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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)
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 eigen-functions 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)
Gaussian process regression is a machine learning paradigm, where the regressor functions are modeled as realizations from an a priori Gaussian process model. We study abstract continuous-space Gaussian regression problems where the training set covers the whole input space instead of consisting of a finite number of distinct points. The model can be used(More)