Warren S. Sarle. Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Group International Conference, April 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of neurons which enable a massively parallel processing of information by the brain. Therefore, in the relevant literature they are often characterized as adaptive and fault tolerating systems for information processing [16, p. 211] Accordingly, a number of surveys (e.g. 4] 6] 10] [21], 23] or [26] dealing with a managerial or economic background state that Artificial Neural Networks are characterized by their superior performance over statistical concepts (mostly regression models) Denton summarizes this fact as follows: The results of the designed experiment clearly ....

W. S. Sarle, "Neural networks and statistical models", in "Proceedings of the Nineteenth Annual SAS Users Group International Conference", April 1994.

....the internals of the architecture, and are based on the structure and function of biological neurons. Because of this opposite viewpoints about ANNs emerged. To reflect two different opinions about ANNs versus Statistics and Mathematics citations from two articles are given below. The first one[Sarle, 1994] is concerned with ANNs for data analysis, a classical field for statisticians, and gives a comprehensive comparison of ANNs and statistical models. Many NN researchers are engineers, physicists, neurophysiologists, psychologists, or computer scientists who know little about statistics and ....

....computers such as ordinary PCs. On a serial computer, NNs can be trained more efficiently by standard numerical optimization algorithms such as those used for non linear regression. Nonlinear regression algorithms can fit most NN models orders of magnitude faster than standard NN algorithms. [Sarle, 1994]. On the other side ANN researchers see developments in the ANN area as reflecting novel ideas. A reply on the claim backpropagation was just statics is given by Hanson: It s true. It s just statistics. And we re all just made out of atoms and so are tables. I mean really observations like ....

Sarle, W. S. (1994). Neural networks and statistical models. In Proceedings of the 19th Annual SAS Users Group International Conference, pages 1538--1550.

....that quantifies spatial autocorrelation is introduced in the spatial autoregression model (SAR) The logistic regression finds a discriminant surface, which is a hyperplane in feature space, as shown in Figure 4. Formally, a logistic regression based classifier is equivalent to a perceptron [12] [27], 11] which can only separate linearly separable classes. 2.2 Bayesian Classifiers Bayesian classifiers estimate fc using Bayes rule and compute the probability of the class labels ci given the data X as: Pr(cil X) Pr(Xlci)Pr(ci) 1) Pt(X) In the case of the location prediction problem, ....

W.S. Sarle. Neural Networks and Statistical Models. In Ptvceeding of 9th Annual SAS user gtvup conference. SAS Institue, 1994.

....network models with traditional statistical methods. In their paper, perceptrons like the feedforward neural networks are shown to have strong associations with discriminant analysis and regression, and unsupervised networks such as self organizing neural networks with cluster analysis. Sarle [23] translates neural network jargon into statistical terminology and illustrates the relationship between neural networks and statistical models such as generalized linear models, projection pursuit and cluster analysis. Warner and Misra [30] contrast neural networks to regression models. Schumacher ....

W.S. Sarle, Neural networks and statistical models, in: Proceedings of the 19th Annual SAS Users Group International Conference, 1994.

....of neurons which enable a massively parallel processing of information by the brain. Therefore, in the relevant literature they are often characterized as adaptive and fault tolerating systems for information processing [16, p. 211] Accordingly, a number of surveys (e.g. 4] 6] 10] [21], 23] or [26] dealing with a managerial or economic background state that Artificial Neural Networks are characterized by their superior performance over statistical concepts (mostly regression models) Denton summarizes this fact as follows: The results of the designed experiment clearly ....

W. S. Sarle, "Neural networks and statistical models", in "Proceedings of the Nineteenth Annual SAS Users Group International Conference", April 1994.

....a new approach to building predictive models for identifying prospective households. The new methodology combines genetic algorithms (GA s) for choosing predictive demographic variables with artificial neural networks (ANN s) for developing a model of consumer response. ANN s (Riedmiller, 1994; Sarle, 1994) and GA s (Goldberg, 1989; Yang and Honavar, 1998; Krishna and Murty, 1999) have been widely used in machine learning, pattern recognition, image analysis and data mining. In particular, ANN s have been recognized as a relatively new approach in finance and marketing applications such as stock ....

Sarle, W. (1994). Neural networks and statistical models. In Proc. 19th Annual SAS Users Group International Conference, pages 1538--1550. SAS Institute.

....[2] Table 1 compares models for the nave LIBOR prediction based 1 Note: It is our belief that neural network models for time series modeling and prediction are mainly nonlinear regression models. To avoid confusion we identify parameter model estimation with learning or adaption. See also [4]. 4 model RMSE random walk 0.4235 AR(1) 0.4236 ARIMA(1,1,1) 0.4233 MLP(i=1,h=0,o=1) 0.4229 MLP(i=1,h=5,o=1) 0.3985 MLP(i=5,h=5,o=1) 0.3922 traders estimated profit threshold 0.06 Table 1: RMSE for random walk, linear and nonlinear models, as well as estimated profit threshold (see ....

Warren Sarle. Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Group International Conference, 1994.

.... models (e.g. Bates and Watts, 1988; Borowiak, 1989) and, when applicable, the more traditional polynomial functional representations (e.g. Box and Draper, 1987; Myers, 1995) An in depth comparison between the statistical nonlinear regression and discriminant models and ANNs is given in (Sarle, 1994). Artificial neural networks and polynomial approximations are compared in (Carpenter and Barthelemy, 1993) There is, in addition, some related work that does not use ANNs for representation of a design space. Chen et al. 1995) propose a response surface based approach to robust design which ....

Sarle, W. S. (1994), "Neural Networks and Statistical Models," Proceedings of the Nineteenth Annual SAS Users Group International Conference, Cary, NC (SAS Institute), April.

.... and O 1 , O 2 , O 3 and O 4 are full length and motif neural network outputs for positive and negative classes, respectively (i.e. F, M, F and M scores, Figure 1) The logistic regression model is equivalent to a two layered neural network (i.e. perceptron) with a logistic activation function [Sarle, 1994]. We implemented the two layer perceptron by adopting the same feed forward and back propagation functions [Wu et al. 1992] A positive sequence is considered to be accurately predicted (i.e. true positive) if both the P score and the average neural network score (i.e. the average of the F ....

Sarle, W. S. (1994) Neural networks and statistical models.Proc. 9th Annual SAS Users Group Intn'l Conf.

....times the size of the training set in both olvq1 and lvq1. We use the default values of 0.3 and 0.03 for , the learning rate parameter, in olvq1 and lvq1, respectively. 6 T. S. LIM, W. Y. LOH AND Y. S. SHIH RBF: This is the radial basis function network implemented in the Sas tnn3.sas macro [44] for feedforward neural networks (http: www.sas.com) The network architecture is speci ed with the ARCH=RBF argument. In this study, we construct a network with only one hidden layer. The number of hidden units is chosen to be 20 of the total number of input and output units [2.5 (5 hidden ....

W. S. Sarle. Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Groups International Conference, pages 1538-1550, Cary, NC, 1994. SAS Institute, Inc. (ftp://ftp.sas.com/pub/neural/neural1.ps).

....which hitherto has not been accessible. In more recent years, however, these hopes have been dampened by revealing that artificial neural networks do not seem to be much more than reimplementations or modest extensions of classical models from mathematical statistics, pattern recognition (compare [Sarle 94, Ripley 96] or in this case signal processing. In this discussion of thesis and antithesis, many research groups have either struggled to prove that neural networks can indeed be superior to alternative techniques, or ventured to argue for the contrary. ANNDEE ( Enhancement of ....

....of neural networks for pattern recognition can be classified within the framework of mathematical statistics in a relatively straight forward way. Thus, at first sight, they do not seem to contribute much to the large body of statistical theory of data analysis. Partly following the outline in [Sarle 94] among others the following neural network models investigated within ANNDEE can be reinterpreted as statistical models: ffl perceptrons = linear discriminant analysis or regression ffl multilayer perceptrons = non linear variant of discriminant analysis or regression using superpositions ....

Sarle W.S.: Neural Networks and Statistical Models, Proceedings of the Nineteenth Annual SAS Users Group International Conference, Cary, NC: SAS Institute, pp 15381550, 1994.

....category and 0 otherwise, except for the last one which is the reference category. To avoid local optima, 10 preliminary trainings were conducted and the best estimates used for subsequent training. More details on the radial basis function network can be found in Bishop (1995) Ripley (1996) and Sarle (1994). 3 Descriptions of datasets In this section, we briefly describe the 16 datasets used in the study as well as any modifications that were made for our experiment. Fourteen of them are from real domains while two are artificially created. Thirteen datasets are obtained from the UCI Repository of ....

Sarle, W. S. (1994). Neural networks and statistical models, Proceedings of the Nineteenth Annual SAS Users Groups International Conference, SAS Institute, Inc., Cary, NC, pp. 1538--1550.

....lvq1. The number of iterations is ten times the size of the training set in both olvq1 and lvq1. We use the default values of 0.3 and 0.03 for ff, the learning rate parameter, in olvq1 and lvq1, respectively. RBF: This is the radial basis function network implemented in the SAS tnn3.sas macro (Sarle, 1994) for feedforward neural networks (http: www.sas.com) The network architecture is specified with the ARCH=RBF argument. In this study, we construct a network with only one hidden layer. The number of hidden units is chosen to be 20 of the total number of input and output units [2.5 (5 hidden ....

Sarle, W. S. (1994). Neural networks and statistical models, Proceedings of the Nineteenth Annual SAS Users Groups International Conference, SAS Institute, Inc., Cary, NC, pp. 1538--1550.

....good for generalization Our intent was not to introduce a novel learning algorithm and prove that it is better than other ones. Our intent was to introduce another way of using neural network to implement traditional statistical techniques, in accordance with the analysis in the other direction by [Sarle 1994] and [Ripley 1992] We do this in the realm of suggesting that for different types of data distribution different types of estimation techniques, and thus different types of neural networks, might be appropriate. Even though it can be proven that the well known types multilayer perceptron and ....

Sarle W.S.: Neural Networks and Statistical Models, Proceedings of the Nineteenth Annual SAS Users Group International Conference, 1994.

....before, a number of the constructive procedures have been inspired by statistical techniques like MARS, PPR, and GMDH. The close relationship between various statistical methodologies (like discriminant analysis, regression and cluster analysis) and neural network models has been discussed in [5, 9, 10, 27, 77, 78, 85]. A number of other nonlinear regression techniques may possibly also have neural network formulations. Also, although the approximation capabilities of many network architectures have been examined extensively in recent years, the convergence properties of most constructive procedures are still ....

W.S. Sarle. Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Group International Conference, April 1994.

....Proben1 Database, Pattern Recognition, Artificial Neural Networks. 1 INTRODUCTION Recently artificial neural networks (ANNs) have been widely advocated as tools for solving many decision modeling problems. Basically, most ANNs can be considered as non linear, non parametric regression [GBD92, Sar94] techniques. Contrary to parametric regression in which rigid assumptions are made about the model structure, artificial neural networks, being non parametric, make no assumption about the distribution of the data and are thus 1 This research was supported by the National Science Foundation ....

Sarle, W.S. 1994. Neural Networks and Statistical Models. In Proceedings of the 19th Annual SAS Users Group International Conference, 1--13.

....and estimating generalization performance of neural networks also occur in a much wider context within statistics, and have been practised by statisticians for decades. The close relationship between various statistical methodologies and neural network models has been discussed widely [23] 134] [139], and there is still ongoing research to see how to borrow strength from each other. Finally, note that the various approaches to the control of network complexity, namely, regularization, and constructive and pruning algorithms, should not be treated as independent rivals. There are algorithms ....

W.S. Sarle, "Neural networks and statistical models," in Proceedings of the Nineteenth Annual SAS Users Group International Conference, Apr. 1994.

....tools such as confidence intervals and hypothesis testing which are missing in the field of neural networks. Recently, statisticians published works which established ties between statistics and neural networks, sometimes showing the equivalence of statistical and neural network models. Sarle [48] shows relationships between many neural networks and statistical models and translates the jargons in the two fields. Ripley [47] provides a very interesting overview of the similarities of neural networks and statistical models. 2.4.1 Perceptrons A perceptron with a linear output function ....

....perceptron like processing elements, such as the architecture that we will introduce later in this thesis. 2.4.2 Multi Layer Perceptrons Like a perceptron, a MLP has counterparts in statistics as well, depending on the number of hidden layers and the number of neurons in the hidden layers. Sarle [48] categorizes MLP s into the following three groups: ffl Small number of hidden neurons. MLP can be considered as a parametric model such as polynomial regression. ffl Moderate number of hidden neurons. MLP can be considered a quasi parametric model similar to projection pursuit regression. ....

Sarle, W. S. (1994) Neural Networks and Statistical Models. In Proc. Nineteenth Annual SAS Users Group Internat. Conference, April 1994.

....Extraction module can adversely affect classification performance. Consequently, a more accurate module was sought. Although single hidden layer MLPs are universal approximators, it has been suggested that networks with multiple hidden layers can be useful for extremely nonlinear problems [32, 34]. Consequently, several four layer MLPs were tried. They converged more rapidly, and to a smaller residual error. However, as with the single hidden layer networks, they were very sensitive to the learning rate, suggesting that a more sophisticated learning algorithm might be more appropriate. ....

Warren S. Sarle. Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Group International Conference, April 1994.

....scholarly discussions of these links see the excellent overview of Cheng Titterington [9] Responses to their article by, amongst others, Ripley [10] Amari [11] and McClelland [12] also commented on these relationships and suggested avenues for potential cross disciplinary work. Warren Sarle [13] has described how some of the simpler neural network models can be described in terms of, and implemented by, standard statistical techniques. Ripley s work [14] 15] along the same lines presents some empirical results comparing networks trained with different algorithms with nonparametric ....

W. S. Sarle, "Neural networks and statistical models," in Nineteenth Annual SAS Users Group International Conference, 1994.

.... excellent recent papers have been devoted to the subject [1 11, 13] Most of these publications are quite technical, however, either proving an equivalence property, e.g. 3, 11] comparing different techniques in the same framework [4, 5] or proposing a pierre de rosette for the statistician [9]. We take a different approach here, trying to provide a candid view on the resemblances and differences between the two fields. Our paper is therefore somewhat philosophical, rather than mathematical or experimental, and the reader in search of formulas and algorithms will be referred to the ....

....of the network can be used to predict the value of the output y when a new pattern x is presented at the input. Even on such a trivial example, there are many illuminating differences between the neural and statistical approach. The most obvious is, of course, the different jargons used (see [9] for a short statistics NNs dictionary) There is also the fact that statisticians tend to rely on formulas and equations to describe their methods, while graphical descriptions of NN architectures or NN algorithms are common practice in the neural network literature. However, there are more ....

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W.S. Sarle, "Neural Networks and Statistical Models," in Proceedings of the Nineteenth Annual SAS Users Group International Conference, Cary, NC, SAS Institute, April 3-4, 1994, pp. 1538-1550.

....of the graph of a feedforward network is its homogeneous modularity. Because of its modular architecture, the natural implementation of this network is a parallel one, whether in software or in hardware. Although most current activity is in software implementations on serial computers [49], the unique benefit of the feedforward network, i.e. fast speed of execution, can only be achieved through its realization in parallel hardware: electronic or optical, analog or digital. Of these parallel realizations, the digital electronic is the one that holds the most interest currently ....

W. S. Sarle. Neural network and statistical models. In Proceedings of the 19th Annual SAS Users Group International Conference, Cary, NC, April 1994. Also available as ftp://ftp.sas.com/pub/sugi19/neural/neural1.ps.

....computations. For ordinary computers that are not massively parallel, optimization algorithms such as those in several SAS procedures are usually far more efficient. This talk shows how to fit neural networks using SAS OR R fl , SAS ETS R fl , and SAS STAT R fl software. Introduction As Sarle (1994) points out, many types of neural networks (NNs) are similar or identical to conventional statistical methods. However, many NN training methods converge slowly or not at all. Hence, for data analysis, it is usually preferable to use statistical software rather than conventional NN software. For ....

Sarle, W.S. (1994), "Neural Networks and Statistical Models, " Proceedings of the Nineteenth Annual SAS Users Group International Conference, Cary, NC: SAS Institute.

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Warren S. Sarle. Neural networks and statistical models. In Proceedings of the Nineteenth Annual SAS Users Group International Conference, April 1994.

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Sarle Warren S. " Neural Networks and Statistical Models " Proceedings of the Nineteenth Annual SAS Users Group International Conference, April 1994

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Sarle W. S. "Neural Networks and Statistical Models" Proceedings of the Nineteenth Annual SAS Users Group International Conference, April, 1994

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W. S. Sarle, " Neural Networks and Statistical Models ", in Proceedings of the Nineteenth Annual SAS Users Group International Conference, pp. 1538 - 1550, Cary, NC, ( 1994 ).

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W. S. Sarle, "Neural networks and statistical models," presented at the 9th Annu. SAS User Group Conf., 1994.

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Sarle, W. S. 1994. Neural networks and statistical models. Proceedings of the 19th Annual SAS Users Group International Conference.

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W.S. Sarle, Neural networks and statistical models, Proceedings of the Nineteenth Annual SAS Users Group International Conference, 1994.

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W. Sarle, Neural Networks and Statistical Models, Proceedings of the 19 th SAS Users Group Int. Conf. (1994).

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Sarle, W. S. (1994b). Neural Networks and Statistical Models. In Proceedings of the Nineteenth Annual SAS Users Group, Cary, NC:, pp. 1538--1550. SAS Institute.

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Sarle WS. Neural networks and statistical models. Proceedings of the 19th Annual SAS Users Group International Conference. 1994.

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