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Authors: Klaus, Florian
Title: Mixed-precision data mining for sparse grids
Other Titles: Data Mining auf Dünnen Gittern in gemischter Genauigkeit
Issue Date: 2019 Abschlussarbeit (Bachelor) 53
Abstract: The concept of sparse grids has been introduced to allow the treatment of high-dimensional problems, including data mining tasks like classification and regression. In the process of solving these problems, a discrete approximation of a complex function is required, which is accomplished by locating weighted basis functions on the nodes of a sparse grid. Meanwhile, an implementation of such methods on a computer executes many floating-point operations. These are traditionally performed in double precision to achieve accurate results. The hierarchical structure of sparse grids often leads to a rapid decline of basis coefficients on higher levels. Hence, the use of double precision throughout all floating-point operations is not strictly necessary. Single and half precision can be incorporated to save computation time and storage space, and a mixed-precision approach has the potential to increase efficiency, while keeping a comparable level of accuracy. In this work, the alternation of floating-point precision in the classification and regression on sparse grids is investigated. Different mixed-precision strategies are developed with the hierarchical sparse grid structure in mind. They are incorporated into established algorithms for function approximation on sparse grids. The effects of these mixed-precision strategies on the convergence and accuracy are examined, and compared with homogeneous double (FP64), single (FP32) and half (FP16) precision. Tests were conducted on prominent data sets varying in size, dimension and complexity. The test results suggest that the partial or temporary use of a lower precision has the potential to improve efficiency, while ensuring an accuracy which can compete with uniform double precision.
Appears in Collections:05 Fakultät Informatik, Elektrotechnik und Informationstechnik

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