Paper: Inherently Interpretable Time Series Classification via Multiple Instance Learning (ICLR-2024)

Reviewer comment (Experiments):
The paper does not provide a detailed comparison of MILLET with other state-of-the-art TSC models. Although the authors claim that “We design three MILLET DL models by adapting existing backbone models that use GAP: FCN, ResNet, and InceptionTime. While extensions of these methods and other DL approaches exist (see Foumani et al., 2023), we do not explore these as none have been shown to outperform InceptionTime (Middlehurst et al., 2023).” the application of MILLET to other models and further comparisons with other state of the art TSC is missing and is relevant better to measure the effectiveness and generalizability of the proposed approach.

Author response:
1. *Application of MILLET to other TSC methods (Weakness 1 / Question 1)*  
In the work we focused on applying MILLET to the deep learning family of TSC methods. As stated in the paper, “we choose to focus on DL approaches due to their popularity, strong performance, and scope for improvement” (Section 2). We agree that extending MILLET to other families of TSC methods is a worthwhile area of further study, but believe that our analysis against the current versions of SOTA methods is sufficiently comprehensive to demonstrate the effectiveness of MILLET. While MILLET should still be applicable to other TSC methods, it is not as trivial as applying it to other deep learning methods and warrants standalone future work. We feel that our time during the rebuttal is best served delivering more insights into MILLET for deep learning methods, as this was the main focus of the work.

Reviewer comment (Experiments):
The paper does not provide a detailed comparison with other TSC interpretability methods. (e.g. LIME)

Author response:
2. *Other interpretability methods (Weakness 2 / Question 2)*  
Thank you for the suggestion of comparing with LIME. With LIME, we expect the analysis to uncover a similar issue as to what we discovered with SHAP: LIME will be very expensive to run as it makes many repeated forwarded passes of the model. We will include a discussion of the alternative interpretability methods in a new section in the Appendix.

Reviewer comment (Theory):
The paper does not provide a detailed algorithm complexity analysis. While the authors provide information on the run time of MILLET (see E.3), a more detailed analysis of the algorithm complexity would help establish its scalability and feasibility in large-scale applications.

Author response:
3. *Time complexity analysis (Weakness 3 / Question 3)*  
We have begun conducting time complexity analysis of the pooling methods, and will expand Appendix E.3 to include these results. This will go beyond run time and number of forward passes, rather looking at actual time complexity and how the pooling methods scale with the number of classes and time series length. Please see the general rebuttal for initial results.

Reviewer comment (Experiments):
How does MILLET perform with other TSC models?

Author response:
1. *Application of MILLET to other TSC methods (Weakness 1 / Question 1)*  
In the work we focused on applying MILLET to the deep learning family of TSC methods. As stated in the paper, “we choose to focus on DL approaches due to their popularity, strong performance, and scope for improvement” (Section 2). We agree that extending MILLET to other families of TSC methods is a worthwhile area of further study, but believe that our analysis against the current versions of SOTA methods is sufficiently comprehensive to demonstrate the effectiveness of MILLET. While MILLET should still be applicable to other TSC methods, it is not as trivial as applying it to other deep learning methods and warrants standalone future work. We feel that our time during the rebuttal is best served delivering more insights into MILLET for deep learning methods, as this was the main focus of the work.

Reviewer comment (Experiments):
How does MILLET compare with other TSC interpretability methods?

Author response:
2. *Other interpretability methods (Weakness 2 / Question 2)*  
Thank you for the suggestion of comparing with LIME. With LIME, we expect the analysis to uncover a similar issue as to what we discovered with SHAP: LIME will be very expensive to run as it makes many repeated forwarded passes of the model. We will include a discussion of the alternative interpretability methods in a new section in the Appendix.

Reviewer comment (Theory):
Can you provide a more detailed analysis of the algorithm complexity?

Author response:
3. *Time complexity analysis (Weakness 3 / Question 3)*  
We have begun conducting time complexity analysis of the pooling methods, and will expand Appendix E.3 to include these results. This will go beyond run time and number of forward passes, rather looking at actual time complexity and how the pooling methods scale with the number of classes and time series length. Please see the general rebuttal for initial results.

Reviewer comment (Experiments):
Have you considered the potential impact of the choice of hyperparameters on the performance of MILLET?

Author response:
4. *Impact of hyperparameter choice (Question 4)*  
As discussed in Appendix B.2, we chose fixed hyperparameter values based on those used to train the original backbone models (i.e. no hyperparameter tuning was used). This was done to ensure a fair comparison and provide a set of default hyperparameter values for use in derivative works. We will happily expand Appendix B.2 to mention the impact of hyperparameter choice. For example, MILLET had varying convergence rates for different datasets: sometimes it converged very quickly (so a lower LR might be better), but sometimes it took a long time to converge, so more epochs may be required. Scheduled/adaptive LR might be appropriate in some cases.

Reviewer comment (Evaluation):
Have you considered the potential impact of class imbalance on the performance of MILLET?

Author response:
5. *Impact of class imbalance (Question 5)*  
As mentioned in your review, MILLET was the best approach in our evaluation of balanced accuracy performance. This suggests it is more robust to class imbalance than other methods. This was also without any specific focus on optimising for class imbalance, e.g. weighted cross entropy loss could be used during training to further improve performance on imbalanced datasets. However, further analysis of the effect of class imbalance would indeed be insightful. We will expand Appendix E.1 to include this. Our initial results have shown that performance improvements are demonstrated for MILLET on datasets with a high level of imbalance compared to InceptionTime, HC2, and Hydra-MR.

Reviewer comment (Experiments):
I would have appreciated a comparison against ROCKET or MiniROCKET at least as competitor for the TSC task. Further usage of MILLETS also for ROCKET will completely fulfill the purpose of proposing this approach as a model-agnostic one.

Author response:
In the work we focused on applying MILLET to the deep learning family of TSC methods. As stated in the paper, “we choose to focus on DL approaches due to their popularity, strong performance, and scope for improvement” (Section 2). We agree that extending MILLET to other families of TSC methods is a worthwhile area of further study, but believe that our analysis against the current versions of SOTA methods is sufficiently comprehensive to demonstrate the effectiveness of MILLET. Convolutional methods such as ROCKET often use a different form of pooling to deep learning methods: while deep learning employs GAP, convolutional models use alternative approaches such as max pooling and proportion of positive values (PPV) pooling. While MILLET should still be applicable to these methods, it is not as trivial as applying it to other deep learning methods and warrants standalone future work. We feel that our time during the rebuttal is best served delivering more insights into MILLET for deep learning methods, as this was the main focus of the work.

Reviewer comment (Presentation):
To fully understand the paper the reader is constrained to refer to the Supplementary Material. A suggestion is to save some space and anticipate in the main paper some of the details of the Supplementary Material.

Author response:
We appreciate there are a lot of references to the appendix throughout the work. We attempted to signpost the relevant appendices as much as possible to aid clarity and indicate where readers should look for further detail. We are happy to improve the clarity of the main body in our revised submission.

Reviewer comment (Experiments):
Experiments with the synthetic dataset should have been performed by varying the number of records, time stamps, classes.

Author response:
One of the strengths of our synthetic dataset (WebTraffic) is indeed that it facilitates precise control of dataset properties (dataset size, time series length, number of classes, etc.). However, in this work we relied on the 85 UCR datasets to cover a broad range of TSC domains and properties, but WebTraffic could certainly be used for this purpose. We hope that it may be used in derivative works to further investigate interpretable TSC.

Reviewer comment (Experiments):
I wonder if the method can be applied to other domains.

Author response:
Thank you for your time in reviewing our work. Please see our response to your review below in addition to the general rebuttal given above.  

We believe there could be some scope for applying our work in other machine learning paradigms (we assume this the ‘other domains’ that you are referring to – please correct us if this is not the case!). The existing pooling methods we study (instance, attention, and additive) are applicable in other machine learning paradigms (e.g. MIL for vision), so our novel pooling method (conjunctive) should also be applicable elsewhere. We will mention this in a new appendix section.

Reviewer comment (Experiments):
Lack of comparison against previous benchmarks for saliency maps for feature attribution in time series classification from TSR [1], DynaMask [2], WinIT [3], and TimeX [4]. All of these works provide additional synthetic datasets for evaluating interpretability methods and show performance against more general methods like Feature Occlusion and Integrated Gradients. While MILLET seems likely to improve on such methods due to the better computational efficiency, it is not thoroughly evaluated in the paper, except in counting the number of forward passes in the difference between SHAP, CAM, and MILLET.

Author response:
1. *Other interpretability methods (Weakness 1)*  
Thank you for the references to additional interpretability metrics for TSC. We will include a discussion in a new appendix section contrasting our approach with these methods.  
2. *Time complexity analysis (Weakness 1 cont.)*  
We have begun conducting time complexity analysis of the pooling methods, and will expand Appendix E.3 to include these results. This will go beyond run time and number of forward passes, rather looking at actual time complexity and how the pooling methods scale with the number of classes and time series length. Please see the general rebuttal for initial results.