An approximate inference with Gaussian process to latent functions from uncertain data

Dallaire, Patrick; Besse, Camille; Chaib-draa, Brahim

doi:10.1016/j.neucom.2010.09.024

Cited by 20 publications

(25 citation statements)

References 4 publications

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“…Among such tools, Gaussian processes (GP) is a powerful and commonly used regression framework, since it is generally considered to be the most flexible and provides prediction uncertainty information [12]. Two important limitations of GP are its computational complexity [13]- [16] and its sensitivity to uncertain inputs [14], [17]- [21]. To alleviate the computational complexity, various sparse GP techniques have been proposed in [13]- [15], while online and distributed GP were treated in [16], [22], [23] and [24]- [26], respectively.…”

Section: Introductionmentioning

confidence: 99%

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Spatial Wireless Channel Prediction under Location Uncertainty

Muppirisetty

Svensson

Wymeersch

2016

IEEE Trans. Wireless Commun.

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Abstract-Spatial wireless channel prediction is important for future wireless networks, and in particular for proactive resource allocation at different layers of the protocol stack. Various sources of uncertainty must be accounted for during modeling and to provide robust predictions. We investigate two channel prediction frameworks, classical Gaussian processes (cGP) and uncertain Gaussian processes (uGP), and analyze the impact of location uncertainty during learning/training and prediction/testing, for scenarios where measurements uncertainty are dominated by large-scale fading. We observe that cGP generally fails both in terms of learning the channel parameters and in predicting the channel in the presence of location uncertainties. In contrast, uGP explicitly considers the location uncertainty. Using simulated data, we show that uGP is able to learn and predict the wireless channel.Index Terms-Gaussian processes, uncertain inputs, location uncertainty, spatial predictability of wireless channels.

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Section: Introductionmentioning

confidence: 99%

“…No framework has yet been developed to mathematically characterize and understand the spatial predictability of wireless channels with location uncertainty. In this paper, we build on and adapt the framework from [17], [18] to CQM prediction in wireless networks. Our main contributions are as follows:…”

Section: Introductionmentioning

confidence: 99%

Spatial Wireless Channel Prediction under Location Uncertainty

Muppirisetty

Svensson

Wymeersch

2016

IEEE Trans. Wireless Commun.

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“…Therefore, the resulting stochastic process that represents f under random inputs is no longer Gaussian and lacking an analytic formulation [4,5]. However, as demonstrated in [3], based on the work of [5], we can still recover a Gaussian process approximation for f by using the mean and the covariance of the resulting stochastic process under the influence of input noise. In particular, in the case of a constant deterministic mean function µ 0 (x) = m 0 , the mean and the covariance of this noisy process are:…”

Section: Gaussian Process Priors With Uncertain Inputsmentioning

confidence: 99%

“…The posterior of the stochastic process representing f ∼ GP(µ 0 , k) under input noise is not Gaussian due to the complicated forms of Equation 4 and Equation 5 with respect to x and X. Yet we can still obtain a suitable approximation [3,5] for the original f in the noisy input setting by doing inference over a GP with mean m 0 and covariance function k p , as defined in Equation 11. This approximation is obtained as:…”

Section: Gaussian Process Priors With Uncertain Inputsmentioning

confidence: 99%

Bayesian Optimisation for Safe Navigation Under Localisation Uncertainty

Oliveira

Ott

Guizilini

et al. 2019

Springer Proceedings in Advanced Robotics

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In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.

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“…A regression problem could be solved by the gaussian process as follows [14] [19]: Suppose the training set with m data instances is Dataset = < X training , y training >, where the input matrix X training = [x 1 , x 2 , · · · , x m ] consists of n-feature input instances x i (i = 1,2,...m), and y training = [y 1 , y 2 , · · · , y m ] is the output vector which is generated by…”

Section: A Gaussian Process Regressionmentioning

confidence: 99%

An adaptive nonparametric particle filter for state estimation

Wang

Chaib-draa

2012

2012 IEEE International Conference on Robotics and Automation

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Particle filter is one of the most widely applied stochastic sampling tools for state estimation problems in practice. However, the proposal distribution in the traditional particle filter is the transition probability based on state equation, which would heavily affect estimation performance in that the samples are blindly drawn without considering the current observation information. Additionally, the fixed particle number in the typical particle filter would lead to wasteful computation, especially when the posterior distribution greatly varies over time. In this paper, an advanced adaptive nonparametric particle filter is proposed by incorporating gaussian process based proposal distribution into KLD-Sampling particle filter framework so that the high-qualified particles with adaptively KLD based quantity are drawn from the learned proposal with observation information at each time step to improve the approximation accuracy and efficiency. Our state estimation experiments on univariate nonstationary growth model and two-link robot arm show that the adaptive nonparametric particle filter outperforms the existing approaches with smaller size of particles.

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An approximate inference with Gaussian process to latent functions from uncertain data

Cited by 20 publications

References 4 publications

Spatial Wireless Channel Prediction under Location Uncertainty

Spatial Wireless Channel Prediction under Location Uncertainty

Bayesian Optimisation for Safe Navigation Under Localisation Uncertainty

An adaptive nonparametric particle filter for state estimation

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