Gaussian processes are a versatile tool for data processing. Unfortunately, due to storage and runtime requirements, standard Gaussian process (GP) methods are limited to a few thousand data points. Thus, they are infeasible in most biomedical, spatio-temporal problems. The methods treated in this work cover GP inference and hyperparameter optimization, exploiting the Kronecker structure of covariance matrices. To solve regression and source separation problems, two different approaches are

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... ented. The first approach uses efficient matrix-vector-products, whilst the second approach is based on efficient solutions to the eigendecomposition. The latter also enables efficient hyperparameter optimization. In comparison to standard GP methods, the proposed methods can be applied to very large biomedical datasets without any further performance loss and perform substantially faster. The performance is demonstrated on esophageal manometry data, where the cardiac and respiratory signal components are to be inferred by source separation.