Bayesian updating normal distribution

We discuss different modeling choices and a selected number of important algorithms.The algorithms include optimization-based smoothing and filtering as well as computationally cheaper extended Kalman filter and complementary filter implementations.The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive.This paper develops a new principled framework for deploying Gaussian process probabilistic models in the streaming setting, providing principled methods for learning hyperparameters and optimising pseudo-input locations.

The result clearly shows that the IMEKF and the NLS-based method are superior to q-IEKF and all three outperform the non-iterative methods.Third, we show that the posterior distribution in these models is a m Gv M distribution which enables development of an efficient variational free-energy scheme for performing approximate inference and approximate maximum-likelihood learning. Consequently, a wealth of GP approximation schemes have been developed over the last 15 years to address these key limitations.Many of these schemes employ a small set of pseudo data points to summarise the actual data.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.

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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.

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