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Learning and Inference in Hilbert Space with Quantum Graphical Models
Siddarth Srinivasan · Carlton Downey · Byron Boots

Thu Dec 06 07:45 AM -- 09:45 AM (PST) @ Room 210 #20

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.

Author Information

Siddarth Srinivasan (Georgia Institute of Technology)
Carlton Downey (Carnegie Mellon University)
Byron Boots (Georgia Tech / Google Brain)

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