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      • Department of Electrical and Electronics Engineering
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      Twice-universal piecewise linear regression via infinite depth context trees

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      Author
      Vanlı, Nuri Denizcan
      Sayın, Muhammed O.
      Göze, T.
      Kozat, Süleyman Selim
      Date
      2015
      Source Title
      Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, IEEE 2015
      Print ISSN
      1520-6149
      Publisher
      IEEE
      Pages
      2051 - 2055
      Language
      English
      Type
      Conference Paper
      Item Usage Stats
      133
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      102
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      Abstract
      We investigate the problem of sequential piecewise linear regression from a competitive framework. For an arbitrary and unknown data length n, we first introduce a method to partition the regressor space. Particularly, we present a recursive method that divides the regressor space into O(n) disjoint regions that can result in approximately 1.5n different piecewise linear models on the regressor space. For each region, we introduce a universal linear regressor whose performance is nearly as well as the best linear regressor whose parameters are set non-causally. We then use an infinite depth context tree to represent all piecewise linear models and introduce a universal algorithm to achieve the performance of the best piecewise linear model that can be selected in hindsight. In this sense, the introduced algorithm is twice-universal such that it sequentially achieves the performance of the best model that uses the optimal regression parameters. Our algorithm achieves this performance only with a computational complexity upper bounded by O(n) in the worst-case and O(log(n)) under certain regularity conditions. We provide the explicit description of the algorithm as well as the upper bounds on the regret with respect to the best nonlinear and piecewise linear models, and demonstrate the performance of the algorithm through simulations.
      Keywords
      Infinite depth context tree
      Nonlinear
      Piecewise linear
      Regression
      Sequential
      Permalink
      http://hdl.handle.net/11693/27963
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/ICASSP.2015.7178331
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      • Department of Electrical and Electronics Engineering 3524
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