Advances in Neural Information Processing Systems, 2021, 34: 3635-3649.
[4] Wang D, Shelhamer E, Liu S, et al. Tent: Fully Test-Time Adaptation by Entropy Minimization[C]//International Conference on Learning Representations. 2020.
[5] Zhou A, Levine S. Bayesian Adaptation for Covariate Shift[J]. Advances in Neural Information Processing Systems, 2021, 34: 914-927.
[6] Wang Q, Fink O, Van Gool L, et al. Continual test-time domain adaptation[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022: 7201-7211.
[7] Ben-David S, Blitzer J, Crammer K, et al. Analysis of representations for domain adaptation[J]. Advances in neural information processing systems, 2006, 19.
[8] Ben-David S, Blitzer J, Crammer K, et al. A theory of learning from different domains[J]. Machine learning, 2010, 79(1): 151-175.
limitations: 1. Line 170 and 199: typos "adaption".
2. The upper case and lower case are not consistent: "KL-divergence" in line 95 and "KL-Divergence" in line 110, "Adaptive prior" in line 126 and "adaptive prior" in line 268.
3. In Eq. 8, "w" appears for the first time. It should be "wt" according to Eq. 2.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper proposes a variational Bayesian inference framework to perturb source model parameters to address source-free domain adaptation.

The paper proposes framework simultaneously adapts the source model to the target domain and preserves the discriminability of the model and 

The paper introduces a parameter sharing strategy to achieve more efficient adaptation.

The paper provides a theoretical connetion between Bayesain learning and the proposed method.

The paper conducts experiments on three source-free domain adaptation frameworks to verify the performance of the proposed method.
strengths_and_weaknesses: Strength:

The general idea is interesting. Prior works on fine-tuning also take techniques to reduce the divergence between the fine-tuned model and the original. This paper directly models the perturbation, which naturally limited the divergence between the tuned model and the original model, which can simultaneously avoids catestraphic forgetting and the enables adaptation.

The authors adaptively adjust the prior distribution for different convolution kernels, which avoids the influence of the variance in convolutional kernel parameters in the pretrained model.

The connection to Bayesian learning provides a theoretical basis for the proposed method.

The paper does not introduce too many extra parameters and could be trained efficiently.

The Quantification of weight uncertainty is interesting, which shows that different layers have different uncertainty on the parameters. The observation could guide following works on source-free domain adpatation.


Weakness:

On line 3-4, source-free domain adaptation assumes that both source data and labeled target data are not available but not 'or'.

On line 38-40, the paper argus that the performance on the source domain will degrade. However, in many domain adaptation settings, only the performance in the target domain is important. For the source domain, we can directly use the model trained on the source domain to perform prediction. Thus, different from continual learning, degrading the source performance may not be a shortcoming of domain adaptation methods.

On line 40-42, the bias to a specific target domain may not be a problem for the domain adaptation to a single domain but a problem for multi-target domain adaptation. However, for multi-target domain adaptation, we can also merge all the domains and perform a single target domain adaptation. 

On line 91-94, the authors defautly assume that \Delta \omega has a zero mean, which means that \Delta \omega has the highest density according to the property of the Gaussian distribution. However, \Delta \omega = 0 indicates that the source network should be directly applied to the target network, which is a clearly suboptimal solution for \Delta \omega. Why does the authors use a obviously suboptimal solution at the point of the highest density for \Delta \omega.

The parameter sharing strategy is natural and should not be considered as a significant contribution. The parameters in the same kernel has strong correlations and should not be treated separately. Thus, sharing the same perturbation is a natural choice but not a special strategy.

In section 4.3, what does parameter non-shareing mean in the paragraph 'Parameter sharing strategy'?
questions: As discussed in the weakness, the two limitations of fine-tuning may not be severe for the domain adaptation setting, could the authors discuss some main limitations of fine-tuning such as overfitting on the target data or limited to settings with target labeled data and cannot be applied to unsupervised domain adaptation?

Does the method only limited to the computer vision setting. In the paper, the authors only gives an instatiation of the cnovolutional layer.
limitations: The authors do not discuss the limitations of the method. Could the authors discuss this in the response or point out at which place in the paper the authors discuss this?
review_title: null

Meta-review: metareview: This paper proposes a novel probabilistic framework for source-free domain adaptation, in which the source model serves as the invariant part (mean) while a perturbation (variance) is applied to the source model parameters to derive the target model that accounts for the target-specific distribution. All four reviewers provided detailed and constructive comments, which were well taken into account by the authors in their revision and rebuttal. After discussion, all reviewers were positive about the paper. AC agreed with the reviewers that this paper introduces a novel, solid, and parameter-simple approach to source-free domain adaptation with comprehensive empirical evaluation for several settings, which will be widely interested by the community. A further comment of AC is that the connection to Shai Ben-David et al.'s seminal bound is rather off-topic to this paper, making the discussion subject to flaw --- there is no formal modeling of the source and target data distributions that is required by the bound, while the bound cannot describe domain relatedness in terms of model parameters. So I suggest the authors to remove this part to make the paper more convincing.
confidence: Certain
Decision: Accept