Training and assessment the generalization ability of interpolation methods

Bakhvalov Y.N., Kopylov I.V.
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We investigate machine learning methods with a certain kind of decision rule. In particular, inverse-distance method of interpolation, method of interpolation by radial basis functions, the method of multidimensional interpolation and approximation, based on the theory of random functions, the last method of interpolation is kriging. This paper shows a method of rapid retraining “model” when adding new data to the existing ones. The term “model” means interpolating or approximating function constructed from the training data. This approach reduces the computational complexity of constructing an updated “model” from $O(n^3)$ to $O(n^2)$. We also investigate the possibility of a rapid assessment of generalizing opportunities “model” on the training set using the method of cross-validation leave-one-out cross-validation, eliminating the major drawback of this approach — the necessity to build a new “model” for each element which is removed from the training set.

Keywords: machine learning, interpolation, random function, the system of linear equations, crossvalidation
Citation in English: Bakhvalov Y.N., Kopylov I.V. Training and assessment the generalization ability of interpolation methods // Computer Research and Modeling, 2015, vol. 7, no. 5, pp. 1023-1031
Citation in English: Bakhvalov Y.N., Kopylov I.V. Training and assessment the generalization ability of interpolation methods // Computer Research and Modeling, 2015, vol. 7, no. 5, pp. 1023-1031
DOI: 10.20537/2076-7633-2015-7-5-1023-1031
URL: http://crm-en.ics.org.ru/journal/article/2368/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
According to Crossref, this article is cited by:
  • Ivan Vladimirovich Kopylov. Reduction of decision rule of multivariate interpolation and approximation method in the problem of data classification. // Computer Research and Modeling. — 2016. — V. 8, no. 3. — P. 475. DOI: 10.20537/2076-7633-2016-8-3-475-484
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