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Gaussian Process Approach to Stochastic Spiking Neurons with Reset
"... . This article theoretically examines the behavior of spiking neurons whose input spikes obey an inhomogeneous Poisson process. Since the probability density of the membrane potential converges to a Gaussian distribution, the stochastic process becomes a Gaussian process. With a frequentlyused spik ..."
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. This article theoretically examines the behavior of spiking neurons whose input spikes obey an inhomogeneous Poisson process. Since the probability density of the membrane potential converges to a Gaussian distribution, the stochastic process becomes a Gaussian process. With a frequently
Bayes Meets Bellman: The Gaussian Process Approach to Temporal Difference Learning
 Proc. of the 20th International Conference on Machine Learning
, 2003
"... We present a novel Bayesian approach to the problem of value function estimation in continuous state spaces. We de ne a probabilistic generative model for the value function by imposing a Gaussian prior over value functions and assuming a Gaussian noise model. ..."
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Cited by 75 (8 self)
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We present a novel Bayesian approach to the problem of value function estimation in continuous state spaces. We de ne a probabilistic generative model for the value function by imposing a Gaussian prior over value functions and assuming a Gaussian noise model.
Gaussian processes for machine learning
 in: Adaptive Computation and Machine Learning
, 2006
"... Abstract. We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions. We present the simple equations for incorporating training data and examine how to learn the hyperpar ..."
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Cited by 631 (2 self)
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Abstract. We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions. We present the simple equations for incorporating training data and examine how to learn
Gaussian Process Approach to Spiking Neurons for Inhomogeneous Poisson Inputs
"... This article presents a new theoretical framework to consider the dynamics of a stochastic spiking neuron model with general membrane response to input spike. We assume that the input spikes obey an inhomogeneous Poisson process. The stochastic process of the membrane potential then becomes a Gaussi ..."
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Cited by 6 (1 self)
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Gaussian process. When a general type of the membrane response is assumed, the stochastic process becomes a MarkovGaussian process. We present a calculation method for the membrane potential density and the firing probability density. Our new formulation is the extension of the existing formulation based
A Case Study on MetaGeneralising: A Gaussian Processes Approach
"... We propose a novel model for metageneralisation, that is, performing prediction on novel tasks based on information from multiple different but related tasks. The model is based on two coupled Gaussian processes with structured covariance function; one model performs predictions by learning a const ..."
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Cited by 1 (0 self)
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We propose a novel model for metageneralisation, that is, performing prediction on novel tasks based on information from multiple different but related tasks. The model is based on two coupled Gaussian processes with structured covariance function; one model performs predictions by learning a
154 Bayes Meets Bellman: The Gaussian Process Approach to Temporal Difference Learning
"... We present a novel Bayesian approach to the problem of value function estimation in continuous state spaces. We define a probabilistic generative model for the value function by imposing a Gaussian prior over value functions and assuming a Gaussian noise model. Due to the Gaussian nature of the rand ..."
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We present a novel Bayesian approach to the problem of value function estimation in continuous state spaces. We define a probabilistic generative model for the value function by imposing a Gaussian prior over value functions and assuming a Gaussian noise model. Due to the Gaussian nature
Capacity of multiantenna Gaussian channels
 EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS
, 1999
"... We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such form ..."
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Cited by 2878 (6 self)
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We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate
Blind Beamforming for Non Gaussian Signals
 IEE ProceedingsF
, 1993
"... This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray mani ..."
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Cited by 704 (31 self)
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This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors, etc ... so that neither array calibration nor physical modeling are necessary. Rather surprisingly, `blind beamformers' may outperform `informed beamformers' in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption blind identification relies on is the statistical independence of the sources, which we exploit using fourthorder cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4thorder cumulant matrices
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 514 (17 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 668 (15 self)
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In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fairing, to lowpass filtering. We describe a very simple surface signal lowpass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimizationbased fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/image generation  display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  curve, surface, solid, and object representations;J.6[Com puter Applications]: ComputerAided Engineering  computeraided design General Terms: Algorithms, Graphics. 1
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