L. Csat o and M. Opper. Sparse online Gaussian processes. Neural Computation, 14:641--668, 2002. Home/Search Document Not in Database Summary Related Articles Check |
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Fast Sparse Gaussian Process Methods: The Informative.. - Lawrence, Seeger.. (2003) (6 citations) (Correct)
....case running time between O(n ) and O(n d) with memory requirements significantly less than n . Note, however, that without any restrictions on the data distribution, d can rise to n. In an e#ort to overcome scaling problems a range of sparse GP approximations have been proposed [1, 8, 9, 10, 11]. However, none of these has fully achieved the goals of being a nontrivial approximation to a non sparse GP model and matching the SVM w.r.t. both prediction performance and run time. The algorithm proposed here accomplishes these objectives and, as our experiments show, can even be significantly ....
.... posterior ) u, S) for some non training point x is identical to the conditional prior ) u) In general, computing Q is also infeasible, but several authors have proposed to approximate the global moment matching by iterative schemes which locally focus on one training pattern at a time [1, 4]. These schemes (at least in their simplest forms) result in a parametric form for the approximating Gaussian Q(u) i=1 exp p i (u i m i ) 1) This may be compared with the form of the true posterior P (u S) i=1 P (y i i ) and shows that Q(u) is obtained from P (u S) by a ....
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Lehel Csato and Manfred Opper. Sparse online Gaussian processes. N. Comp., 14:641-- 668, 2002.
Transductive and Inductive Methods for Approximate Gaussian.. - Schwaighofer (2002) (1 citation) (Correct)
....while keeping the total number of basis functions B minimal. As for the case of SGMA, this algorithm can be formulated such that its asymptotic computational complexity is O(NB ) where B is the total number of basis functions selected. 2. 3 Online Gaussian Processes Csat o and Opper [2] present an online learning scheme that focuses on a sparse model of the posterior process that arises from combining a Gaussian process prior with a general This method was not developed particularly for GPR, yet we expect this basis selection scheme to be superior to a purely random choice. ....
Csat o, L. and Opper, M. Sparse online gaussian processes. Neural Computation, 14(3):641-- 668, 2002.
Fast Sparse Gaussian Process Methods: The Informative.. - Lawrence, Seeger.. (2003) (1 citation) (Correct)
....the active set size d is much smaller than n, an SVM classi er can be trained in average case running time between O(n d ) and O(n d) with memory requirements signi cantly less than . In an e ort to overcome scaling problems a range of sparse GP approximations have been proposed [8, 11, 1, 10, 9]. However, none of these has fully achieved the goals of being a nontrivial approximation to a non sparse GP model and matching the SVM w.r.t. both prediction performance and resource requirements. The method proposed here accomplishes these objectives and, as our experiments show, can even be ....
.... P (u(x )ju; S) for some non training point x is identical to the conditional prior P (u(x )ju) In general, computing Q is also infeasible, but several authors have proposed to approximate the global moment matching by iterative schemes which locally focus on one training pattern at a time [1, 5]. These schemes (at least in their simplest forms) result in a parametric form for the approximating Gaussian Q(u) P (u) Y i=1 exp p i (u i m i ) 1) This may be compared with the form of the true posterior P (ujS) P (u) Q n i=1 P (y i ju i ) and shows that Q(u) is ....
[Article contains additional citation context not shown here]
Lehel Csato and Manfred Opper. Sparse online Gaussian processes. Neural Computation, 14:641-668, 2002.
PAC-Bayesian Theorems for Gaussian Process Classification - Seeger (2002) (Correct)
.... of GPC (the proposed methods are too numerous to list here see [9] for references) All one has to do is plug S and S (see (6) for a method at hand into (8) and (7) We did this for two methods we refer to as Laplace GPC [13] and sparse greedy GPC (a fast variant of Csat o and Opper [2], recently proposed by Lawrence and Herbrich, see [10] the latter being especially interesting in practice since it shows comparable running time and performance to Support Vector machines, yet is based on a probabilistic model and much simpler to implement. Details can be found in [9] The ....
Lehel Csato and Manfred Opper. Sparse online Gaussian processes. Neural Computation, 14:641-668, 2002.
Notes on Minka's Expectation Propagation for Gaussian process.. - Seeger (2002) (2 citations) (Correct)
.... expectation propagation (EP) a general scheme for approximate Bayesian inference, and applies it to Bayesian Gaussian process classi cation (GPC) The scheme can be applied to the problem of sparse GPC, resulting in a generalization of the sparse online GPC algorithm proposed by Csat o and Opper [1]. In this paper, we provide some notes concerning this application. Please note that this paper is not self contained, but relies heavily on the presentation in [4] especially on chapter 5. 1.1 The Gaussian process classi cation model In this paper, we focus on binary classi cation problems, ....
....As mentioned above, we start with Q(w) P (w) and as long as we include points that have not been considered before, there is no need to remove their in uence on Q(w) prior to that. In fact, this pure ADF variant of Bayesian linear discrimination has been proposed before by Csat o and Opper [1]. Obviously, if we stop ADF after having included k points only, we end up with a sparse discriminant. The nal Q(w) and the discriminant will strongly depend on which points we have selected. In line with the general online character of the algorithm, and chie y because exhaustive search over all ....
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Lehel Csato and Manfred Opper. Sparse online Gaussian processes. Technical report, NCRG, Aston University, 2001. To appear in Neural Computation.
A Slightly Refined Lossy Compression Bound - Seeger (Correct)
....Vector machine can be seen as d permutation invariant d compression scheme, where d is the number of support vectors. In both applications, d cannot be xed a priori, but depends on the data sample S. Our main interest is in a greedy variant of a sparse Gaussian process classi cation scheme [1], which has been proposed in [3] Implementations of this scheme typically run through two di erent phases. In the rst one, a xed number d rand of patterns are selected from the sample S and are included into an active set (each inclusion leads to a parameter update, just as in the perceptron ....
Lehel Csato and Manfred Opper. Sparse online Gaussian processes. Technical report, NCRG, Aston University, 2001. To appear in Neural Computation.
Sparse and Semi-supervised Visual Mapping with the S³GP - Williams, Blake, Cipolla (2006) (Correct)
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L. Csat o and M. Opper. Sparse online Gaussian processes. Neural Computation, 14:641--668, 2002.
Sparse Gaussian Processes using Pseudo-inputs - Edward Snelson Zoubin (2006) (1 citation) (Correct)
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L. Csat o. Sparse online Gaussian processes. Neural Computation, 14:641--668, 2002.
Gaussian Processes for Ordinal Regression - Chu, Ghahramani (2005) (1 citation) (Correct)
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L. Csat o and M. Opper. Sparse online Gaussian processes. Neural Computation, The MIT Press, 14:641--668, 2002.
Bayesian Gaussian Process Models: PAC-Bayesian Generalisation.. - Seeger (2003) (3 citations) (Correct)
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Lehel Csato and Manfred Opper. Sparse online Gaussian processes. Neural Computation, 14:641--668, 2002.
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