Learning with Feature Evolvable Streams
Learning with streaming data has attracted much attention during the past few years. Though most studies consider data stream with fixed features, in real practice the features may be evolvable. For example, features of data gathered by limitedlifespan sensors will change when these sensors are substituted by new ones. In this paper, we propose a novel learning paradigm: Feature Evolvable Streaming Learning where old features would vanish and new features would occur. Rather than relying on only the current features, we attempt to recover the vanished features and exploit it to improve performance. Specifically, we learn two models from the recovered features and the current features, respectively. To benefit from the recovered features, we develop two ensemble methods. In the first method, we combine the predictions from two models and theoretically show that with the assistance of old features, the performance on new features can be improved. In the second approach, we dynamically select the best single prediction and establish a better performance guarantee when the best model switches. Experiments on both synthetic and real data validate the effectiveness of our proposal.
This paper presents two new methods for learning with streaming data under the assumption that feature spaces may evolve so old features vanish and new features occur. Examples of this scenario are environmental monitoring sensors or RFIDs for moving goods detection. Two different approaches are proposed, both based on the combination of two models: one trained with the old features and the other one based on the new features. Depending on how these models are combined, the authors propose two different methods for Feature Evolvable Streaming Learning (FESL): FESL-c that combines the predictions of both models, and FESL-s that selects the best model each time. Theoretical bounds on the cumulative loss of the both FESL methods as a function of the cumulative loss of the two models trained over different feature spaces are also provided. Experiments on datasets from the UCI Machine Learning Repository, Reuter’s data, and RFID real data have been conducted, and results show that the proposed models are able to provide competitive results in all cases when compared to three baseline methods.
Overall, I think this is a very interesting paper that addresses a real-world problem that is quite common, for example, in environmental sensoring applications. I think that the paper is well-written and well-organized, and the experiments show the significance of the proposed methodology. Additionally, I positively value the use of RFID real data. 
* Contribution with respect to transfer learning. My main concern is about the quantification of the degree of contribution of this work, as I cannot see clearly the difference what is the difference between the proposed approach and the use of transfer learning in two different feature sets (of course, taking into account that transfer learning cannot be applied from t=1,…, T1-B). I would like the authors to clarify this point. 
* Theorems 1 and 2. I would also like the authors to discuss about the practical implications of Theorem 1 and Theorem 2, as in both cases convergence to 0 is obtained when T2 is large enough but that is not the case in Figures 1 and 2. Additionally, it seems to me that although the upper bound for FESL-s algorithm is tighter than for the FESL-c method, the convergence is slower. Please, clarify this point.
* Optimal value for s. I do not understand why there is an inequality in Equation 9 instead of an equality according to the assumptions made (the first model is better than the second one for t smaller than s, and the second model is better than the first one for t larger than s). In this regard, I can see in Figure 3 that this assumption holds in practice, but the value for s depends on the problem you are working on. Providing some intuition about the range of values for s would be valuable.
* Datasets and experimental setup. I have some questions:
  - I would like the authors to clarify why the Gaussian noise was added to the UCI datasets instead of considering two different subsets of features. I guess that this is because it is assumed that the features spaces are not so different, but I would like the authors to discuss this point.
  - Please, provide more details about how batch datasets was transformed into streaming data. I suppose it was done randomly, but then I am wondering whether results on 10 independent rounds are enough to have reliable results and I would like to see the variability of the results provided in terms of the cumulative loss.
  - It is not clear to me how the hyperparameters of the methods (delta and eta) were adjusted. Were they set according to Theorems 1 and 2? What about the hyperparameters in the baseline methods?
  - I do not understand the sentence (page 7): “So for all baseline methods and our methods, we use the same parameters and the comparison is fair”.
* Results. It would be desirable to provide similar tables to Table 1 for the Reuter’s and RFID data.