Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(6)
Covariance Function
Markov Chain Monte Carlo
Optimization Technique
Point Estimation
Gaussian Process
Gaussian Process Regression
Related Publications
(3)
Nonstationary Covariance Functions for Gaussian Process Regression
Adaptive NonStationary Kernel Regression for Terrain Modeling
Nonstationary Gaussian Processes for Regression and Spatial Modelling
Subscribe
Academic
Publications
Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness
Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness,10.1007/9783540874812_14,Christian Plagemann,Kristian Kersting
Edit
Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness
(
Citations: 7
)
BibTex

RIS

RefWorks
Download
Christian Plagemann
,
Kristian Kersting
,
Wolfram Burgard
Gaussian processes using nonstationary covariance functions are a powerful tool for Bayesian regression with inputdependent 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 gradientbased optimization techniques for learning the parameters of the latent and the observed processes jointly. Extensive experiments on both synthetic and realworld data, including challenging problems in robotics, show the relevance and feasibility of our approach.
Conference:
Principles of Data Mining and Knowledge Discovery  PKDD
, pp. 204219, 2008
DOI:
10.1007/9783540874812_14
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
www.springerlink.com
)
(
www.springerlink.com
)
(
dx.doi.org
)
(
www.stanford.edu
)
(
www.informatik.unifreiburg.de
)
(
wwwkd.iai.unibonn.de
)
(
www.informatik.unitrier.de
)
More »
Citation Context
(6)
...Work on modeling nonstationary processes, ones in which the smoothness of the process is state dependent, can be found in (Paciorek 2003) and (
Plagemann et al. 2008
)...
Jonathan Ko
,
et al.
GPBayesFilters: 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 “hyperGP” (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 Vasudevan
,
et 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 Hadsell
,
et al.
Accurate Rough Terrain Estimation with SpaceCarving Kernels
...Other model extensions that aim at increasing the expressiveness of Gaussian processes include, e.g., heteroscedastic GPs for modeling inputdependent noise (Le et al. 2005; Kersting et al. 2007; Snelson and Ghahramani 2006b), nonstationary GPs for modeling inputdependent smoothness (Paciorek and Schervish 2003;
Plagemann et al. 2008;
Schmidt and O’Hagan 2003), or special covariance functions for nonvectorial inputs (Driessens et al. ...
Cyrill Stachniss
,
et al.
Learning gas distribution models using sparse Gaussian process mixture...
...Work on modeling nonstationary processes, ones in which the smoothness of the process is state dependent, can be found in (Paciorek 2003) and (
Plagemann et al. 2008
)...
Jonathan Ko
,
et al.
GPBayesFilters: Bayesian filtering using Gaussian process prediction ...
References
(19)
Gaussian Process Models for Sensorcentric Robot Localisation
(
Citations: 8
)
Alex Brooks
,
Alexei Makarenko
,
Ben Upcroft
Conference:
International Conference on Robotics and Automation  ICRA
, pp. 5661, 2006
Bayesian curvefitting with freeknot splines
(
Citations: 154
)
I. Dimatteo
,
C. R. Genovese
,
R. E. Kass
Journal:
Biometrika
, vol. 88, no. 4, pp. 10551071, 2001
Most likely heteroscedastic Gaussian process regression
(
Citations: 21
)
Kristian Kersting
,
Christian Plagemann
,
Patrick Pfaff
,
Wolfram Burgard
Conference:
International Conference on Machine Learning  ICML
, pp. 393400, 2007
Adaptive NonStationary Kernel Regression for Terrain Modeling
(
Citations: 8
)
Tobias Lang
,
Christian Plagemann
,
Wolfram Burgard
Conference:
Robotics: Science and Systems  RSS
, 2007
Nonstationary Gaussian Process Regression using a Latent Extension of the Input Space
(
Citations: 3
)
Tobias Pfingsten
,
Malte Kuss
,
Carl Edward Rasmussen
Published in 2006.
Sort by:
Citations
(7)
Spacecarving Kernels for Accurate Rough Terrain Estimation
(
Citations: 1
)
Raia Hadsell
,
J. Andrew Bagnell
,
Daniel F. Huber
,
Martial Hebert
Journal:
International Journal of Robotic Research  IJRR
, vol. 29, no. 8, pp. 981996, 2010
GPBayesFilters: Bayesian filtering using Gaussian process prediction and observation models
(
Citations: 10
)
Jonathan Ko
,
Dieter Fox
Journal:
Autonomous Robots  AROBOTS
, vol. 27, no. 1, pp. 7590, 2009
Gaussian Process modeling of large scale terrain
(
Citations: 7
)
Shrihari Vasudevan
,
Fabio T. Ramos
,
Eric Nettleton
,
Hugh F. Durrantwhyte
,
Allan Blair
Conference:
International Conference on Robotics and Automation  ICRA
, vol. 26, no. 10, pp. 10471053, 2009
Accurate Rough Terrain Estimation with SpaceCarving Kernels
(
Citations: 4
)
Raia Hadsell
,
J. Andrew Bagnell
,
Daniel Huber
,
Martial Hebert
Conference:
Robotics: Science and Systems  RSS
, 2009
Learning gas distribution models using sparse Gaussian process mixtures
(
Citations: 2
)
Cyrill Stachniss
,
Christian Plagemann
,
Achim J. Lilienthal
Journal:
Autonomous Robots  AROBOTS
, vol. 26, no. 23, pp. 187202, 2009