Uncertainty-aware Guided Diffusion for Missing Data in Sequential Recommendation

Question 3:

Based on the performance of DreasMiss, can we say that DreamRec has an overfitting problem? With more rounds of iteration, DreamRec has inferior performance.

Thanks for your insightful question! We think it is not an overfitting problem for DreamRec. Below we clarify the misunderstanding for DreamRec's inferior performance.

• We first explain that the more iterative steps in DreamRec come from the DDPM's reverse process in the inference phase, over that of DDIM we employed in DreamMiss, as shown in Table R3. Since they are trained similarly and there is no training or updating of model parameters in the inference phase, overfitting is not a concern. The inferior performance of DreamRec can be primarily attributed to its oversight of the missing data issue.

Table R3: Running time comparison of DreamRec and DreamMiss per epoch.

• Then we conduct additional experiments to demonstrate that it is the DTS rather than DDIM that brings performance improvement for DreamRec. Specifically, we apply DDPM and DDIM for DreamRec and DreamMiss respectively to validate their impact on the performance of diffusion-based recommenders. The experimental results are presented in Table R4.

Table R4: Performance comparison of DDPM and DDIM for diffusion-based recommenders.

As shown in Table R4, the performance of DDPM and DDIM is comparable, as evidenced by the similar results for DreamRec (DDPM) and DreamRec (DDIM). This validates that the rounds of iteration in the inference phase will not cause performance improvement. Furthermore, DreamMiss consistently outperforms DreamRec, demonstrating the effectiveness of our DTS in enhancing the robustness of diffusion models. Thus it is the DTS that results in performance improvement instead of the accelerated sampling with fewer iterative rounds in DDIM.

• We believe that the inferior performance of DreamRec stems from training solely on the observed sequence, struggling with complex missing data. The DTS of DreamMiss generates uncertainty-aware missing data, enhancing the robustness of diffusion models in real-world scenarios through consistency regularization.

We sincerely hope that our additional response has adequately addressed your concerns. If so, we would greatly appreciate your consideration in raising the score. If there are any remaining concerns, please let us know, and we will continue to actively address your comments and improve our work.

Weakness 3:

The reasonableness of stability scores In recommendation model training, data are often shuffled to remove the dependency among samples. However, the stability scores seem the opposite way; it used the batch information for sampling. It contradicts the traditional way.

Thank you for your insightful question regarding the handling of data dependencies in recommendation tasks. You are correct that dependency among samples is a common concern in many recommendation settings. Below we clarify the misunderstanding for the reasonableness of stability scores.

• Dataset Processing: In our sequential recommendation tasks, the sequence samples are shuffled during batch loading, thereby eliminating dependencies among the samples in a batch.
• Stability score calculation: The Stability scores are calculated by the entropy of item continuity scores within this sequence. For example, a sequence consists of 10 items, the normalized continuity scores for these items are $con=0.11,0.02,0.08,0.05,0.09,0.05,0.3,0.2,0.1$, and the sum of them is $1$. Then the stability score of this sequence is $h=-\sum_{n=1}^{n=9}con_n \log con_n\approx2.27$, representing the entropy of the continuity scores for this sequence. Greater uniformity in item continuity within a sequence results in higher entropy (indicating greater sequence stability), independent of other sequence samples. We normalize stability scores $h$ as $sta$ with softmax in a single batch, which does not affect their relative values; selecting sequences with relatively high stability in a batch does not contradict traditional methods. We will improve the clarification for the calculation of stability scores in our revision.

Question 1:

Typo: The line 7 of Algorithm 1 lacks a square root.

Thank you for reviewing our work so conscientiously! We sincerely apologize for the oversight and will carefully address the presentation issues in the revised version. Additionally, we will review the presentation throughout the entire manuscript.

Weakness 2 and Question 2:

More explanation for the rationale of accelerated sampling

Thank you for your valuable feedback! The accelerated sampling arises from DDIM, which reduces the number of iterative steps in the reverse process. Below, we provide a more detailed explanation of the rationale behind DDIM's accelerated sampling.

• We first explain the different rationale of DDPM [1] and DDIM [2]. For DDPM, the forward process and reverse processes are both Markovian chains. The number of iterative steps in the reverse process is equal to that in the forward process due to the reliance on the Markov assumption. To ensure the generation quality, DDPM needs a substantial number of sampling steps in the reverse process. Unlike DDPM, DDIM accelerates the reverse process by relaxing the Markov assumption, achieving comparable generation quality with significantly fewer sampling steps. Below we list the difference between DDPM and DDIM in Table R2.

Table R2: The rationale comparison for DDPM and DDIM.

Both DDPM and DDIM are trained under the same objective, the difference lies in the reverse process of the inference phase. For DDIM, the $\sigma\_t = \eta \sqrt{\frac{1-\bar \alpha\_{t-1}}{1-\bar \alpha\_{t}}}\sqrt{1-\frac{ \bar \alpha\_{t}}{ \bar \alpha\_{t-1}}}$ is an arbitrary vector. When $\eta = 0$, the sampling process becomes a deterministic process as DDIM, and when $\eta = 1$, it corresponds to DDPM. Since the training objective does not depend on the specific forward process as long as $q\_\sigma(x\_t|x\_0)$ is fixed, the deterministic sampling process of DDIM does not rely on the Markov chain and can adopt a forward process with steps fewer than $T$. Thus the step-by-step sampling process in DDPM, which operates over $1\sim T$, can be modified to iterate over a subset $\{\tau\_1,...,\tau\_S\}$ of $\{1,...,T\}$. This change enables the acceleration of the sampling process of DDIM.

We will include this rationale explanation for DDIM's accelerating sampling in Appendix C of our revision.

[1] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In NeurIPS, 2020a.

[2] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. In ICLR. OpenReview.net, 2021a.

Dear Reviewer:

We would like to express our sincere gratitude for your valuable feedback and constructive suggestions. We have detailed our responses point-by-point to your comments. We sincerely hope that our additional response has adequately addressed your concerns.

Weakness 1:

More discussion on the missing data issue: Thompson sampling can not tackle all the missing data issues. How the proposed model can address which kind of missing data should be discussed in the paper.

Thank you for your valuable feedback regarding the missing data issue. We acknowledge that Thompson sampling does not address all types of missing data. Below we clarify how our proposed method specifically handles certain types of missing data.

• Clarification for types of missing data issue: The missing data issue refers to the absence of behaviors in interaction sequences, which can lead to incomplete observed sequences in sequential recommendation tasks. For example, the complete sequence is $A \rightarrow B \rightarrow C \rightarrow D \rightarrow E \rightarrow F$. However, due to complex factors, we may only observe the partial interaction sequence $A\rightarrow C\rightarrow E \rightarrow F$ with $B$ and $D$ missing. Since the complete sequence is unavailable, the data missing in the observed sequence is uncertain. Such missing data issues can be roughly divided into two types: missing at random and missing not at random, as discussed in the related work of our original submitted manuscript. Missing not at random often reflects bias, such as popularity bias and exposure bias. Missing at random is often caused by factors such as technical issues or privacy concerns.

• Clarification for missing data issue addressed by DTS: DTS can effectively address the missing data issues when the observed sequence accurately reflects users' complete preferences, regardless of the specific factors (such as popularity bias, exposure bias, or technique issues). According to the probability models which reflect user preference evolution, DTS tends to remove items which have little impact on understanding users' original preference evolution, as shown in the consistent green curves in Figure 1 (c) of our original submitted manuscript. By simulating uncertain missing data while maintaining the evolution of user preferences, DTS enables DDMs to generalize and effectively address the original missing data that does not disrupt users' complete preferences.

• Experimental Validation: To validate the effectiveness of DreamMiss in addressing the specific missing data issue, we construct two synthetic datasets: the R is constructed with missing data that occurs randomly and may not fully reflect user preferences; the P is designed with missing data aligned with user preferences. We conduct experiments on these two synthetic datasets, and the results are presented in Table R1.

Table R1: Performance of DreamMiss and DreamRec on the two synthetic datasets.

As shown in Table R1, DreamMiss is more effective on the "P" dataset, demonstrating a more significant improvement than on the dataset "R". This validates that DreamMiss can effectively address the missing data issue which do not change users' complete preferences.

We will include this discussion in Appendix F.3 of our revision.

Dear Reviewer VkFH,

We deeply appreciate your valuable feedback and the time you've taken to review our work with these insights, especially during this busy period.

Regarding your primary concern about the clarification for missing data issue, we have clarified the missing data issue that DTS can address with additional experiments. For the point you raised about the rationale of accelerated sampling for DDIM, we have provided a more detailed explanation of the rationale behind DDIM's accelerated sampling and compared it with DDPM. Concerning reasonability of stability scores, we have clarified the calculation of stability scores, which are based on item continuity scores within a sequence and align with traditional methods.

We hope that our responses have addressed most of your concerns. If so, we kindly ask if you could consider revising the overall rating of our paper. If there are any remaining concerns, we would be more than happy to further discuss them with you, especially since the rebuttal period is nearing its end. Please let us know if you have any additional questions.

Thank you once again for your support and understanding!

Best regards,

Authors

Dear Reviewer VkFH,

As the discussion phase is coming to an end, we sincerely hope to address your concerns and engage in further discussion. If you have any remaining questions, please feel free to reach out directly. We would like to take this final opportunity to improve our work.

Best regards,

Authors of Paper 7669

Dear Reviewer VkFH,

As the discussion phase is coming to an end, we sincerely hope to address your concerns thoroughly. If you find our responses satisfactory, we would greatly appreciate your consideration of revising your score. Thank you once again for your valuable feedback and thoughtful suggestions.

Best regards,

Authors of Paper 7669

Dear Reviewer:

Thank you for your feedback and for the score you provided. We appreciate your honesty regarding your familiarity with this research area. We have made revisions and improvements to the content in response to the comments received. We hope these changes enhance the clarity of our work and assist in your understanding of the paper.

We would be grateful for any additional insights or suggestions you might have, as your perspective is valuable to us.

Thank you once again for your time and consideration.

Weakness 4

Scalability Limitations: Insufficient discussion of performance on large-scale recommendation systems. Limited analysis of computational resource requirements for real-world deployment. Need for more detailed discussion of potential optimization strategies for larger datasets.

Thank you for your valuable suggestion. Below we provide a more detailed discussion of DreamMiss's application to larger-scale recommendation systems.

• We first analyze the computational complexity of DreamMiss and discuss its performance on large-scale recommendation systems.

  • Computational complexity: DreamMiss employs a Transformer as the sequence encoder and a multi-layer perceptron (MLP) as the denoising model. Training phase: The Transformer model consists of a Self-Attention Mechanism, a Feed-Forward Neural Network, and Layer Normalization. Let $L$ be the length of the input sequence, $d$ be the embedding dimension, and $N$ be the number of layers in the model. The complexity for computing self-attention at each layer is $O(L^2\cdot d)$, and the complexity for the MLP network is $O(L\cdot d^2)$. For $N$ layers, the overall computational complexity becomes $O(N\cdot (L^2\cdot d+L\cdot d^2))$. Inference phase: Let $K$ be the number of reverse steps, the computational complexity of DreamMiss can be $O(K\cdot N\cdot (L^2\cdot d+L\cdot d^2))$.

  • Complexity comparison: The computational complexity of DreamMiss for training each epoch is nearly similar to other diffusion-based recommenders and traditional recommenders that use the same sequence encoder. Furthermore, since we employ DDIM to accelerate sampling during the inference phase, the value of $K$ for DreamMiss is significantly lower than that of DreamRec. In addition to Table 5 of the appendix of our original submitted manuscript, we compare the time cost per epoch of DreamMiss and other methods. As shown in Table R6. DreamMiss substantially reduces the time cost during the inference phase than DreamRec, and has a similar training time cost with other methods.

    Table R6: Running time comparison of DreamMiss and other methods on three datasets per epoch.

    Methods	YooChoose		KuaiRec		Zhihu
    	Training	Inferencing	Training	Inferencing	Training	Inferencing
    SASRec	01m 38s	00m 06s	02m 07s	00m 08s	00m 10s	00m 01s
    AdaRanker	02m 29s	00m 08s	03m 38s	00m 09s	00m 14s	00m 01s
    DreamRec (DDPM)	01m 31s	21m 32s	03m 59s	32m 40s	00m 14s	01m 31s
    DreamMiss (DDIM)	01m 22s	00m 13s	02m 23s	00m 11s	00m 11s	00m 01s

• Computational resource requirements in deployment. In our experiments, we set the batch size as 256. In this setting, the GPU memory usage is around 2000 MB, which is comparable with SASRec. The time cost for each epoch is presented in Table R6. In large-scale recommendation systems, although the number of users and items increases, the sequence encoder (Transformer) and denoising models (MLP) we employ do not require excessive computational resources. Furthermore, Thompson sampling consumes almost no computational resources without involving model parameters. These factors enable our approach to be effectively applied in large-scale systems. Furthermore, optimizing the computational efficiency of Denoising Diffusion Models (DDMs) during both training and inference has become an important research focus. Improvements in this area would enhance the practical use of our proposed approach.

• Finally, we conduct experiments to validate the reliability of the continuity and stability metrics of probability models.

  • Notably, there is a gap in the existing research on metrics for measuring the observed sequences. One of our contributions is the proposal of two new metrics: local item continuity and global sequence stability.

  • To demonstrate their effectiveness, we have conducted an ablation study with experimental results presented in Table 2 of our original submitted manuscript. This study assesses the recommendation performance with and without continuity and stability metrics.

  • Here, in addition to our original ablation study, we propose other metrics and carry out further experiments to compare their performance. Specifically, we introduce additional metrics including item popularity, item diversity within a sequence, item position in the sequence, and sequence length for the probability models. The results of these experiments are displayed in Table R4.

    Table R4: Performance comparison of different metrics for probability models.

    Methods	YooChoose		KuaiRec		Zhihu
    	H@20(%)	N@20(%)	H@20(%)	N@20(%)	H@20(%)	N@20(%)
    Base	4.78	2.23	5.16	4.11	2.26	0.79
    w/o GL	6.24	3.91	5.37	4.19	2.30	0.80
    w/o L	6.41	4.26	5.44	4.63	2.34	0.86
    w/o G	6.48	4.29	5.43	4.64	2.44	0.81
    w Popularity	6.28	4.18	5.46	4.57	2.38	0.80
    w Diversity	6.26	4.20	5.45	4.52	2.29	0.81
    w Seq_len	6.27	4.30	5.46	4.54	2.30	0.83
    w Item_pos	6.28	3.96	5.20	4.55	2.24	0.79
    DreamMiss	6.90	4.34	5.48	4.77	2.65	0.88

  Specifically, 'w/o G', 'w/o L', and 'w/o GL' represent the absence of global sequence stability metric, local item continuity metric, or both, respectively. The metric of item popularity is measured by the frequency of each item in all interactions, which reflects popularity bias. The metric of item diversity within a sequence is calculated to indicate the diversity of user preferences. The metric of sequence length serves as a measure of user activity, while the metric of item position reflects short-term and long-term preferences. As shown in Table R3, w/o G, w/o L, w Popularity, w Diversity, w Seq-len, and w Item-pos outperform the Base and w/o GL, highlighting the robustness of probability models in helping to alleviate the missing data issue. Moreover, the superior performance of DreamMiss demonstrates the reliability of continuity and stability metrics for probability models.

• To further validate the robustness of the probability models, we have conducted experiments over five experimental runs with different random seeds and on different datasets, reporting the average performance with their corresponding standard deviations in the tables of our submission. The experimental results are relatively stable as the standard deviations of DreamMiss are similar to those of baselines. Additionally, we validate the robustness of DreamMiss to the proportion of missing data in Table 8 of our revision and the sensitivity of DreamMiss to the threshold of simulation in Appendix F.2 of our revision. Experimental results demonstrate the robustness of probability models.

We include the explanation and experiments in Sections 4.3 and Appendix B.2, F.4, and F.5 in our revision.

• Then we conduct experiments to verify the advantages of the Thompson sampling strategy compared to other sampling strategies, including random-based sampling (sample uniformly without exploiting known information), time-based sampling (sample based on timestamps), and model-based sampling (sample based on another model while lacking supervision signals). More details are introduced in Appendix B.2 of our revision. The experimental results are presented in Table R3. The Base represents the diffusion-based recommender without a sampling strategy.

  Table R3: The performance comparison of different sampling strategies for uncertainty-aware guided diffusion for recommendation.

  Methods	YooChoose		KuaiRec		Zhihu
  	H@20(%)	N@20(%)	H@20(%)	N@20(%)	H@20(%)	N@20(%)
  Base	4.78	2.23	5.16	4.11	2.26	0.79
  Random-based	6.24	3.91	5.37	4.19	2.30	0.80
  Time-based	6.28	3.96	5.20	4.55	2.24	0.79
  Model-based	6.49	3.62	5.18	4.59	2.36	0.80
  DreamMiss	6.90	4.34	5.48	4.77	2.65	0. 88

  The experimental results in Table R3 indicate that different sampling strategies have a noticeable impact on the diffusion-based recommender compared to the Base approach. However, DreamMiss demonstrates superior performance than other sampling strategies, confirming the advantages of DTS.

Weakness 2

Limited Validation of Dual-side Thompson Sampling (DTS): The reason for DTS is specifically effective for diffusion-based sequential recommenders should be justified. Theoretical analysis or empirical validation of the reliability of the continuity and stability metrics should be provided. The generalizability of DTS to other recommendation architectures needs a more thorough investigation. The robustness of the probability models used in DTS requires more comprehensive validation.

Thanks for your valuable suggestions! We would conduct additional experiments and make a deeper analysis of the Dual-side Thompson Sampling (DTS).

• First, we explain why DTS is specifically effective for diffusion-based sequential recommenders.

  • For diffusion-based recommenders: Introducing missing data with DTS can be considered as introducing a form of noise within the sequence, which can enhance DDMs' denoising ability to missing data rather than Gaussian noise. Additionally, DTS can be a general algorithm to enhance various recommendation architectures' robustness against uncertain missing data, by simulating missing data without disrupting user preference evolution.
  • For DTS strategy: The advantage of DTS lies in that it can simulate missing data stochastically without disrupting user preference. By balancing the exploration and exploitation based on the known user preference in probability models, DTS is more likely to remove behavior that has little impact on understanding user preference evolution, as evidenced by the consistent green curves between the observed sequence and the one edited by DTS in Figure 1 of our original submitted manuscript.

• Next, we conduct additional experiments to validate the generalizability of DTS to different recommendation architectures. In addition to the experimental results in Table 4 of our original submitted manuscript (generalizing DTS to GRU4Rec, SASRec, CL4Rec), we conduct further experiments to assess the generalizability of DTS across other recommendation architectures (Caser [1], AdaRanker [2], and DiffuASR [3]). The results of these experiments are presented in Table R2.

  Table R2: Experimental results for the generalizability of DTS across other recommendation architectures.

  Methods	YooChoose		KuaiRec		Zhihu
  	H@20(%)	N@20 (%)	H@20 (%)	N@20(%)	H@20(%)	N@20(%)
  GRU4Rec	3.89	1.62	3.32	1.23	1.78	0.67
  + DTS	3.96	1.72	3.43	1.40	1.83	0.68
  improv.	1.77%	5.81%	3.21%	12.14%	2.73%	1.47%
  SASRec	3.68	1.63	3.92	1.53	1.62	0.60
  +DTS	3.98	1.58	3.96	1.63	1.70	0.72
  improv.	7.54%	-3.07%	1.01%	6.13%	4.71%	11.11%
  CL4Rec	4.45	1.86	4.25	2.01	2.03	0.74
  +DTS	4.63	1.88	4.57	2.25	2.16	0.78
  improv.	3.89%	1.06%	7.00%	10.67%	6.02%	5.13%
  Caser	4.06	1.88	2.88	1.07	1.57	0.59
  +DTS	4.27	2.01	3.19	1.09	1.72	0.65
  improv.	4.92%	6.47%	9.72%	1.83%	8.72%	9.23%
  AdaRanker	3.74	1.67	4.14	1.89	1.70	0.61
  +DTS	4.16	1.97	4.33	1.93	1.64	0.67
  improv.	10.10%	15.22%	4.39%	2.07%	-3.53%	8.96%
  DiffuASR	4.48	1.92	4.53	3.30	2.05	0.71
  +DTS	4.66	2.08	4.58	3.98	2.05	0.73
  improv.	3.86%	7.69%	1.09%	17.09%	0.00%	2.82%
  DreamRec	4.78	2.23	5.16	4.11	2.26	0.79
  +DTS	6.90	4.34	5.48	4.77	2.65	0.88
  improv.	30.72%	48.62%	5.84%	13.84%	14.72%	10.23%

  The experimental results indicate that applying DTS across various recommendation architectures leads to consistent improvements in recommendation performance, demonstrating that DTS is a general algorithm for enhancing the robustness of recommendation systems. Furthermore, the significant performance gains observed with DTS in DreamRec underscore its effectiveness for diffusion-based models (DDMs), owing to their capability in modeling complex data distributions and denoising the missing data.

  [1] Jiaxi Tang and Ke Wang. Personalized top-n sequential recommendation via convolutional sequence embedding. In WSDM, pp. 565–573. ACM, 2018.

  [2] Xinyan Fan, Jianxun Lian, Wayne Xin Zhao, Zheng Liu, Chaozhuo Li, and Xing Xie. Ada-ranker: A data distribution adaptive ranking paradigm for sequential recommendation. In SIGIR, pp.1599–1610. ACM, 2022a

  [3] Qidong Liu, Fan Yan, Xiangyu Zhao, Zhaocheng Du, Huifeng Guo, Ruiming Tang, and Feng Tian. Diffusion augmentation for sequential recommendation. In CIKM, pp. 1576–1586. ACM, 2023.

• Consistency regularization: To ensure the effectiveness of extrapolation, we leverage consistency regularization to minimize $\|f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)-f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\tilde{\mathbf{g}},\tau\_s)\|$. Since the interaction sequences are edited stochastically across different epochs, $\hat{\mathbf{g}}$ and $\tilde{\mathbf{g}}$ can serve as the perturbated pairs. Let the ground-truth label of the next item be $\mathbf{e}\_N^0$. By completing the square, we obtain the inequality: $||f\_\theta(\mathbf{e}\_N^{\tau\_s},\hat{\mathbf{g}}, \tau\_{s})-f\_\theta(\mathbf{e}\_N^{\tau\_s},\tilde{\mathbf{g}}, \tau\_{s})||\_2^2 \leq 2\left(||f\_\theta(\mathbf{e}\_N^{\tau\_s},\hat{\mathbf{g}},\tau\_{s})-\mathbf{e}\_N^0||\_2^2+||f\_\theta(\mathbf{e}\_N^{\tau\_s},\tilde{\mathbf{g}}, \tau\_{s})-\mathbf{e}\_N^0||\_2^2\right)$. Consequently, we can achieve consistency regularization of minimizing the left-hand side by minimizing the right-hand side, which stems from our reconstruction loss.

  We improve the explanation in section 3.3 of revision, and include more explanation for our motivation and method in Appendix B.1 and B.3 of our revision.

[1] David Krueger, Ethan Caballero, Jörn-Henrik Jacobsen, Amy Zhang, Jonathan Binas, Dinghuai Zhang, Rémi Le Priol, and Aaron C. Courville. Out-of-distribution generalization via risk extrapolation (rex). In ICML, volume 139 of Proceedings of Machine Learning Research, pp. 5815–5826. PMLR, 2021.

[2] Han Zhang, Zizhao Zhang, Augustus Odena, and Honglak Lee. Consistency regularization for generative adversarial networks. In ICLR. OpenReview.net, 2020.

• Finally, we conduct experiments to validate the superiority of DreamMiss over data completion methods, we make a comparison for the three methods (i.e., simulating missing data, leveraging observed data, and recovering missing data) on the missing data scenarios.

  • In Table 1 of our original submitted manuscript, we have compared DreamMiss with some imputation-based baseline methods (DiffuASR, CaDiRec, and PDRec). The superior performance of DreamMiss demonstrates the effectiveness of simulating missing data.

  • Additionally, following the setting of section 5.4 of our original submitted manuscript, we create synthetic datasets with missing data proportions of 10%, 20%, and 30%. We compare the three methods on the synthetic datasets and the detailed results are shown in Table R1.

    Table R1: Performance comparison for the three methods (i.e., simulating missing data with DreamMiss, leveraging observed data with DreamRec, and recovering missing data with DreamImp).

    Methods	YooChoose		KuaiRec		Zhihu
    	H@20(%)	N@20(%)	H@20(%)	N@20(%)	H@20(%)	N@20(%)
    DreamRec (10%)	5.11	2.16	4.99	4.16	1.95	0.68
    DreamImp (10%)	5.32	2.28	4.89	4.07	1.98	0.68
    DreamMiss (10%)	6.49	3.98	5.04	4.32	2.05	0.69
    DreamRec (20%)	4.87	2.03	4.59	3.81	1.89	0.68
    DreamImp (20%)	4.91	2.55	4.65	3.76	1.91	0.70
    DreamMiss (20%)	6.26	3.66	4.77	4.07	2.22	0.71
    DreamRec (30%)	4.74	1.97	4.18	3.48	1.89	0.67
    DreamImp (30%)	4.73	2.18	4.21	3.59	1.93	0.68
    DreamMiss (30%)	5.92	3.29	4.49	3.69	2.12	0.70

    DreamImp is our imputation-based algorithm designed for diffusion models. In the absence of prior knowledge about the complete sequence, we use the average of two adjacent items for imputation at random positions. Experimental results indicate that the method of simulating missing data (DreamMiss) outperforms approaches that rely solely on observed data (DreamRec) or attempt to recover missing data (DreamImp). We include the experiments in Appendix F.3 of our revision.

• Then we justify how generating additional missing data helps address the original missing data problem through extrapolation [1] and consistency regularization [2].

  • Extrapolation: Let $\hat{\mathbf{g}}$, $\bar{\mathbf{g}}$, and $\tilde{\mathbf{g}}$ denote the guidance encoded from observed sequence $\mathbf{e}\_{1:N-1}$, complete sequence $\mathbf{e}\_{1:N-1}\oplus \delta$ and simulated sequence $\mathbf{e}\_{1:N-1}\ominus \delta'$, respectively. Our objective is to demonstrate the validity of the extrapolation, specifically the inequality $\|f\_\theta(\mathbf{e}^{\tau\_s}\_N,\bar{\mathbf{g}},\tau\_s)-f\_\theta(\mathbf{e}^{\tau\_s}\_N,\hat{\mathbf{g}},\tau\_s)\|\le C\|f\_\theta(\mathbf{e}^{\tau\_s}\_N,\hat{\mathbf{g}},\tau\_s)-f\_\theta(\mathbf{e}^{\tau\_s}\_N,\tilde{\mathbf{g}},\tau\_s)\|$ for some constant $C$, where $\mathbf{e}^{\tau\_s}\_N$ represents the next interacted item with noise of $\tau\_s$ time steps, $f\_\theta$ is the denoising model. Applying Taylor's Formula, we can express the two functions as follows:

\begin{aligned} f_\theta(\mathbf{e}^{\tau_s}_{N},\bar{\mathbf{g}},\tau_s)=f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)+(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)+o(|\bar{\mathbf{g}}-\hat{\mathbf{g}}|),\\f_\theta(\mathbf{e}^{\tau_s}_{N},\tilde{\mathbf{g}},\tau_s)=f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)+(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)+o(|\tilde{\mathbf{g}}-\hat{\mathbf{g}}|). \end{aligned}

Then, combining the above two equalities, we have

\begin{aligned}&f_\theta(\mathbf{e}^{\tau_s}_{N},\bar{\mathbf{g}},\tau_s)-f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)\\&=(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)+o(|\bar{\mathbf{g}}-\hat{\mathbf{g}}|)\\&=\frac{(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)}{(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)}(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)+o(|\bar{\mathbf{g}}-\hat{\mathbf{g}}|)\\&=\frac{(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)}{(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)}(f_\theta(\mathbf{e}^{\tau_s}_{N},\tilde{\mathbf{g}},\tau_s)-f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s))+o(|\bar{\mathbf{g}}-\hat{\mathbf{g}}|)+o(|\tilde{\mathbf{g}}-\hat{\mathbf{g}}|),\end{aligned}

where we assume that $(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla\_gf\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)\neq 0$. Thus, we obtain the following inequality:

\begin{aligned}&|f_\theta(\mathbf{e}^{\tau_s}_{N},\bar{\mathbf{g}},\tau_s)-f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)|\\&\le\left|\frac{(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)}{(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla_g f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)}\right||f_\theta(\mathbf{e}^{\tau_s}_{N},\hat{\mathbf{g}},\tau_s)-f_\theta(\mathbf{e}^{\tau_s}_{N},\tilde{\mathbf{g}},\tau_s)|+o(|\bar{\mathbf{g}}-\hat{\mathbf{g}}|)+o(|\tilde{\mathbf{g}}-\hat{\mathbf{g}}|),\end{aligned}

where $\|f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)-f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\tilde{\mathbf{g}},\tau\_s)\|$ is the distance between the prediction from observed sequence and simulated sequence. To bound the coefficients $\left|\frac{(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla\_g f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)}{(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla\_g f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)}\right|$, we need to analyze the two inner products, ${(\bar{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla\_g f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)}$ and ${(\tilde{\mathbf{g}}-\hat{\mathbf{g}})^\top\nabla\_g f\_\theta(\mathbf{e}^{\tau\_s}\_{N},\hat{\mathbf{g}},\tau\_s)}$. If the simulated missing data process from $\mathbf{e}\_{1:N-1}$ to $\mathbf{e}\_{1:N-1}\ominus \delta'$ can align well with that from $\mathbf{e}\_{1:N-1}\oplus\delta$ to $\mathbf{e}\_{1:N-1}$---the difference between the two pair of data will be roughly equivalent. Consequently, the two differences in guidance, $\bar{\mathbf{g}}-\hat{\mathbf{g}}$ and $\hat{\mathbf{g}}-\tilde{\mathbf{g}}$, will also be approximately equal. In this scenario, the coefficient will be close to 1, resulting in a bounded value $C>0$.

Dear Reviewer:

We would like to express our sincere gratitude for your valuable feedback and constructive suggestions. We have detailed our responses point-by-point to address your concerns.

Weakness 1

Conceptual Clarity and Methodology Concerns: Clear theoretical justification for how generating additional missing data helps address the original missing data problem and why this approach is superior to data completion methods are needed.

Thank you for your valuable feedback, which is of great help in improving the clarity of our method. Formally, we denote the original missing data as $\delta$, the observed sequence as $\mathbf{e}\_{1:N-1}$, the simulated missing data as $\delta'$, the complete sequence as $\mathbf{e}\_{1:N-1}\oplus \delta$, and the simulated sequence as $\mathbf{e}\_{1:N-1}\ominus \delta'$

• We first explain why we did not adopt completion methods:
  • Unavailability of complete sequence: Due to the lack of prior knowledge for the complete sequence $\mathbf{e}\_{1:N-1}\oplus \delta$ from an omniscient perspective, we cannot pinpoint where the missing data $\delta$ occurs or what specific content it pertains to.
  • Uncertainty of missing data: Due to the variability of user preferences, the missing data $\delta$ is uncertain in the observed interaction sequence $\mathbf{e}\_{1:N-1}$. User interaction may miss anywhere stochastically in the observed sequence.

Thus, compensating for missing data may introduce additional errors as shown in Figure 1 (a) of our original submitted manuscript. The unavailability of complete sequence $\mathbf{e}\_{1:N-1}\oplus\delta$ and the uncertainty of missing data motivates us to generate additional missing data $\delta'$ stochastically from the observed sequence $\mathbf{e}\_{1:N-1}$, treating $\mathbf{e}\_{1:N-1}$ as the complete sequence for the simulated sequence $\mathbf{e}\_{1:N-1} \ominus \delta'$.

• Then we conduct experiments to compare the performance of DreamMiss with diverse baselines on the three datasets. Experimental results are presented in Table R8. The baseline methods are the same as those in Table 1 of our original submitted manuscript.

Table R8: Overall performance of different methods for the sequential recommendation on diverse datasets (Beauty and Toys) from different domains. The best score and the second-best score are bolded and underlined, respectively.

Our method consistently outperforms various baselines on larger dataset (Steam) and diverse datasets (Amazon-beauty and Amazon-toys), further highlighting the effectiveness of DreamMiss. We include additional experimental results in Appendix F.1 of our revision.

We sincerely hope that our additional response has adequately addressed your concerns. If so, we would greatly appreciate your consideration in raising the score. If there are any remaining concerns, please let us know, and we will continue to actively address your comments and improve our work.

• Then, we detail some potential optimization strategies for larger datasets.
  • Model Selection [1]: Choose lightweight architectures with lower computational complexity as the sequence encoder.
  • Accelerating inference for DDMs: Reduce the iterative steps in the inference phase by consistency models [2], knowledge distillation [3], or Reflow [4].
  • Starting Item [5]: Instead of using pure noise as the starting item, use the mean of the sequence to reduce the iteration times during inference.

We include these analyses in Appendix F.7 of our revision. [1] Yang Li, Tong Chen, Peng-Fei Zhang, and Hongzhi Yin. Lightweight self-attentive sequential recommendation. In CIKM, pp. 967–977. ACM, 2021a.

[2] Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. In ICML, volume 202 of Proceedings of Machine Learning Research, pp. 32211–32252. PMLR, 2023a.

[3] Chenlin Meng, Robin Rombach, Ruiqi Gao, Diederik P. Kingma, Stefano Ermon, Jonathan Ho, and Tim Salimans. On distillation of guided diffusion models. In CVPR, pp. 14297–14306. IEEE, 2023a.

[4] Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. In ICLR. OpenReview.net, 2023b.

[5] Xiao Lin, Xiaokai Chen, Chenyang Wang, Hantao Shu, Linfeng Song, Biao Li, and Peng Jiang. Discrete conditional diffusion for reranking in recommendation. In WWW (Companion Volume), pp. 161–169. ACM, 2024a.

Weakness 5

Dataset Limitations: Need for validation on more diverse and larger-scale datasets. Limited demonstration of effectiveness across different domains and data distributions.

We appreciate your valuable suggestion! To demonstrate the effectiveness of DreamMiss on larger and more diverse datasets, we have included additional experiments on the Steam dataset, one of the largest datasets commonly used in research, as well as on the Amazon-Beauty and Amazon-Toys datasets, which come from different domains.

• We first introduce the details of the three datasets. The Steam dataset is a collection of data related to the Steam gaming platform, with over three million interactions. Amazon Beauty and Amazon Toys are two categories of datasets from the Amazon platform. They consist of user reviews and ratings for beauty/toy products available on the Amazon website. We treat all ratings as implicit feedback and organize them chronologically by the timestamps. Items and users with fewer than 5 interactions are filtered. The statistics of this dataset are listed in Table R7.

Table R7: Statistics of the Steam, Beauty, and Toys datasets.

Weakness 3

Incomplete Baseline Comparisons: [1] STEAM: A Self-Correcting Sequential Recommender. [2] SSDRec: Self-Augmented Sequence Denoising for Sequential Recommendation. Thanks for your valuable suggestion! Based on your suggestions, we have made additional experiments on these baseline methods.

Thank you for your valuable suggestion! We conduct additional experiments to implement the two baselines on our three datasets (YooChoose, KuaiRec, and Zhihu) and we include the results in our main experiments of revision.

Table R5: Performance of additional baseline methods.

From the experimental results, we observe that the performance of STEAM and SSDRec surpasses that of SASRec, but falls short compared to our method, DreamMiss, further validating the effectiveness of DreamMiss. We include these results in Table 1 of our revision.

Dear Reviewer fpPx,

We deeply appreciate your valuable feedback and the time you've taken to review our work with these insights, especially during this busy period.

Regarding your primary concern about the theoretical justification for the method of simulation, we have clarified why we simulate missing data instead of compensating for it, supported by additional experimental results. Moreover, we provide a theoretical analysis of our method through extrapolation and consistency regularization. For the point you raised about validation of Dual-side Thompson Sampling (DTS), We have clarified the advantages of DTS and diffusion models. To validate these claims, we have conducted additional experiments to assess the generalizability of DTS to other recommenders and compared different sampling strategies with DTS. Moreover, we have proposed additional metrics to evaluate the reliability of continuity and stability, as well as the robustness of the probability models through experiments. Concerning more baselines and more datasets, we have conducted experiments on two additional baselines and expanded our methods to include larger datasets (Steam) as well as more diverse datasets (Beauty and Toys). For the point about scalability limitations, we have analyzed the computational complexity and computational resource requirements of DreamMiss in comparison to other recommenders. Additionally, we have discussed the potential optimization strategies for larger datasets. We have included all these clarifications and experiments in our revision.

We are reaching out to kindly inquire about the current status of your review regarding our response and revision. We sincerely hope that our responses have adequately addressed your concerns. Furthermore, we are eager to address any additional queries you might have, which will enable us to enhance our work further.

Thank you once again for your support and understanding!

Best regards,

Authors

Dear Reviewer fpPx,

As the discussion phase is coming to an end, we sincerely hope to address your concerns and engage in further discussion. If you have any remaining questions, please feel free to reach out directly. We would like to take this final opportunity to improve our work.

Best regards,

Authors of Paper 7669

Dear Reviewer fpPx,

As the discussion phase is coming to an end, we sincerely hope to address your concerns thoroughly. If you find our responses satisfactory, we would greatly appreciate your consideration of revising your score. Thank you once again for your valuable feedback and thoughtful suggestions.

Best regards,

Authors of Paper 7669

Dear Reviewer:

We would like to express our sincere gratitude for your valuable feedback and constructive suggestions. We have detailed our responses point-by-point to your comments. We sincerely hope that our additional response has adequately addressed your concerns.

Weakness 1

Typo: The first character in line 72 should be capitalized.

Thanks again for your thorough review and feedback on our paper. Regarding your comment about the capitalization of the first character in line 72, we have carefully examined the context. Since there is a comma preceding that character at the end of page 1, it should indeed remain lowercase, and we believe this is consistent with standard conventions. It may be that the formatting of this sentence immediately following Figure 1 led to this misunderstanding, and we will work on improving our clarity in the revision.

Weakness 3

Evaluation on larger datasets: Experiments on larger datasets should be conducted to further demonstrate the effectiveness of the proposed method.

We appreciate your suggestion to further improve our work. To illustrate the effectiveness of DreamMiss on larger datasets, we perform an additional experiment on the steam Dataset which is one of the largest datasets commonly used in research.

• Details of the Steam dataset: The Steam dataset is a collection of data related to the Steam gaming platform, containing over three million user-game interactions. we treat all ratings as implicit feedback and organize them chronologically by the timestamps. Items and users with fewer than 5 interactions are filtered. The statistics of this dataset are listed in Table R2.

  Table R2: Statistics of the Steam dataset.

  	Sequence	Items	Ineteractions
  Steam	281,428	13,044	3,485,022

• Experimental results: We compare the performance of DreamMiss with diverse baselines on the Steam in Table R3. The baseline methods are the same as those in Table 1 of our original submitted manuscript.

  Table R3: Overall performance of different methods for the sequential recommendation on Steam. The best score and the second-best score are bolded and underlined, respectively.

  Methods	Steam (HR@20 %)	Steam (NDCG@20 %)
  GRU4Rec	9.23	3.56
  Caser	15.20	6.62
  SASRec	13.61	5.36
  Bert4Rec	12.73	5.20
  CL4SRec	15.06	6.12
  IPS	15.65	6.46
  AdaRanker	15.71	6.68
  DiffuASR	15.74	6.59
  CaDiRe	15.65	6.42
  PDRec	$\underline{15.78}$	6.51
  DiffRec	15.09	$\underline{6.89}$
  DreamRec	15.08	6.39
  DreamMiss	16.19	7.52
  improv.	2.53%	8.38%

  Based on the experimental results, our method consistently outperforms various baselines on larger dataset, further highlighting the effectiveness of DreamMiss. We include additional experimental results in Appendix F.1 of our revision.

References

[1] Ian Osband and Benjamin Van Roy. Bootstrapped thompson sampling and deep exploration. CoRR, abs/1507.00300, 2015a.

[2] Ehsan K. Ardestani and Jose Renau. ESESC: A fast multicore simulator using time-based sampling. In HPCA, pp. 448–459. IEEE Computer Society, 2013.

[3] Xiaohui Chen, Jiankai Sun, Taiqing Wang, Ruocheng Guo, Li-Ping Liu, and Aonan Zhang. Graph-based model-agnostic data subsampling for recommendation systems. In KDD, pp. 3865–3876. ACM, 2023.

We sincerely hope that our additional response has adequately addressed your concerns. If so, we would greatly appreciate your consideration in raising the score. If there are any remaining concerns, please let us know, and we will continue to actively address your comments and improve our work.

Weakness 2

Motivation for Thompson Sampling: The reason for Thompson sampling as the best choice to derive the guide signal for diffusion-based recommendation is not clear. Related experiments should be conducted to verify the best of the Thompson sampling strategy compared to other sampling strategies.

Thank you for your valuable feedback, which is of great help in improving the clarity of our motivation.

Table R1: The performance comparison of different sampling strategies in uncertainty-aware guided diffusion for recommendation.

• We first explain why we use the Dual-side Thompson Sampling to create uncertainty-aware guidance for recommendation, which can simulate missing data stochastically while maintaining user preference.

  • Characteristics of TS: TS [1] strategy can balance the exploration and exploitation based on the known user preference in probability models. To capture user preference evolution, the probability models are established based on item continuity and sequence stability metrics. The Dual-side Thompson Sampling is more likely to remove items with high continuity in sequence with greater stability. Such removal has little impact on understanding user preference evolution pattern, as evidenced by the consistent green curves between the observed sequence and the one edited by DTS in Figure 1 of our original submitted manuscript.

  • Comparison with other sampling strategies: We compare DTS with different sampling strategies, such as random-based sampling, time-based sampling [2], and model-based sampling [3]. Random sampling samples items uniformly without exploiting known information, making it difficult to capture key patterns. Time-based sampling samples items based on the timestamps of interaction, which may overlook long-term or short-term preference. Model-based sampling samples items based on another trained model, which requires additional training resources and lacks supervision signals. All three strategies may disrupt users' original preference evolution when sampling, as the green curves of user preference evolution change in (a), (b), and (c) of Figure 6 of our revision.

• We then conduct experiments to verify the advantages of the TS strategy compared to other sampling strategies. The experimental results are presented in Table R1. The Base represents the diffusion-based recommender without a sampling strategy. The results of random-based are from w/o GL in Table 2 of our original submitted manuscript, which replaces probability models with random sampling. The experimental results indicate that different sampling strategies have a noticeable impact on the diffusion-based recommender compared to the Base approach. However, DreamMiss demonstrates superior performance relative to other sampling strategies, confirming the advantages of DTS.

• Clarification: We propose DTS as a promising solution to address missing data in the diffusion-based sequential recommendation. It offers a simple yet effective implementation of the idea to simulate uncertain missing data while preserving user preferences, thus achieving DDMs' consistency regularization. While DTS offers distinct advantages, we may not claim it to be the best sampling strategy; rather, it is a well-performing strategy compared with other competitive strategies in our task as shown in Table R1.

We will include the motivation for DTS and experimental results in Appendix B.2 and F.5 of our revision.

Dear Reviewer jqjS,

We deeply appreciate your valuable feedback and the time you've taken to review our work with these insights, especially during this busy period.

Regarding your primary concern about the motivation for TS, we have clarified the advantages of TS and compared it with other sampling strategies with experiments. For the point you raised about experiments on larger datasets, we have conducted additional experiments using the Steam dataset, one of the largest datasets commonly utilized in research. We have included these clarifications and experiments in our revision.

We are reaching out to kindly inquire about the current status of your review regarding our response and revision. We sincerely hope that our responses have adequately addressed your concerns. Furthermore, we are eager to address any additional queries you might have, which will enable us to enhance our work further.

Thank you once again for your support and understanding!

Best regards,

Authors