Sequential input selection algorithm for long-term prediction of time series

Tikka, Jarkko; Hollmén, Jaakko

doi:10.1016/j.neucom.2007.11.037

Cited by 23 publications

(16 citation statements)

References 7 publications

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“…Recent years have seen an increasing interest on the development of reconstruction techniques for prediction purposes [12,[30][31][32][33][34][35][36][37][38][39]. These recent studies have focused on producing nonuniform delay coordinate vectors whereby each component is associated to a different delay time.…”

Section: A Backgroundmentioning

confidence: 99%

“…However, several alternatives exist ranging from derivative coordinates [44] or global principal value decomposition [45] to nonuniform DC vectors. The latter possibility has been extensively explored in the literature in recent years [12,[30][31][32][33][34][35][36][37][38][39][40][41][42]46]. All of these approaches can be described in terms of Fig.…”

Section: B Reconstruction Strategiesmentioning

confidence: 99%

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Optimal reconstruction of dynamical systems: A noise amplification approach

2011

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In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series.

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Section: A Backgroundmentioning

confidence: 99%

Section: B Reconstruction Strategiesmentioning

confidence: 99%

Optimal reconstruction of dynamical systems: A noise amplification approach

2011

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“…The traditional Forward-Backward strategy differs from the original Forward and Backward ones [20,19,18], in that it tries to alleviate some of the shortcomings of them both. It offers the flexibility to reconsider input variables previously discarded and vice versa to discard input variables Figure 3: Classical Forward-Backward: three steps define the algorithm; a Forward step, in which each unselected variable is considered separately for selection; a Backward step, in which each variable selected is considered for elimination; a decision step, in which the set of variables Θ tmp yielding the minimum error is retained.…”

Section: Variable Selection Strategy: Modified Forwardbackwardmentioning

confidence: 99%

“…In this paper, the aim is to predict one-step ahead for all 1 http://snap.stanford.edu/data/volumeseries.html 1000 time series [17,6,18,10,8,7,16,1] at once; that is, the prediction of the next hour volume for all the Meme phrases. In Section 2, the data preparation as well as the assumptions made on the underlying data structure.…”

Section: Introductionmentioning

confidence: 99%

Fast variable selection for memetracker phrases time series prediction

Miché

Chistiakova

Akusok

et al. 2012

Proceedings of the 5th International Conference on PErvasive Technologies Related to Assistive Environments

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This paper proposes a methodology using a fast variable selection as a modified version of the Forward-Backward algorithm. This methodology is adapted to the specificities of the data used: very small number of samples and high number of variables. Such data is generated using underlying dependencies and seasonality assumptions, from Meme phrases volume data. By the use of a resampling technique along with the proposed variable selection scheme, significant results are obtained, and the test Normalized Mean Square Error performances are improved. The results indicate that with the assumptions made on the data structure, variable selection is desirable. Also, the obtained information on the selected variables seem to cluster the time series in two very different classes: a set of approximately 600 series, which yield good NMSE, and seem to require very similar sets of variables for the prediction; and another set of 300 − 400 series, for which only the previous series value is of interest for the prediction. This first analysis clearly illustrates the future need to perform a more thorough analysis of the selected variables for each of the batch of series. * IKERBASQUE, Also, taking a close look at the possible dependences between the series inside a batch should give information as to why and how they are similar and have found themselves to be grouped under the same batch.

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“…In the first phase, input selection is carried out using a simple model, for example, linear models [7,48] or linear-in-the-parameter models, e.g. polynomials [26].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous input variable and basis function selection for RBF networks

Tikka¹

2009

Neurocomputing

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Input selection is advantageous in regression problems. For example, it might decrease the training time of models, reduce measurement costs, and circumvent problems of high dimensionality. Inclusion of useless inputs into the model increases also the likelihood of overfitting. Neural networks provide good generalization in many cases, but their interpretability is usually limited. However, selecting a subset of variables and estimating their relative importances would be valuable in many real world applications. In the present work, a simultaneous input and basis function selection method for the radial basis function (RBF) network is proposed. The selection is performed by minimizing a constrained cost function, in which sparsity of the network is controlled by two continuous valued shrinkage parameters. Each input dimension is weighted and the constraints are imposed on these weights and the output layer coefficients. Direct and alternating optimization procedures are presented to solve the problem. The proposed method is applied to simulated and benchmark data. In the comparison with existing methods, the resulting RBF networks have similar prediction accuracies with the smaller numbers of inputs and basis functions.

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Sequential input selection algorithm for long-term prediction of time series

Cited by 23 publications

References 7 publications

Optimal reconstruction of dynamical systems: A noise amplification approach

Optimal reconstruction of dynamical systems: A noise amplification approach

Fast variable selection for memetracker phrases time series prediction

Simultaneous input variable and basis function selection for RBF networks

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