In this paper, we explore a novel online learning setting, where the online learners are presented with “doubly-streaming” data. Namely, the data instances constantly streaming in are described by feature spaces that over-time evolve, with new features emerging and old features fading away. The main challenge of this problem lies in the fact that the newly emerging features are described by very few samples, resulting in weak learners that tend to make error predictions. A seemingly plausible idea to overcome the challenge is to establish a relationship between the old and new feature spaces, so that an online learner can leverage the knowledge learned from the old features to better the learning performance on the new features. Unfortunately, this idea does not scale up to high-dimensional feature spaces that entail very complex feature interplay. Specifically. a tradeoff between onlineness, which biases shallow learners, and expressiveness, which requires deep models, is inevitable. Motivated by this, we propose a novel paradigm, named Online Learning Deep models from Data of Double Streams (OLD3S), where a shared latent supspace is discovered to summarize information from the old and new feature spaces, building an intermediate feature mapping relationship. A key trait of OLD3S is to treat the model capacity as a learnable semantics, aiming to yield optimal model depth and parameters jointly in accordance with the complexity and non-linearity of the input data streams in an online fashion. To ablate its efficacy and applicability, two variants of OLD3S are proposed namely, OLD-Linear that learns the relationship by a linear function; and OLD-FD learns that two consecutive feature spaces pre-and-post evolution with fixed deep depth. Besides, instead of re-starting the entire learning process from scratch, OLD3S learns multiple newly emerging feature spaces in a lifelong manner, retaining the knowledge from the learned and vanished feature space to enjoy a jump-start of the new features' learning process. Both theoretical analysis and empirical studies supstantiate the viability and effectiveness of our proposed approach. The code is available online atgithub.com/X1aoLian/OLD3S-L.

Learning with feature evolution studies the scenario where the features of the data streams can evolve, i.e., old features vanish and new features emerge. Its goal is to keep the model always performing well even when the features happen to evolve. To tackle this problem, canonical methods assume that the old features will vanish simultaneously and the new features themselves will emerge simultaneously as well. They also assume that there is an overlapping period where old and new features both exist when the feature space starts to change. However, in reality, the feature evolution could be unpredictable, which means that the features can vanish or emerge arbitrarily, causing the overlapping period incomplete. In this article, we propose a novel paradigm: prediction with unpredictable feature evolution (PUFE) where the feature evolution is unpredictable. To address this problem, we fill the incomplete overlapping period and formulate it as a new matrix completion problem. We give a theoretical bound on the least number of observed entries to make the overlapping period intact. With this intact overlapping period, we leverage an ensemble method to take the advantage of both the old and new feature spaces without manually deciding which base models should be incorporated. Theoretical and experimental results validate that our method can always follow the best base models and, thus, realize the goal of learning with feature evolution.

Feature evolvable learning has been widely studied in recent years where old features will vanish and new features will emerge when learning with streams. Conventional methods usually assume that a label will be revealed after prediction at each time step. However, in practice, this assumption may not hold whereas no label will be given at most time steps. A good solution is to leverage the technique of manifold regularization to utilize the previous similar data to assist the refinement of the online model. Nevertheless, this approach needs to store all previous data which is impossible in learning with streams that arrive sequentially in large volume. Thus we need a buffer to store part of them. Considering that different devices may have different storage budgets, the learning approaches should be flexible subject to the storage budget limit. In this paper, we propose a new setting: Storage-Fit Feature-Evolvable streaming Learning (SF2EL) which incorporates the issue of rarely-provided labels into feature evolution. Our framework is able to fit its behavior for different storage budgets when learning with feature evolvable streams with unlabeled data. Besides, both theoretical and empirical results validate that our approach can preserve the merit of the original feature evolvable learning i.e., can always track the best baseline and thus perform well at any time step.

This paper explores a new online learning problem where the data streams are generated from an over-time varying feature space, in which the random variables are of mixed data types including Boolean, ordinal, and continuous. The crux of this setting lies in how to establish the relationship among features, such that the learner can enjoy 1) reconstructed information of the missed-out old features and 2) a jump-start of learning new features with educated weight initialization. Unfortunately, existing methods mainly assume a linear mapping relationship among features or that the multivariate joint distribution could be modeled as Gaussians, limiting their applicability to the mixed data streams. To fill the gap, we in this paper propose to model the complex joint distribution underlying mixed data with Gaussian copula, where the observed features with arbitrary marginals are mapped onto a latent normal space. The feature correlation is approximated in the latent space through an online EM process. Two base learners trained on the observed and latent features are ensembled to expedite convergence, thereby minimizing prediction risk in an online setting. Theoretical and empirical studies substantiate the effectiveness of our proposed approach. Code is released in https://github.com/xiexvying/OVFM.

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 limited-lifespan sensors will change when these sensors are substituted by new ones. In this article, 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 a mapping from the overlapping period to recover old features and then 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 and we provide a tighter bound when the loss function is exponentially concave. 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.

The interpretability of deep learning models has raised extended attention these years. It will be beneficial if we can learn an interpretable structure from deep learning models. In this article, we focus on recurrent neural networks (RNNs), especially gated RNNs whose inner mechanism is still not clearly understood. We find that finite-state automaton (FSA) that processes sequential data have a more interpretable inner mechanism according to the definition of interpretability and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. With the learned FSA and via experiments on artificial and real data sets, we find that FSA is more trustable than the RNN from which it learned, which gives FSA a chance to substitute RNNs in applications involving humans' lives or dangerous facilities. Besides, we analyze how the number of gates affects the performance of RNN. Our result suggests that gate in RNN is important but the less the better, which could be a guidance to design other RNNs. Finally, we observe that the FSA learned from RNN gives semantic aggregated states, and its transition graph shows us a very interesting vision of how RNNs intrinsically handle text classification tasks.

By using abundant unlabeled data, semi-supervised learning approaches have been found very useful in various tasks. Existing approaches, however, neglect the fact that the storage available for the learning process is different under different situations, and thus, the learning approaches should be flexible subject to the storage budget limit. In this paper, we focus on graph-based semi-supervised learning and propose two storage fit learning approaches which can adjust their behaviors to different storage budgets. Specifically, we utilize techniques of low-rank matrix approximation to find a low-rank approximator of the similarity matrix so as to reduce the space complexity. The first approach is based on stochastic optimization, which is an iterative approach that converges to the optimal low-rank approximator globally. The second approach is based on Nystrom method, which can find a good low-rank approximator efficiently and is suitable for real-time applications. Experiments on classification tasks show that the proposed methods can fit dynamically different storage budgets and obtain good performances in different scenarios.

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 limited lifespan 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.