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Topic: Gaussian process

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	The Gaussian Processes Web Site
		The simplest uses of Gaussian process models are for (the conjugate case of) regression with Gaussian noise.
		Gaussian processes are in my view the simplest and most obvious way of defining flexible Bayesian regression and classification models, but despite some past usage, they appear to have been rather neglected as a general-purpose technique.
		We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting.
	www.gaussianprocess.org (10721 words)

	PlanetMath: Gaussian process
		As an example, any Wiener process is Gaussian.
		Cross-references: manifold, subset, Wiener process, jointly normal, random variables, joint distribution, integer, positive, words, joint normal distributions, finite dimensional distributions, stochastic process
		This is version 2 of Gaussian process, born on 2005-07-07, modified 2006-02-24.
	planetmath.org /encyclopedia/GaussianRandomField.html (124 words)

	Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification - Neal (ResearchIndex)
		Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables.
		In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases.
		Gaussian Processes for Ordinal Regression - Chu, Ghahramani (2005)
	citeseer.ist.psu.edu /neal97monte.html (564 words)

	G03 Manual: RUNNING
		Gaussian will generate names for the first two segments, and the third will be given the name my_job.
		If Gaussian is being used on a machine with limited physical memory, so that the default of 48 MB is not available, the default algorithms as well as the default memory allocation should be set appropriately during installation.
		Gaussian may be run using the NQS batch facility on those UNIX systems that support it.
	www.gaussian.com /g_ur/m_running.htm (1906 words)

	Using G03 with Linda
		The Linda parallel programming model involves a master process, which runs on the current processor, and a number of worker processes which can run on other nodes of the network.
		So a Gaussian 03 /Linda run must specify the number of processors to use, the list of processors where the jobs should be run, and occasionally other job parameters.
		A corollary of this is that if you forget to include %NProcLinda within the Gaussian 03 input file or -L- in the Default.Route file, then the job will not run in parallel, although there may be an idle Linda process on each of the nodes in the node list.
	www.gaussian.com /g_tech/linda_use.htm (1378 words)

	Examples of Gaussian Process inference (Site not responding. Last check: 2007-11-03)
		It is important that the average needed for the posterior process to be implemented is one-dimensional (or two, but definitely does not scale with the number of examples as with the normal use of GP inference).
		Gaussian, or its type is not known but there is the possibility of having outliers in the data.
		The likelihood model Gaussian regression, thus the novelty of this type of learning is the inclusion of the special information about the test points.
	www.ncrg.aston.ac.uk /Projects/SSGP/examples/index.html (528 words)

	How to prove the output of Linear Filtering a Gaussian Process is still Gaussian?
		By definition, a Gaussian process is a function x such that for any finite integer k, and for any arbitary time t1, t2,..., tk, that x(t1), x(t2),...., x(tk) are jointly Gaussian RV.
		It is quite obvious that a Gaussian RV remains Gaussian after linear filtering it, but for a Gaussian process, I am not sure what to use to prove that.
		The decretised integral is a linear combination of jointly Gaussian variables, and is therefore Gaussian.
	www.physicsforums.com /showthread.php?t=84197 (372 words)

	Fast Gaussian Process Latent Variable Model - MATLAB Software (Site not responding. Last check: 2007-11-03)
		The sparse approximation used in this toolbox is based on the Sparse Pseudo-input Gaussian Process model described by Snelson and Ghahramani.
		Gaussian process using the DTC approximation with nine inducing variables.
		At the Sheffield Gaussian Process Round Table Lehel Csato pointed out that the Bayesian Committee Machine of Schwaighofer and Tresp can also be viewed within the same framework.
	www.dcs.shef.ac.uk /~neil/fgplvm (1912 words)

	Documentation for GPML Matlab Code (Site not responding. Last check: 2007-11-03)
		Basic Gaussian process regression (GPR) code allowing flexible specification of the covariance function.
		Gaussian process classification (GPC) demonstrates implementations of Laplace and EP approximation methods for binary GP classification.
		A table of other sources of useful Gaussian process software, unrelated to the book, may be found
	www.gaussianprocess.org /gpml/code/matlab/doc (272 words)

	Bayesian Classification with Gaussian Processes - Williams, Barber (ResearchIndex)
		A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points.
		5.2%: Prediction With Gaussian Processes: From Linear Regression To..
		C. Williams and D. Barber, Bayesian Classification with Gaussian Processes, IEEE Trans Pattern Analysis and Machine Intelligence, 20 13421351, (1998).
	citeseer.ist.psu.edu /williams98bayesian.html (667 words)

	Sparse Gaussian Process Tooblox - Demonstration (Site not responding. Last check: 2007-11-03)
		Gaussian processes (GPs) have gained popularity among researchers in the machine learning community.
		Despite their attractive simplicity and generality, due to the large time-, and resource requirements, GPs have not been usable for large practical problems.
		The posterior process is approximated by a Gaussian process, which allows eg robust regression (Laplace noise), classification and an interesting noise model, which is exponential, but the noise is constrained to only positive values.
	www.kyb.tuebingen.mpg.de /de/publication.html?publ=2689 (276 words)

	Gaussian process - Wikipedia, the free encyclopedia
		A Gaussian process is a stochastic process which generates samples over time {X
		It is not stationary, but it has stationary increments.
		(Given any set of N points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of your N points with some desired kernel, and sample from that Gaussian.) Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, or Kriging.
	en.wikipedia.org /wiki/Gaussian_process (333 words)

	Gaussian Process Approach to Spiking Neurons for Inhomogeneous Poisson Inputs -- Amemori and Ishii 13 (12): 2763 -- ... (Site not responding. Last check: 2007-11-03)
		Gaussian Process Approach to Spiking Neurons for Inhomogeneous Poisson Inputs -- Amemori and Ishii 13 (12): 2763 -- Neural Computation
		Gaussian Process Approach to Spiking Neurons for Inhomogeneous Poisson Inputs
		of the membrane potential then becomes a gaussian process.
	neco.mitpress.org /cgi/content/abstract/13/12/2763 (186 words)

	Gaussian processes (Site not responding. Last check: 2007-11-03)
		For an introduction to Gaussian processes, try my review paper
		For an octave-based demonstration of Gaussian processes please grab this tar file from my lecture course.
		This is our reason for going for the `optimization' approach, which we hope will be a good approximation.
	www.inference.phy.cam.ac.uk /mackay/GP (957 words)

	Gaussian Process Networks (Site not responding. Last check: 2007-11-03)
		In the Bayesian framework, this is done by evaluating the marginal likelihood of the data given a candidate structure.
		This term can be computed in closed-form for standard parametric families (e.g., Gaussians), and can be approximated, at some computational cost, for some semi-parametric families (e.g., mixtures of Gaussians).
		We present a new family of continuous variable probabilistic networks that are based on Gaussian Process priors.
	ai.stanford.edu /people/nir/Abstracts/FN1.html (168 words)

	Mixtures of Gaussian process priors
		Stochastic process priors have, compared to priors over parameters
		Gaussian processes, in particular, always correspond to simple quadratic error surfaces, i.e., concave densities.
		Arbitrary prior processes, however, can easily be built by using mixtures of Gaussian processes without loosing the advantage of an explicit prior implementation [
	pauli.uni-muenster.de /~lemm/papers/biqt/node15.html (110 words)

	GPDM (Site not responding. Last check: 2007-11-03)
		This project introduces Gaussian process dynamical models (GPDM) for nonlinear time series analysis, and aims to explore potential applications to people tracking and data-driven animation.
		A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space.
		We marginalize out the model parameters in closed-form, which amounts to using Gaussian process (GP) priors for both the dynamics and the observation mappings.
	www.dgp.toronto.edu /~jmwang/gpdm (233 words)

	Abstract for ``Regression and classification using Gaussian process priors'' (Site not responding. Last check: 2007-11-03)
		Abstract for ``Regression and classification using Gaussian process priors''
		Gaussian processes are a natural way of specifying prior distributions over functions of one or more input variables.
		Neal, R. (1997) ``Monte Carlo implementation of Gaussian process models for Bayesian regression and classification'', Technical Report No. 9702, Dept. of Statistics, University of Toronto, 24 pages: abstract, postscript, pdf, associated software.
	www.cs.toronto.edu /~radford/valencia.abstract.html (269 words)

	List of topics named after Carl Friedrich Gauss - Wikipedia, the free encyclopedia
		Gauss' theorem may refer to the divergence theorem, which is also known as the Ostrogradsky-Gauss theorem.
		Gaussian distribution, also called the normal distribution, a type of probability distribution.
		This page was last modified 01:58, 29 November 2006.
	en.wikipedia.org /wiki/Gaussian (174 words)

	Neil Lawrence's Gaussian Process Software Available Online
		GP-LVM and Gaussian Process Regression using sparse approximations described at NIPS 2005 by Snelson and Ghahramani as well as extensions given by Quinonero-Candela and Rasmussen
		A Gaussian process interpretation of Kernel Fisher Discriminants.
		A set of Gaussian process demos, sampling from covariance functions etc..
	www.dcs.shef.ac.uk /~neil/gpsoftware.html (335 words)

	Glasgow ePrints Service - Gaussian Process priors with uncertain inputs? Application to multiple-step ahead time series ...
		Girard, A. and Rasmussen, C.E. and Quinonero-Candela, J. and Murray-Smith, R. Gaussian Process priors with uncertain inputs?
		We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model.
		For a state-space model of the form y t = f(Yt-1,..., Yt-L), the prediction of y at time t + k is based on the point estimates of the previous outputs.
	eprints.gla.ac.uk /3117 (198 words)

	Glasgow ePrints Service - Adaptive, cautious, predictive control with Gaussian process priors
		Murray-Smith, R. and Sbarbaro, D. and Rasmussen, C.E. and Girard, A. Adaptive, cautious, predictive control with Gaussian process priors.
		Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law.
		The general method and its main features are illustrated on a simulation example.
	eprints.gla.ac.uk /3112 (184 words)

	The Neuroinformatics Portal Pilot - Connectionists: Gaussian Process Classification ... (Site not responding. Last check: 2007-11-03)
		The Neuroinformatics Portal Pilot - Connectionists: Gaussian Process Classification...
		It is well known in the statistics literature that augmenting binary and
		Plone makes heavy use of CSS, which means it is accessible to any internet browser, but the design needs a standards-compliant browser to look like we intended it.
	www.neuroinf.de /News/2005/11/21_11-47-20 (272 words)

	Learning a Gaussian Process Prior for Automatically Generating Music Playlists
		Advances in Neural Information Processing Systems 14, pp.
		This paper presents AutoDJ: a system for automatically generating music playlists based on one or more seed songs selected by a user.
		This learned kernel is shown to be more effective at predicting users’ playlists than a reasonable hand-designed kernel.
	research.microsoft.com /~jplatt/abstracts/autoDJ.html (128 words)

	MIT OpenCourseWare \| Error Page (Site not responding. Last check: 2007-11-03)
		Sorry, the page you requested was not found.
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	ocw.mit.edu /NR/rdonlyres/Electrical-Engineering-and-Computer-Scienc... (96 words)

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