Multilayer feedforward networks are universal approximators

Hornik, Kurt; Stinchcombe, Maxwell B.; White, Halbert

doi:10.1016/0893-6080(89)90020-8

Cited by 18,334 publications

(8,751 citation statements)

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“…ear function to an arbitrary degree of accuracy (Hornik et al, 1989;Poggio et al, 1990). In the EBP-based training of an MLP network, the weights are adjusted iteratively such that the network, in response to the input patterns in the example set, accurately predicts the corresponding output values.…”

Section: Ann-ga and Ann-spsa Hybrid Modeling-optimization Formalismsmentioning

confidence: 99%

Genetic Programming Assisted Stochastic Optimization Strategies for Optimization of Glucose to Gluconic Acid Fermentation

Cheema

Sankpal

Tambe

et al. 2002

Biotechnology Progress

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This article presents two hybrid strategies for the modeling and optimization of the glucose to gluconic acid batch bioprocess. In the hybrid approaches, first a novel artificial intelligence formalism, namely, genetic programming (GP), is used to develop a process model solely from the historic process input-output data. In the next step, the input space of the GP-based model, representing process operating conditions, is optimized using two stochastic optimization (SO) formalisms, viz., genetic algorithms (GAs) and simultaneous perturbation stochastic approximation (SPSA). These SO formalisms possess certain unique advantages over the commonly used gradient-based optimization techniques. The principal advantage of the GP-GA and GP-SPSA hybrid techniques is that process modeling and optimization can be performed exclusively from the process input-output data without invoking the detailed knowledge of the process phenomenology. The GP-GA and GP-SPSA techniques have been employed for modeling and optimization of the glucose to gluconic acid bioprocess, and the optimized process operating conditions obtained thereby have been compared with those obtained using two other hybrid modeling-optimization paradigms integrating artificial neural networks (ANNs) and GA/SPSA formalisms. Finally, the overall optimized operating conditions given by the GP-GA method, when verified experimentally resulted in a significant improvement in the gluconic acid yield. The hybrid strategies presented here are generic in nature and can be employed for modeling and optimization of a wide variety of batch and continuous bioprocesses.

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Section: Ann-ga and Ann-spsa Hybrid Modeling-optimization Formalismsmentioning

confidence: 99%

Genetic Programming Assisted Stochastic Optimization Strategies for Optimization of Glucose to Gluconic Acid Fermentation

Cheema

Sankpal

Tambe

et al. 2002

Biotechnology Progress

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show abstract

“…Artificial neural networks (ANN) may be viewed as a generalization of these classical approaches, which allows us to model another type of nonlinearities in the data in addition to long memory. Concisely, neural networks are semi-parametric non-linear models, which are able to approximate any reasonable function Haykin (2007); Hornik et al (1989).…”

Section: Artificial Neural Network For Predicting Volatilitymentioning

confidence: 99%

“…The most widely used artificial neural network in financial applications with one hidden layer (Hornik et al, 1989) is the feed-forward neural network. The general feedforward or multilayered perception (MLP) network we use for volatility ν t forecasting may be described by the following equations:…”

Section: Artificial Neural Network For Predicting Volatilitymentioning

confidence: 99%

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Coupling High-Frequency Data with Nonlinear Models in Multiple-Step-Ahead Forecasting of Energy Markets' Volatility

Baruník

Křehlík

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: Terms of use: Documents inIn the past decade, the popularity of realized measures and various linear models for volatility forecasting has attracted attention in the literature on the price variability of energy markets. However, results that would guide practitioners to a specifc estimator and model when aiming for the best forecasting accuracy are missing. This paper contributes to the ongoing debate with a comprehensive evaluation of multiple-step-ahead volatility forecasts of energy markets using several popular high-frequency measures and forecasting models. To capture the complex patterns hidden to linear models commonly used to forecast realized volatility, this paper also contributes to the literature by coupling realized measures with artificial neural networks as a forecasting tool. Forecasting performance is compared across models as well as realized measures of crude oil, heating oil, and natural gas volatility during three qualitatively distinct periods covering the precrisis period, recent global turmoil of markets in 2008, and the most recent post-crisis period. We conclude that coupling realized measures with arti_cial neural networks results in both statistical and economic gains, reducing the tendency to over-predict volatility uniformly during all tested periods. Our analysis favors the median realized volatility, as it delivers the best performance and is a computationally simple alternative for practitioners.

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“…In this case, there is an optimal, fixed number of logistic transitions that can be understood as the number of limiting regimes (Trapletti, Leisch, and Hornik 2000, Medeiros and Veiga 2000, Medeiros, Teräsvirta, and Rech 2006. On the other hand, for ∞, the neural network model is a representation of any Borel-measurable function over a compact set (Hornik, Stinchombe, and White 1989, Hornik, Stinchcombe, White, and Auer 1994, Chen and Shen 1998, Chen and White 1998, Chen, Racine, and Swanson 2001. For large , this representation suggests a nonparametric interpretation as series expansion, sometimes referred to as sieveapproximator.…”

Section: The Nonlinear Har Modelmentioning

confidence: 99%

Forecasting Realized Volatility with Linear and Nonlinear Models

McAleer

Medeiros

2009

SSRN Journal

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In this paper we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 futures. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high frequency intra-day returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analyzed.

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Multilayer feedforward networks are universal approximators

Cited by 18,334 publications

References 1 publication

Genetic Programming Assisted Stochastic Optimization Strategies for Optimization of Glucose to Gluconic Acid Fermentation

Genetic Programming Assisted Stochastic Optimization Strategies for Optimization of Glucose to Gluconic Acid Fermentation

Coupling High-Frequency Data with Nonlinear Models in Multiple-Step-Ahead Forecasting of Energy Markets' Volatility

Forecasting Realized Volatility with Linear and Nonlinear Models

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