Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations

Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector $\boldsymbol x = (x_1,\dots,x_d)$ such that for each node $v$ in a social network, $v$ could be activated as a seed of diffusion with probability $h_v(\boldsymbol x)$, where $h_v$ is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix $\boldsymbol x$ with constraint $\sum_i x_i \le k$ where $k$ is a budget constraint, such that the total number of activated nodes after the diffusion process, called influence spread and denoted as $g(\boldsymbol x)$, is maximized. In this paper, we extend CIM to consider budget saving, that is, each strategy mix $\boldsymbol x$ has a cost $c(\boldsymbol x)$ where $c$ is a convex cost function, we want to maximize the balanced sum $g(\boldsymbol x) + \lambda(k - c(\boldsymbol x))$ where $\lambda$ is a balance parameter, subject to the constraint of $c(\boldsymbol x) \le k$. We denote this problem as CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular or concave, and thus neither the greedy algorithm nor the standard result on gradient method could be directly applied. Our key innovation is the combination of the gradient method with reverse influence sampling to design algorithms that solve CIM-BS: For the general case, we give an algorithm that achieves $\left(\frac{1}{2}-\varepsilon\right)$-approximation, and for the case of independent strategy activations, we present an algorithm that achieves $\left(1-\frac{1}{e}-\varepsilon\right)$ approximation.Comment: To appear in AAAI-20, 43 page

Learning Graph Convolutional Network for Skeleton-based Human Action Recognition by Neural Searching

Human action recognition from skeleton data, fueled by the Graph Convolutional Network (GCN), has attracted lots of attention, due to its powerful capability of modeling non-Euclidean structure data. However, many existing GCN methods provide a pre-defined graph and fix it through the entire network, which can loss implicit joint correlations. Besides, the mainstream spectral GCN is approximated by one-order hop, thus higher-order connections are not well involved. Therefore, huge efforts are required to explore a better GCN architecture. To address these problems, we turn to Neural Architecture Search (NAS) and propose the first automatically designed GCN for skeleton-based action recognition. Specifically, we enrich the search space by providing multiple dynamic graph modules after fully exploring the spatial-temporal correlations between nodes. Besides, we introduce multiple-hop modules and expect to break the limitation of representational capacity caused by one-order approximation. Moreover, a sampling- and memory-efficient evolution strategy is proposed to search an optimal architecture for this task. The resulted architecture proves the effectiveness of the higher-order approximation and the dynamic graph modeling mechanism with temporal interactions, which is barely discussed before. To evaluate the performance of the searched model, we conduct extensive experiments on two very large scaled datasets and the results show that our model gets the state-of-the-art results.Comment: Accepted by AAAI202