Sum-product network (SPN) is a deep probabilistic representation that allows for exact and tractable inference. There has been a trend of online SPN structure learning from massive and continuous data streams. However, online structure learning of SPNs has been introduced only for the generative settings so far. In this paper, we present an online discriminative approach for SPNs for learning both the structure and parameters. The basic idea is to keep track of informative and representative examples to capture the trend of time-changing class distributions. Specifically, by estimating the goodness of model fitting of data points and dynamically maintaining a certain amount of informative examples over time, we generate new sub-SPNs in a recursive and top-down manner. Meanwhile, an outlier-robust margin-based log-likelihood loss is applied locally to each data point and the parameters of SPN are updated continuously using most probable explanation (MPE) inference. This leads to a fast yet powerful optimization procedure and improved discrimination capability between the genuine class and rival classes. Empirical results show that the proposed approach achieves better prediction performance than the state-of-the-art online structure learner for SPNs, while promising order-of-magnitude speedup. Comparison with state-of-the-art stream classifiers further proves the superiority of our approach.

中文翻译：

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用于数据流分类的求和网络的判别结构学习。

和积网络（SPN）是一种深度的概率表示形式，可以进行精确且易于处理的推断。从大量和连续的数据流中学习在线SPN结构的趋势已经出现。但是，到目前为止，仅针对生成环境引入了SPN的在线结构学习。在本文中，我们提出了一种针对SPN的在线判别方法，用于学习结构和参数。基本思想是跟踪内容丰富且具有代表性的示例，以捕获随时间变化的班级分布趋势。具体来说，通过估计数据点模型拟合的优劣并随着时间动态地维护一定数量的信息示例，我们以递归和自上而下的方式生成新的子SPN。同时，将基于异常稳健的基于余量的对数似然损失局部应用于每个数据点，并使用最可能的解释（MPE）推理连续更新SPN的参数。这导致了快速而强大的优化过程，并提高了真品级和竞争对手级之间的区分能力。实验结果表明，与SPNs的最新在线结构学习器相比，所提出的方法具有更好的预测性能，同时有望实现数量级的加速。与最新的流分类器的比较进一步证明了我们方法的优越性。这导致了快速而强大的优化过程，并提高了真品级和竞争对手级之间的区分能力。实验结果表明，与SPNs的最新在线结构学习器相比，所提出的方法具有更好的预测性能，同时有望实现数量级的加速。与最新的流分类器的比较进一步证明了我们方法的优越性。这导致了快速而强大的优化过程，并提高了真品级和竞争对手级之间的区分能力。实验结果表明，与SPNs的最新在线结构学习器相比，所提出的方法具有更好的预测性能，同时有望实现数量级的加速。与最新的流分类器的比较进一步证明了我们方法的优越性。