
On an optimal interpolation formula in K_2(P_2) space
The paper is devoted to the construction of an optimal interpolation for...
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Sparse data interpolation using the geodesic distance affinity space
In this paper, we adapt the geodesic distancebased recursive filter to ...
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Graph signal interpolation with Positive Definite Graph Basis Functions
For the interpolation of graph signals with generalized shifts of a grap...
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Learning in High Dimension Always Amounts to Extrapolation
The notion of interpolation and extrapolation is fundamental in various ...
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Predicting optimal value functions by interpolating reward functions in scalarized multiobjective reinforcement learning
A common approach for defining a reward function for Multiobjective Rei...
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Exposure Interpolation Via Fusing Conventional and Deep Learning Methods
Deep learning based methods have penetrated many image processing proble...
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Mathematical Construction of Interpolation and Extrapolation Function by Taylor Polynomials
In this present paper, I propose a derivation of unified interpolation a...
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A New Interpolation Approach and Corresponding InstanceBased Learning
Starting from finding approximate value of a function, introduces the measure of approximationdegree between two numerical values, proposes the concepts of "strict approximation" and "strict approximation region", then, derives the corresponding onedimensional interpolation methods and formulas, and then presents a calculation model called "sumtimesdifference formula" for highdimensional interpolation, thus develops a new interpolation approach, that is, ADB interpolation. ADB interpolation is applied to the interpolation of actual functions with satisfactory results. Viewed from principle and effect, the interpolation approach is of novel idea, and has the advantages of simple calculation, stable accuracy, facilitating parallel processing, very suiting for highdimensional interpolation, and easy to be extended to the interpolation of vector valued functions. Applying the approach to instancebased learning, a new instancebased learning method, learning using ADB interpolation, is obtained. The learning method is of unique technique, which has also the advantages of definite mathematical basis, implicit distance weights, avoiding misclassification, high efficiency, and wide range of applications, as well as being interpretable, etc. In principle, this method is a kind of learning by analogy, which and the deep learning that belongs to inductive learning can complement each other, and for some problems, the two can even have an effect of "different approaches but equal results" in big data and cloud computing environment. Thus, the learning using ADB interpolation can also be regarded as a kind of "wide learning" that is dual to deep learning.
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