Incorporating Prior Knowledge into Kernel Based Regression

Sun, Zhe; Zhang, Zengke; Wang, Huangang

doi:10.3724/sp.j.1004.2008.01515

Cited by 5 publications

(7 citation statements)

References 5 publications

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“…Once the coefficients of the prior sample are obtained, the second objective function can be formulated as given in Equation (14) is the scalar value that determining the significant of the second objective as compared to the first objective and ξ is the predefined tolerance of the estimated weight, the value is between 0.01 and 0.1 . …”

Section: ( )mentioning

confidence: 99%

“…In related works, many forms of prior knowledge that incorporated to the kernel based regression are available in various fashions such as a bias data points in equality and inequality constraints form [9][10], derivative points [11][12] polyhedral constraints points [13] and discrete points derived from prior function to be represented as prior function space [14]. However, all of the existing techniques tried to find only one optimal solution for a given problem.…”

Section: Introductionmentioning

confidence: 98%

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Enhanced Weighted Kernel Regression with Prior Knowledge in Solving Small Sample Problems

Shapiai

Sudin

Ibrahim

et al. 2011

2011 Third International Conference on Computational Intelligence, Modelling &Amp; Simulation

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In many real-world problems only very few samples are available and sometimes non-informative to help in performing a regression task. Incorporating a prior knowledge to this type of problem might offer a promising solution. In this study, the proposed algorithm translated a given prior knowledge and the available samples into a function space before introducing the idea of Pareto optimality concept to the problem. Instead of a single optimal solution competing with the objectives, the algorithm provides a set of solutions, generally denoted as the Pareto-optimal that offers more flexibility towards the intended solution. Thus the corresponding trade-off between solutions can be chosen in the presence of preference information. The proposed technique also does not require the addition of equality or non-equality constraints in introducing a prior knowledge. We also discussed, the challenges of determining the two objective functions that to be defined in the multi-objective problem environment. A benchmark function is used to validate the proposed technique, and it is shown that prior knowledge incorporation can relatively improve the regression performance.

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Section: ( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Enhanced Weighted Kernel Regression with Prior Knowledge in Solving Small Sample Problems

Shapiai

Sudin

Ibrahim

et al. 2011

2011 Third International Conference on Computational Intelligence, Modelling &Amp; Simulation

View full text Add to dashboard Cite

show abstract

“…A change in the kernel as well as in the regularizer is proposed in [13] to emphasize local features and incorporate invariances. Other approaches include extending the optimization problem with a term penalizing the distance between a prior knowledge function, the data, and the estimate [14]. Note that the incorporation of prior knowledge for conditional density estimation is especially hard as additional constraints have to be asserted to obtain valid conditional densities, i.e., the probability mass of the conditional density estimate has to be non-negative and integrate to one for all fixed input values.…”

Section: Related Workmentioning

confidence: 99%

Incorporating prior knowledge into nonparametric conditional density estimation

Krauthausen

Roschani

Hanebeck

2011

Proceedings of the 2011 American Control Conference

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Abstract-In this paper, the problem of sparse nonparametric conditional density estimation based on samples and prior knowledge is addressed. The prior knowledge may be restricted to parts of the state space and given as generative models in form of mean-function constraints or as probabilistic models in the form of Gaussian mixture densities. The key idea is the introduction of additional constraints and a modified kernel function into the conditional density estimation problem. This approach to using prior knowledge is applicable to all nonparametric conditional density estimation approaches phrased as constrained optimization problems. The quality of the estimates, their sparseness, and the achievable improvements by using prior knowledge are shown in experiments for both Support-Vector Machine-based and integral distancebased conditional density estimation algorithms.

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“…Compared with standard SVR, the incorporation of initial guess may produce a more reasonable model. The detailed implementation of PKBKR can be found in [25] and is ignored here due to the limitation of space.…”

Section: An Introduction To Prior Knowledge Based Kernel Regressionmentioning

confidence: 99%

“…Prior Knowledge Based Kernel Regression (PKBKR) [25] is an extension of SVR [26,27]. Similar to SVR, PKBKR Science and Technology of Nuclear Installations 3 is a sample-based modeling method.…”

Section: An Introduction To Prior Knowledge Based Kernel Regressionmentioning

confidence: 99%

Dynamic Behavior Analysis of Touchdown Process in Active Magnetic Bearing System Based on a Machine Learning Method

Sun

Yan

Zhao

et al. 2017

Science and Technology of Nuclear Installations

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Magnetic bearings are widely applied in High Temperature Gas-cooled Reactor (HTGR) and auxiliary bearings are important backup and safety components in AMB systems. The performance of auxiliary bearings significantly affects the reliability, safety, and serviceability of the AMB system, the rotating equipment, and the whole reactor. Research on the dynamic behavior during the touchdown process is crucial for analyzing the severity of the touchdown. In this paper, a data-based dynamic analysis method of the touchdown process is proposed. The dynamic model of the touchdown process is firstly established. In this model, some specific mechanical parameters are regarded as functions of deformation of auxiliary bearing and velocity of rotor firstly; furthermore, a machine learning method is utilized to model these function relationships. Based on the dynamic model and the Kalman filtering technique, the proposed method can offer estimation of the rotor motion state from noisy observations. In addition, the estimation precision is significantly improved compared with the method without learning. The proposed method is validated by the experimental data from touchdown experiments.

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Incorporating Prior Knowledge into Kernel Based Regression

Cited by 5 publications

References 5 publications

Enhanced Weighted Kernel Regression with Prior Knowledge in Solving Small Sample Problems

Enhanced Weighted Kernel Regression with Prior Knowledge in Solving Small Sample Problems

Incorporating prior knowledge into nonparametric conditional density estimation

Dynamic Behavior Analysis of Touchdown Process in Active Magnetic Bearing System Based on a Machine Learning Method

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