In this paper, we study a new problem of continuous learning from doubly-streaming data where both data volume and feature space increase over time. We refer to the doubly-streaming data as trapezoidal data streams and the corresponding learning problem as online learning from trapezoidal data streams. The problem is challenging because both data volume and data dimension increase over time, and existing online learning [1] , [2] , online feature selection [3] , and streaming feature selection algorithms [4] , [5] are inapplicable. We propose a new Online Learning with Streaming Features algorithm (OL $_{SF}$ for short) and its two variants, which combine online learning [1] , [2] and streaming feature selection [4] , [5] to enable learning from trapezoidal data streams with infinite training instances and features. When a new training instance carrying new features arrives, a classifier updates the existing features by following the passive-aggressive update rule [2] and updates the new features by following the structural risk minimization principle. Feature sparsity is then introduced by using the projected truncation technique. We derive performance bounds of the OL $_{SF}$ algorithm and its variants. We also conduct experiments on real-world data sets to show the performance of the proposed algorithms.

Heterogeneous graphs are commonly used to describe networked data with multiple types of nodes and edges. Heterogeneous Graph Neural Networks (HGNNs) are powerful tools for analyzing heterogeneous graphs. However, designing neural architectures of HGNNs requires extensive domain knowledge and time-consuming manual work. Recently, neural architecture search algorithms have become popular in automatically designing neural architectures for homogeneous graph neural networks. In this paper, we present a Heterogeneous Graph Neural Architecture Search algorithm (HGNAS for short) which allows the automatic design of heterogeneous graph neural architectures. Specifically, HGNAS first designs a new search space based on existing popular HGNNs. Then, HGNAS uses a policy network as the controller to sample and find the best neural architecture from the designed search space by maximizing the expected accuracy of the selected architectures on a given validation dataset. Moreover, we design a new method HGNAS++ to improve the efficiency of HGNAS by training the RNN controller within a generative adversarial learning framework. The basic idea of HGNAS++ is to embed a pairwise ranker into the reinforcement learning based architecture search algorithm. The pairwise ranker can be taken as a discriminator which selects more accurate architectures between pairs of candidate architectures. Then, the RNN controller can be updated more efficiently by only using a relatively small number of candidate architectures selected by the pairwise ranker. Experiments on real-world heterogeneous graph datasets show that HGNAS is capable of designing novel HGNNs that beat the best human-invented HGNNs. On the benchmark datasets, HGNAS++ improves HGNAS in terms of evaluation cost, with a reduction of 50% of the evaluated candidate architectures and a decrease of 24% in search time on average. As a byproduct, HGNAS++ can find sparse yet powerful neural architectures for HGNNs.

Graph classification plays an important role in a wide range of applications from biological prediction to social analysis. Traditional graph classification models built on graph kernels are hampered by the challenge of poor generalization as they are heavily dependent on the dedicated design of handcrafted features. Recently, graph neural networks (GNNs) become a new class of tools for analyzing graph data and have achieved promising performance. However, it is necessary to collect a large number of labeled graph data for training an accurate GNN, which is often unaffordable in real-world applications. Therefore, it is an open question to build GNNs under the condition of few-shot learning where only a few labeled graphs are available. In this article, we introduce a new Structure-aware Prototypical Neural Process (SPNP for short) for a few-shot graph classification. Specifically, at the encoding stage, SPNP first employs GNNs to capture graph structure information. Then, SPNP incorporates such structural priors into the latent path and the deterministic path for representing stochastic processes. At the decoding stage, SPNP uses a new prototypical decoder to define a metric space where unseen graphs can be predicted effectively. The proposed decoder, which contains a self-attention mechanism to learn the intraclass dependence between graphs, can enhance the class-level representations, especially for new classes. Furthermore, benefited from such a flexible encoding-decoding architecture, SPNP can directly map the context samples to a predictive distribution without any complicated operations used in previous methods. Extensive experiments demonstrate that SPNP achieves consistent and significant improvements over state-of-the-art methods. Further discussions are provided toward model efficiency and more detailed analysis.