Neural Networks: A Review from a Statistical Perspective

Cheng, Bing; Titterington, D. M.

doi:10.1214/ss/1177010638

Cited by 873 publications

(405 citation statements)

References 127 publications

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“…This modelling technique has permeated literature in many fields including statistics (e.g., Ripley 1994Ripley , 1996Stern 1996;Cheng and Titterington 1994), remote sensing (e.g., Atkinson and Tatnall 1997;Skidmore et al 1997;Wang and Dong 1997), and ecology (e.g., Lek et al 1996, Lek andGuegan 1999).…”

Section: Artificial Neural Networkmentioning

confidence: 99%

Comparing five modelling techniques for predicting forest characteristics

Moisen

Frescino

2002

Ecological Modelling

375

244

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Broad-scale maps of forest characteristics are needed throughout the United States for a wide variety of forest land management applications. Inexpensive maps can be produced by modelling forest class and structure variables collected in nationwide forest inventories as functions of satellite-based information. But little work has been directed at comparing modelling techniques to determine which tools are best suited to mapping tasks given multiple objectives and logistical constraints. Consequently, five modelling techniques were compared for mapping forest characteristics in the Interior Western United States. The modelling techniques included linear models (LMs), generalized additive models (GAMs), classification and regression trees (CARTs), multivariate adaptive regression splines (MARS), and artificial neural networks (ANNs). Models were built for two discrete and four continuous forest response variables using a variety of satellite-based predictor variables within each of five ecologically different regions. All techniques proved themselves workable in an automated environment. When their potential mapping ability was explored through simulations, tremendous advantages were seen in use of MARS and ANN for prediction over LMs, GAMs, and CART. However, much smaller differences were seen when using real data. In some instances, a simple linear approach worked virtually as well as the more complex models, while small gains were seen using more complex models in other instances. In real data runs, MARS and GAMS performed (marginally) best for prediction of forest characteristics.

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Section: Artificial Neural Networkmentioning

confidence: 99%

Comparing five modelling techniques for predicting forest characteristics

Moisen

Frescino

2002

Ecological Modelling

375

244

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“…Steps (2) and (3) are often coupled and considered in line with each other since learning/fitting techniques have evolved to be highly specific and dependent on the metamodel used. Examples of popular metamodels include polynomials (Montgomery, 2008), Kriging (Sacks et al, 1989), neural networks (Cheng and Titterington, 1994), radial basis functions (Fang and Horstemeyer, 2006;Regis and Shoemaker, 2013), multivariate adaptive regression splines (Friedman, 1991), and inductive learning (Wang and Shan, 2007).…”

Section: Metamodelingmentioning

confidence: 99%

Statistical metamodeling of dynamic network loading

Song

Han

Wang

2018

Transportation Research Part B: Methodological

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Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses the dynamics of flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times. It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult problem, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, while possessing closed-form Jacobians. The implications of these desirable properties for DTA research and model applications are discussed in depth.

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“…Fortunately, to handle such a situation, an extremely versatile approach of "Artificial neural networks" (ANN) is developed rapidly. Cheng and Tittering ton (1994) have reviewed the ANN methodology from a statistical perspective, while Warner and Misra (1996) have laid emphasis on understanding of ANN as a statistical tool. Recently, Pratheepa et al, discussed the utility of ANN models in biological studies (Pratheepa, 2011).…”

Section: Artificial Neural Network Modelsmentioning

confidence: 99%