A sum-product network (SPN) is a graphical model that allows several types of probabilistic inference to be performed efficiently. In this paper, we propose a privacy-preserving protocol which tackles structure generation and parameter learning of SPNs. Additionally, we provide a protocol for private inference on SPNs, subsequent to training. To preserve the privacy of the participants, we derive our protocol based on secret sharing, which guarantees privacy in the honest-but-curious setting even when at most half of the parties cooperate to disclose the data. The protocol makes use of a forest of randomly generated SPNs, which is trained and weighted privately and can then be used for private inference on data points. Our experiments indicate that preserving the privacy of all participants does not decrease log-likelihood performance on both homogeneously and heterogeneously partitioned data. We furthermore show that our protocol's performance is comparable to current state-of-the-art SPN learners in homogeneously partitioned data settings. In terms of runtime and memory usage, we demonstrate that our implementation scales well when increasing the number of parties, comparing favorably to protocols for neural networks, when they are trained to reproduce the input-output behavior of SPNs.

翻译：和积网络（SPN）是一种图模型，能够高效执行多种类型的概率推理。本文提出一种隐私保护协议，用于处理SPN的结构生成与参数学习问题。此外，我们还提供了训练完成后在SPN上进行隐私推理的协议。为保护参与方的隐私，我们基于秘密共享技术构建协议，该协议在诚实但好奇的安全模型下能保证隐私安全，即使最多有半数的参与方合谋试图泄露数据。该协议利用随机生成的SPN森林，通过隐私保护方式进行训练和加权，随后可用于数据点的隐私推理。实验结果表明，在保持所有参与方隐私的前提下，该协议在均匀分区和非均匀分区数据上的对数似然性能均未下降。我们进一步证明，在均匀分区数据场景中，本协议的性能与当前最先进的SPN学习器相当。在运行时间和内存消耗方面，我们验证了当参与方数量增加时，本实现方案具有良好的可扩展性；相较于通过训练神经网络来复现SPN输入输出行为的协议，本方案展现出明显优势。