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Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness

Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness,10.1007/978-3-540-87481-2_14,Christian Plagemann,Kristian Kersting

Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness   (Citations: 7)
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Gaussian processes using nonstationary covariance functions are a powerful tool for Bayesian regression with input-dependent smooth- ness. A common approach is to model the local smoothness by a la- tent process that is integrated over using Markov chain Monte Carlo approaches. In this paper, we show that a simple approximation that uses the estimated mean of the local smoothness yields good results and allows one to employ efficient gradient-based optimization techniques for learning the parameters of the latent and the observed processes jointly. Extensive experiments on both synthetic and real-world data, including challenging problems in robotics, show the relevance and feasibility of our approach.
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    • ...Work on modeling non-stationary processes, ones in which the smoothness of the process is state dependent, can be found in (Paciorek 2003) and (Plagemann et al. 2008)...

    Jonathan Koet al. GP-BayesFilters: Bayesian filtering using Gaussian process prediction ...

    • ...In the recent past, Gaussian Processes have been applied in the context of terrain modeling - [14], [15] and [16]...
    • ...Whereas [14] initializes the kernel matrices evaluated at each point with parameters learnt for the corresponding stationary kernel and then iteratively adapts them to account for local structure and smoothness, [15] and [16] introduce the idea of a “hyper-GP” (using a stationary kernel) to predict the most probable length scale parameters to suit the local structure...
    • ...It also proposes a local approximation methodology to emulate the locally adaptive effect of the techniques proposed in [14], [15] and [15]...
    • ...It also proposes a local approximation methodology to emulate the locally adaptive effect of the techniques proposed in [14], [15] and [15]...
    • ...This process provides two advantages - it tends to achieve the locally adaptive GP effect as exemplified by the works [14], [15] and [16] and it simultaneously addresses the scalability issue that arises when applying this approach to large scale data sets...

    Shrihari Vasudevanet al. Gaussian Process modeling of large scale terrain

    • ...Burgard et al., following on the research done by Paciorek and Schervish [10, 4], have successfully applied Gaussian process regression to the problem of rough terrain modeling, although their approach is computationally expensive and has not been applied to large datasets [13, 12, 9]. Burgard’s research adapts Gaussian process regression for the task of mobile robot terrain estimation by considering issues such as computational ...

    Raia Hadsellet al. Accurate Rough Terrain Estimation with Space-Carving Kernels

    • ...Other model extensions that aim at increasing the expressiveness of Gaussian processes include, e.g., heteroscedastic GPs for modeling input-dependent noise (Le et al. 2005; Kersting et al. 2007; Snelson and Ghahramani 2006b), nonstationary GPs for modeling input-dependent smoothness (Paciorek and Schervish 2003; Plagemann et al. 2008; Schmidt and O’Hagan 2003), or special covariance functions for non-vectorial inputs (Driessens et al. ...

    Cyrill Stachnisset al. Learning gas distribution models using sparse Gaussian process mixture...

    • ...Work on modeling non-stationary processes, ones in which the smoothness of the process is state dependent, can be found in (Paciorek 2003) and (Plagemann et al. 2008)...

    Jonathan Koet al. GP-BayesFilters: Bayesian filtering using Gaussian process prediction ...

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