Williams, C. K. I. (2002) Gaussian Processes To appear in The handbook of Brain Theory and Neural Networks, Second edition MIT Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....alternative solution is presented for iterative k step ahead prediction, with propagation of the prediction uncertainty. 2 Gaussian Process modelling We briefly recall some fundamentals of Gaussian processes. For a comprehensive introduction, please refer to [5] 11] or the more recent review [12]. 2.1 The GP prior model Formally, the random function, or stochastic process, f(x) is a Gaussian process, with mean m(x) and covariance function C(x ) if its values at a finite number of points, are seen as the components of a normally distributed random vector. If we further ....

.... T : 9) The detailed calculations can be found in [2] In [8] we derived the exact expressions of the first and second moments. Rewriting the predictive mean (x ) as a linear combination of the covariance between the new x and the training points (as suggested in [12]) with our choice of covariance function, the calculation of m(x ) then involves the product of two Gaussian functions: x ) j j ; x j )p(x (10) with = K y. This leads to (refer to [9] for details) m( x ; x ) q (11) with q i = jW ( ....

Williams, C. K. I. (2002) Gaussian Processes To appear in The handbook of Brain Theory and Neural Networks, Second edition MIT Press.

....solution is presented for iterative k step ahead prediction, with propagation of the prediction uncertainty. 2 Predicting with Gaussian processes We briefly recall some fundamentals of Gaussian processes. For a comprehensive introduction, please refer to [3] 7] or the more recent review [8]. 2.1 The GP prior model A formal definition of a Gaussian process is that of a random function f(x) with mean m(x) and covariance function C(x ) if its values f(x ) can be seen as the components of a normally distributed random vector. Here, we assume that the process is ....

Williams, C. K. I. (2002) Gaussian Processes To appear in The handbook of Brain Theory and Neural Networks, Second edition MIT Press.

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Williams, C. K. I. (2002) Gaussian Processes To appear in The handbook of Brain Theory and Neural Networks, Second edition MIT Press.

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