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Gaussian process-based machine learning is a powerful Bayesian paradigm for nonparametric nonlinear regression and classification. In this article, we discuss connections of Gaussian process regression with Kalman filtering and present methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models.(More)
In this article we introduce the DRIFTER algorithm, which is a new model based Bayesian method for retrospective elimination of physiological noise from functional magnetic resonance imaging (fMRI) data. In the method, we first estimate the frequency trajectories of the physiological signals with the interacting multiple models (IMM) filter algorithm. The(More)
This paper shows how periodic covariance functions in Gaussian process regression can be reformulated as state space models, which can be solved with classical Kalman filtering theory. This reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The representation is based on expanding(More)
This paper is concerned with application of cubature integration methods to Kalman filtering of discretely observed non-linear stochastic continuous-time systems. We compare two recently proposed variants of the continuous-discrete cubature Kalman filter (CD-CKF), which differ in the order how the discretization and the Gaussian approximation are done.(More)
This paper introduces a spatiotemporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatiotemporal data. The model is derived as a spatial extension of a stochastic harmonic resonator model, which can be formulated in terms of a stochastic differential equation. The spatial structure is(More)
The goal of the MLSP 2014 Schizophrenia Classification Challenge was to automatically diagnose subjects with schizophrenia based on multimodal features derived from their magnetic resonance imaging (MRI) brain scans. This challenge took place between June 5 and July 20, 2014, and was organized on Kaggle. We present how this classification problem can be(More)
Administration of opioid peptides dynorphin A (1-13) and DSLET was followed by a decrease in the stress-induced activation of LPO and increase in SOD activity in the liver tissue of rats. DAGO produced a similar, but less pronounced effect. The observed changes can be related to a specific distribution of opioid receptors in the liver tissue and(More)
Experiments on rats showed that restraint stress is associated with an increase in plasma level of nonesterified fatty acids, total cholesterol, triglycerides, VLDL, and LDL. Administration of opioid peptides DSLET and DAGO alleviated stress-induced shifts in lipid metabolism. The concentrations of nonesterified fatty acids, total cholesterol, and(More)
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure.(More)
We consider parameter estimation in non-linear state space models by using expectation-maximization based numerical approximations to likelihood maximization. We present a unified view of approximative EM algorithms that use either sigma-point or particle smoothers to evaluate the integrals involved in the expectation step of the EM method, and compare(More)