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

The paper develops a connection between quantum graphical models and inference with Hilbert space embeddings (HSE). It shows kernel formulations for sum rule and Bayes rule with quantum graphical models, connecting kernel mean embeddings as well as cross-covariance operators. The paper proposes to use HSE on top of HQMMs, arguing that it improves empirical performance against PSRNN and LSTMs. The paper is nicely written and does a very good job at explaining difficult quantum concepts using tools that should be familiar to a machine learning audience. I personally really enjoyed reading and learning about the connections developed in the paper.