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Krzysztof Choromanski, Mark Rowland, and Adrian Weller.The unreasonable effectiveness of structured random orthogonal embeddings. Abstract: We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation.First we introduce a new multivariate distribution over circular variables, called the multivariate Generalised von Mises (m Gv M) distribution.
Second, we introduce a new probabilistic model for circular regression, that is inspired by Gaussian Processes, and a method for probabilistic principal component analysis with circular hidden variables.These models can leverage standard modelling tools (e.g. A unifying framework for Gaussian process pseudo-point approximations using power expectation propagation. Abstract: Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way.covariance functions and methods for automatic relevance determination). Although elegant, the application of GPs is limited by computational and analytical intractabilities that arise when data are sufficiently numerous or when employing non-Gaussian models.Abstract: Sparse approximations for Gaussian process models provide a suite of methods that enable these models to be deployed in large data regime and enable analytic intractabilities to be sidestepped.However, the field lacks a principled method to handle streaming data in which the posterior distribution over function values and the hyperparameters are updated in an online fashion.
In this way all of the approximation is performed at `inference time' rather than at `modelling time', resolving awkward philosophical and empirical questions that trouble previous approaches. Inertial sensor measurements are obtained at high sampling rates and can be integrated to obtain position and orientation information.