Predicting Time Series with Support Vector Machines

By K. Müller, Alex Smola, Gunnar Rätsch, Bernhard Schölkopf, Jens Kohlmorgen, Vladimir Naumovich Vapnik. 1997

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Citations in the corpus

Scalable Kernel Methods via Doubly Stochastic Gradients (2014, methodology): “gression where l(u;y) = 1 2 (u y)2. We 7 have l0(u;y) = (u y) and the step 5 in Algorithm. 1. becomes i= i(f(x i) y i)˚ ! i (x i): Kernel Robust Regression. Huber’s loss is used for robust regression [22] where l(u;y) = ( 1 2 ( u y)2 if j6 1 ju 1yj 2 if ju yj>1 : We have l0(u;y) = ( (u y) if ju y”
Stability Bounds for Stationary φ-mixing and β-mixing Processes (2008, methodology): “Algorithms such as support vector regression (SVR) (Vapnik, 1998; Sch¨olkopf and Smola, 2002) have been used in the context of time series prediction in which the i.i.d. assumption does not hold, some with good experimental results (M¨uller et al., 1997; Mattera and Haykin, 1999).”
Evolino for recurrent support vector machines (2005, methodology): “A limited way of applying existing SVMs to sequence prediction [4, 5] or classiﬁcation [6] is to build a training set either by transforming the sequential input into some static domain (e.g., a frequency and phase representation, a Hidden Markov model (HMM) [7, 8], a simple frequency count of…”
Improved Learning of Dynamics Models for Control (2016, methodology): “2) utilizing existing supervised learning procedures such as Gaussian Process [8], Kernel Regression [9], and Support-Vector regression [21].”
Short-term load forecasting based on an adaptive hybrid method (2006, background): “…risk minimization principle to estimate a function by minimizing an upper bound of the generalization error, SVMs are shown to be very resistant to the over-fitting problem, eventually achieving a high generalization performance in solving forecasting problems of various time series [16], [17].”
Extrapolation and learning equations (2016, methodology): “By our nomenclature, this is typically rather an interpolation task, when the prediction is based on the behaviour of the series at earlier time steps but with similar value distribution [Györﬁ et al., 2013; Müller et al., 1997].”