标题： 希尔伯特空间中的学习与推理量子图模型 显示英文标题

标题： Learning and Inference in Hilbert Space with Quantum Graphical Models

摘要： 量子图模型（QGMs）通过采用量子力学中关于不确定性的形式化方法，推广了经典的图模型。 与经典图模型不同，QGMs 使用复数希尔伯特空间中的密度矩阵来表示不确定性。 希尔伯特空间嵌入（HSEs）也推广了希尔伯特空间中的贝叶斯推理。 我们研究 QGMs 与 HSEs 之间的联系，并表明 QGMs 的求和规则和贝叶斯规则分别等价于 HSEs 中的核求和规则和 Nadaraya-Watson 核回归的一个特例。 我们证明这些操作可以进行核化，并利用这些见解提出了一种希尔伯特空间嵌入的隐量子马尔可夫模型（HSE-HQMM），以建模动态过程。 我们展示了实验结果，表明 HSE-HQMM 在多个数据集上与最先进的模型如 LSTMs 和 PSRNNs 相当，同时提供了一种非参数方法，在连续值特征上保持概率分布。 显示英文摘要

摘要： Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian inference in Hilbert spaces. We investigate the link between QGMs and HSEs and show that the sum rule and Bayes rule for QGMs are equivalent to the kernel sum rule in HSEs and a special case of Nadaraya-Watson kernel regression, respectively. We show that these operations can be kernelized, and use these insights to propose a Hilbert Space Embedding of Hidden Quantum Markov Models (HSE-HQMM) to model dynamics. We present experimental results showing that HSE-HQMMs are competitive with state-of-the-art models like LSTMs and PSRNNs on several datasets, while also providing a nonparametric method for maintaining a probability distribution over continuous-valued features.