Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The work aims to solve the problem of forecasting for incomplete highly-dynamic time-series data with evolving seasonal patterns (regimes). It uses clever techniques to detect whether seasonal shift occurred in new data and updates the model with the corresponding new regime if necessary. Model training is performed in an online fashion over a data stream and is based on an incremental matrix factorization with adaptive selection of the most appropriate regime. It utilizes minimum description length principle for the task. The authors provide a straightforward learning scheme and demonstrate advantages of the proposed approach on several realistic datasets.
main_review: *Originality*:  
The authors make a good work on positioning their approach among other works and describing the essential differences. The idea of adaptive regimes update/selection is both interesting and novel. The way the task of regime selection is solved with the MDL principle seems to be very appropriate. 

*Quality*:  
The proposed approach is clearly described and the all necessary part for its (re)implementation seem to be in place. Both time and space complexities are provided. The scalability analysis performed by the authors is convincing. However, there are a few issues.

Section 3.2, equation between line 135 and 135: the formulation is based on the number of non-zero elements, which, I believe, implicitly assumes sparse matrices/tensors (with non-negative elements). However, eq. (4) seems to be free of such assumptions. Isn't there a contradiction? If there are additional assumptions on relaxation of any constraints, it would be good to have them explicitly described. Otherwise, the choice of a distribution should be different.

Section 5.1, line 232: I'm not convinced that fixing the same number of components ensures fair comparison. Different methods are likely to require different values of k for achieving the best quality. If there are certain memory constraints, the number of components must be selected w.r.t. the space complexity of each method. If there are any technical limitations for this, then at least he trendline for different k should be demonstrated.

*Clarity*:  
Section 2.1 is named *Matrix Factorization*, but talks a lot about tensor factorization as well, which add to the impression of text inconsistency. The authors mix together these terms.
Moreover, the term SVD is used quite broadly in the text (e.g., line 62). However, it is related to a very specific matrix decomposition method. The authors are probably influenced by the recommender systems literature, with many matrix factorization techniques carrying SVD in their names (e.g., FunkSVD, SVD++, AsySVD, etc.). I'd argue against such terminology as, in general, matrix factorization methods do not provide the same set of algebraic properties as in the case of SVD.

In Section 2.2, line 80, what does the term *non-linear dynamical system* refer to? It is not clear, why this term is used to contrast other approaches against the proposed one. I couldn't find any clarification on that further in the text.

In Section 3, Table 2 is not very helpful and creates a lot of whitespace. It is also excessive. The first two rows are describing the same object X(t). It would be probably better to just introduce proper notation directly in the text.

*Significance*:  
The proposed approach open many perspective for further improvements and modifications. Given its relative simplicity, it may become a source for fruitful future research.

*Minor issues*:  
- line 98: "and r evolves" -> "as r evolves" ? The notation with r = r + 1 is also a bit cumbersome.
- line 51: The link to Dropbox should be explicit, e.g., via footnote.
- line 35: unless we talk about very special cases, they almost never converge to optimal parameters and are likely to find only a local optimum. I'd propose to rephrase the sentence. Probably, it's just enough to leave the second part saying about the lower accuracy.
- line 137: compress -> compresses
- line 134: provide -> provided
limitations_and_societal_impact: I believe that the work doesn't possess any components that may directly lead to negative societal impacts.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This paper studies online tensor factorization for real-time event forecasting with seasonality. The key to solve the event forecasting problem here is to detect the seasonal pattern shift and adapt to the shift for an accurate  event forecasting. The closest related work is SMF [Hooi et al., 2019], which is an online forecasting model based on matrix factorization and taking as well seasonal patterns into account. SMF differs from the proposed SSMF by considering only a single seasonal factor, whereas SSMF model seasonal shifts (regimes) individually.


main_review: The designed regime selection and extraction mechanism enables the prediction model to have stronger adaptability to the seasonal shifts. The experimental results show that the proposed SSMF model outperforms all baselines. An interesting demonstration example is also provided to demonstrate the capability of SSMF on automatically detecting regime shifts caused by a pandemic.   In general, this work is a valuable contribution to the field of event forecasting. 

Authors are suggested to carefully check the writing errors: “how well a given model compress ” and “a x” and so on.

limitations_and_societal_impact: Not applicable
review_title: null

final_score: rating: 5: Marginally below the acceptance threshold
review_content: summary: This paper aims to solve the problem of forecasting future events given a data stream of events. In order to achieve this, the authors propose a method called Shifting Seasonal Matrix Factorization, which can detect the regime shifts in seasonal patterns, and work in online settings. The authors claimed that, the advantages of the proposed method over previous methods are its capability to dealing with sparse data, regime shifts, seasonal patterns, and drifting components. 

The authors conduct experiments on three datasets, NYC-YT, NYC-CB and DISEASE. All the methods are compared in their capability of predicting the events. The authors also show a case study in NYC to show the results of detected events.
main_review: Strength:
1. The authors are working on an interesting problem. Considering data sparsity, seasonality and drifting is an interesting and important problem in the matrix factorization problem. 
2. The description of the method is clear and easy to follow. Readers can easily understand the algorithm through the descriptions in Section 3 and 4.
3. The source code is provided, which can be used for replicating the results.

Weakness:
1. The compared methods are not comprehensive enough and out-of-dated. The authors have mentioned several more advanced baselines in the related work section, e.g., [Takahashi et al., 2017], [Song et al., 2017], [Najafi et al., 2019]. It is not clear why these methods are not compared. In addition, the investigated problem is also highly related to time series prediction. It is not clear why these methods are not compared.

2. The illustration of the case study is not straightforward. For the maps, the authors may consider zooming in and showing more cases. The current examples can only show the changes around JFK area. The authors may also adjust the axis of the time series to better illustrate the change in volume.

3. The authors claim the capability of dealing with data sparsity. Hence, it is preferred if some experiments can be conducted on dealing with different sparse levels.
limitations_and_societal_impact: No separate Limitations and Societal Impact part is provided.

The authors may consider how these event predictions can help with dealing with traffic congestion, reducing the time that people need to get a taxi, or pandemic intervention.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The authors develop a new online tensor factorization method for real-time forecasting. The propose approach is designed for dealing with seasonality patterns and automatically switch between different regimes. The authors have shown this method achieves better accuracy compared to existing methods in forecasting taxi/bike rides and infections. The method has shown to be scalable in terms of its memory and test costs. 
main_review: Overall, I think this is a well-organized paper and the content is solid. I just have a few comments
1. The seasonality patterns are important for many real-world applications, especially in climate and environment modeling. It would be better if the authors could discuss how easy this proposed algorithm can be generally applied to other applications. 
2. The proposed method is shown to outperform several MF-based baselines. I am wondering if the authors can also compare it with deep learning-based algorithms. 
3. In many real-world scenarios, we may have access to when the regime shift occurs (e.g., based on seasonality, human interventions, or other separate analysis). Would the proposed method be able to leverage such information? Also, if we have already known such time partitions, would the proposed method outperform other algorithms, e.g., domain-adaptation?

limitations_and_societal_impact: The authors have proposed a general matrix factorization method that can automatically identify and switch between different regimes. This is an important property for many time series data sets.
review_title: null

Meta-review: The paper studies forecasting of seasonally varying time series using matrix factorisation of a shifting tensor stream. The proposed algorithm, SSMF, makes forecasts by identifying the current regime and applying the corresponding sub-model. SSMF is analysed with respect to time and memory complexity per time point. The approach is evaluated with respect to scalability and real-world effectiveness in a series of empirical experiments. 

The reviwers appreciated the novelty of the formulation and the importance of the problem. They deemed the paper well written and the results sound. Some concerns were raised regarding the clarity of the paper which were addressed in the author response. Finally, two reviewers asked for comparisons with additional baselines, but I understand the choice to focus on matrix factorisation methods in this setting. Overall, most of the reviewers were in favour of accepting the paper and no major issues remained after the discussion phase.
Decision: Accept (Poster)