Incorporating Prior Knowledge into Kernel Based Regression

在一些，样品基于回归任务，观察样品是相当很少足够增进知识。作为结果，在样品和模型复杂性的数字之间的冲突出现，并且回归方法将面对窘境是否选择一个复杂模型。合并优先的知识是这窘境的一个潜在的解决方案。在这份报纸，一种优先的知识被调查，把它合并到核的一个新奇方法基于回归计划被建议。建议优先的 knowledge based 核回归(PKBKR ) 方法包括二 subproblems：在函数空间代表优先的知识，并且联合这个代表和训练样品获得回归函数。为代表的步的一个贪婪算法和为加入步的加权的损失功能被建议。最后，实验被执行验证建议 PKBKR 方法，结果在那里证明建议方法能与适当模型复杂性完成相对高的回归性能，特别当样品的数字是小的或观察噪音大时。

In some sample based regression tasks, the observed samples are quite few or not informative enough. As a result, the conflict between the number of samples and the model complexity emerges, and the regression method will confront the dilemma whether to choose a complex model or not. Incorporating the prior knowledge is a potential solution for this dilemma. In this paper, a sort of the prior knowledge is investigated and a novel method to incorporate it into the kernel based regression scheme is proposed. The proposed prior knowledge based kernel regression （PKBKR） method includes two subproblems： representing the prior knowledge in the function space, and combining this representation and the training samples to obtain the regression function. A greedy algorithm for the representing step and a weighted loss function for the incorporation step axe proposed. Finally, experiments are performed to validate the proposed PKBKR method, wherein the results show that the proposed method can achieve relatively high regression performance with appropriate model complexity, especially when the number of samples is small or the observation noise is large.