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      • Department of Electrical and Electronics Engineering
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      A unified approach to universal prediction: Generalized upper and lower bounds

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      Author
      Vanli, N. D.
      Kozat, S. S.
      Date
      2015
      Source Title
      IEEE Transactions on Neural Networks and Learning Systems
      Print ISSN
      0216-2237X
      Publisher
      Institute of Electrical and Electronics Engineers Inc.
      Volume
      26
      Issue
      3
      Pages
      646 - 651
      Language
      English
      Type
      Article
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      Abstract
      We study sequential prediction of real-valued, arbitrary, and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios, we achieve matching lower and upper bounds, demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result, we also prove that for the worst case scenario, the performance of randomized output algorithms can be achieved by sequential algorithms so that randomized output algorithms do not improve the performance. © 2012 IEEE.
      Keywords
      Online learning
      Computation theory
      Forecasting
      Sequential switching
      Computational learning theory
      Lower and upper bounds
      Online learning
      Sequential learning algorithm
      Sequential prediction
      Squared prediction errors
      Upper and lower bounds
      Worst-case performance
      Algorithms
      Permalink
      http://hdl.handle.net/11693/22325
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/TNNLS.2014.2317552
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