Abstract
We propose a scheme for improving existing tools for recovering and predicting decisions based on singular value decomposition. Our main contribution is an investigation of advantages of using a functional, rather than linear approximation of the response of an unknown, complicated model. A significant attractive feature of the method is the demonstrated ability to make predictions based on a highly filtered data set. An adaptive high-order interpolation is constructed, that estimates the relative probability of each possible decision. The method uses a flexible nonlinear basis, capable of utilizing all the available information. We demonstrate that the prediction can be based on a very small fraction of the training set. The suggested approach is relevant in the general field of manifold learning, as a tool for approximating the response of the models based on many parameters. Our experiments show that the approach is at least competitive with other latent factor prediction methods, and that the precision of prediction grows with the increase in the order of the polynomial basis.
This work was supported by the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract DE-AC02-06CH11357.
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Roderick, O., Safro, I. (2010). Learning of Highly-Filtered Data Manifold Using Spectral Methods. In: Blum, C., Battiti, R. (eds) Learning and Intelligent Optimization. LION 2010. Lecture Notes in Computer Science, vol 6073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13800-3_12
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