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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 subspace 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 capacityas 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 substantiate the viability and effectiveness of our proposed approach.

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.

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.