Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression [1, 2]. The methodologies rely chiefly on the method of maximizing the expected improvement of a score function with respect to adjustments in the hyper-parameters. In this work, we present a novel algorithm that exploits noti...

We present a methodology for generating probabilistic predictions for the Disturbance Storm Time (Dst) geomagnetic activity index. We focus on the One Step Ahead prediction task and use the OMNI hourly resolution data to build our models. Our proposed methodology is based on the technique of Gaussian Process Regression. Within this framework we develop two models; Gaussian Process Autoregressiv...

Classical Volterra and Wiener theory of nonlinear systems does not address the problem of noisy measurements in system identification. This issue is treated in the present part of the report. We first show how to incorporate the implicit estimation technique for Volterra and Wiener series described in Part I into the framework of regularised estimation without giving up the orthogonality proper...

While it is well-known that model can enhance the control performance in terms of precision or energy efficiency, the practical application has often been limited by the complexities of manually obtaining sufficiently accurate models. In the past, learning has proven a viable alternative to using a combination of rigid-body dynamics and handcrafted approximations of nonlinearities. However, a m...

We propose an algorithm that uses Gaussian process regression to learn common hidden structure shared between corresponding sets of heterogenous observations. The observation spaces are linked via a single, reduced-dimensionality latent variable space. We present results from two datasets demonstrating the algorithms’s ability to synthesize novel data from learned correspondences. We first show...

We present a novel marginalized particle Gaussian process (MPGP) regression, which provides a fast, accurate online Bayesian filtering framework to model the latent function. Using a state space model established by the data construction procedure, our MPGP recursively filters out the estimation of hidden function values by a Gaussian mixture. Meanwhile, it provides a new online method for trai...

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any linear, time-varying stochastic differential equation driven by white noise; this allows the possib...

We consider active data selection and test point rejection strategies for Gaussian process regression based on the variance of the posterior over target values. Gaussian process regression is viewed as transductive regression that provides target distributions for given points rather than selecting an explicit regression function. Since not only the posterior mean but also the posterior varianc...

We introduce a nonparametric approach for estimating drift functions in systems of stochastic differential equations from sparse observations of the state vector. Using a Gaussian process prior over the drift as a function of the state vector, we develop an approximate EM algorithm to deal with the unobserved, latent dynamics between observations. The posterior over states is approximated by a ...

We examine the dimensionality of noise-free uplink received signal strength (RSS) data in a distributed multiuser massive multiple-input multiple-output system. Specifically, we apply principal component analysis to the noise-free uplink RSS and observe that it has a low-dimensional principal subspace. We make use of this unique property to propose RecGP a reconstruction-based Gaussian process ...