Neal, R. M. (1999). Regression and classification using Gaussian process priors (with discussion). In Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., editors, Bayesian Statistics 6, pages 475--501. Oxford University Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... two input relevance estimates (section 3) Note that just for prediction purposes it is not always necessary to make input selection, as the ARD type prior makes it possible to have large number of inputs (see section 3) As illustrative examples, we use MLP networks and Gaussian processes (GP) (Neal, 1996, 1999; Lampinen and Vehtari, 2001) in two real world problems (section 3) The first problem was a concrete quality prediction problem, where the primary goal was to make the models used more explainable, so that the concrete expert could more easily analyse the models. The second problem was a forest ....

Neal, R. M. (1999). Regression and classification using Gaussian process priors (with discussion). In Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., editors, Bayesian Statistics 6, pages 475--501. Oxford University Press.

....distribution in the approach described in this paper and in related approaches where the goal is to compare (not assess) the performance of methods instead of the models. To illustrate the discussion we use MLP networks and Gaussian Processes (GP) with Markov Chain Monte Carlo (MCMC) sampling (Neal, 1996, 1999; Lampinen and Vehtari, 2001) in one toy problem and two real world problems (section 3) We assume that the reader has basic knowledge of Bayesian methods (see, e.g. a short introduction in (Lampinen and Vehtari, 2001) Knowledge of MCMC, MLP or GP methods is helpful but not necessary. 2 ....

Neal, R. M. (1999). Regression and classification using Gaussian process priors (with discussion). In Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., editors, Bayesian Statistics 6, pages 475--501. Oxford University Press.

....like variable dimension MCMC method (Green, 1995; Carlin and Chib, 1995; Stephens, 2000) for model selection and still use the expected utilities for final model assessment. As illustrative examples, we use MLP networks and Gaussian Processes (GP) with Markov Chain Monte Carlo (MCMC) sampling (Neal, 1996, 1999; Lampinen and Vehtari, 2001) in one toy problem and two real world problems (section section 3) We assume that reader has basic knowledge of Bayesian methods (see, e.g. short introduction in (Lampinen and Vehtari, 2001) Knowledge of MCMC, MLP or GP methods is not necessary but helpful. 2 ....

....of the local correlations. The # u parameters are multiplied by the coordinate wise distances in input space and thus allow for different distance measures for each input dimension. We use Inverse Gamma prior on # 2 and hierarchical Inverse Gamma prior (producing ARD like prior) on # u . See (Neal, 1999) and Appendix for the details. The second term is the jitter term, where # ij = 1 when i = j .It is used to improve matrix computations by adding constant term to residual model. The third term is the residual model. Specific residual models are mentioned in each case example. See (Neal, 1999) ....

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Neal, R. M. (1999). Regression and classification using Gaussian process priors (with discussion). In Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., editors, Bayesian Statistics 6, pages 475--501. Oxford University Press.

....learning is to use labeled data to train a recognition model to accurately predict class membership from the input. This supervised learning approach includes nonlinear regression techniques such as classification and regression trees [11] neural networks [12 14] Gaussian process regression [15], support vector classifiers [16] and nearest neighborhood type methods, including eigen space methods that compute distances within subspaces [17, 18] In contrast, the approach we take here is to use unlabeled data to train a probability density model of the data (or generative model) in ....

R. M. Neal, "Regression and classification using gaussian process priors," in Bayesian Statistics 6, J. M. Bernardo et al., Ed., pp. 475--501. Oxford University Press, 1998.

....idea about the value of j( in the vicinity of x: A means of describing our uncertainty about a function j( is needed, and we model j( as a Gaussian process. This is an idea that has been used in several applications. Examples of Gaussian processes in regression include O Hagan (1978) and Neal (1999). Neal (1999) also considers the use of Gaussian processes in classification problems. O Hagan (1991) models a computationally expensive function as a Gaussian process in order to make inferences about its integral. For any set of points x 1 , x n ; we represent our uncertainty about j(x 1 ....

....the value of j( in the vicinity of x: A means of describing our uncertainty about a function j( is needed, and we model j( as a Gaussian process. This is an idea that has been used in several applications. Examples of Gaussian processes in regression include O Hagan (1978) and Neal (1999) Neal (1999) also considers the use of Gaussian processes in classification problems. O Hagan (1991) models a computationally expensive function as a Gaussian process in order to make inferences about its integral. For any set of points x 1 , x n ; we represent our uncertainty about j(x 1 ) j(x ....

Neal, R. (1999). Regression and classification using gaussian process priors, in Bayesian Statistics 6 , edited by Bernardo, J. M., Berger, J. O., Dawid, A. P.

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Neal, R. M. (1998). Regression and Classification Using Gaussian Process Priors. In: Bayesian Statistics 6, (J. M. Bernardo, J. O. Berger, A. P. Dawid and A.F.M. Smith, eds.), Oxford: University Press, To appear.

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