Neural Nets WIRN Vietri-99

The Extended Kalman Filter (EKF) algorithm for identification of a state space model is shown to be a sensible tool in estimating a Logistic Regression Model sequentially. A Gaussian probability density over the parameters of the Logistic model is propagated on a sample by sample basis. Two other approaches, the Laplace Approximation and the Variational Approximation are compared with the state space formulation. Features of the latter approach, such as the possibility of inferring noise levels by maximising the ‘innovation probability’ are discussed. Experimental illustrations of these ideas on a synthetic and a real world problems are shown.

The manner in which simple reverberations may be used to explain higher-order cognitive processes is developed from the ideas of Caianiello on reverberations [1]. In Part I, a preliminary description is given as to how such reverberations can be created, held and annihilated in a controlled manner. A discussion is then given, in Part II, of the nature of, and problems associated with, modelling the frontal lobes. In particular the manner they may be used to learn and generate temporal sequences — involving the manipulation of reverberations — is studied as part of analysis of working memory. An earlier model, that of ‘crumbling histories’, is reviewed, and problems it contains considered. A simplified model of the architecture of the frontal lobes, the ACTION network, is then considered. This in its turn is applied to study the task of temporal sequence storage and generation. A hard-wired version of the ACTION network and the representative dynamics of some of its neurons is shown. We then analyse the manner in which the model is affected by damage corresponding to loss of dopamine. A further section analyses the essential neural activity of creation and annihilation of multi-neuron reverberations in these simulations by bifurcation methods. Part III then considers how simple reverberations are relevant in the posterior cortex to support the emergence of consciousness and reaches the conclusion that this takes place in the inferior parietal lobes. Part IV gives conclusions.

Hydroinformatics is the field of study of the flow of information and its processing by knowledge as applied to the flow of fluids and their interaction with the aquatic environment. Many new modeling techniques have been entered in Hydroinformatics successfully. Among them, the application Computational Intelligence methods in Hydroinformatics is a relatively new area of research, even if some successful results have been already obtained. In this review we present a general overview of the applications of Computational Intelligence methods to Hydroinformatics and analyze some promising cases study concerning, namely, estimation of sanitary flows, rainfall prediction, unit hydrograph estimation, groundwater monitoring, flood waves propagation, and pump scheduling.

Support Vector Machines (SVMs) have been recently introduced as a new method for function estimation. In this survey we first review the main theoretical properties of SVMs, then present an implementation of SVMs able to work with training sets of very large size. Finally, we discuss two computer vision applications in which SVMs for both pattern recognition and regression estimation have been successfully employed.

In this paper, two methods named Backward Computation (BC) and Forward Computation (FC) for both on-line and batch backward gradient computation of a system output (for sensitivity analysis) or cost function (for learning) with respect to system parameters are derived by the Signal-Flow-Graph representation theory and its known properties. The system can be any causal, in general non-linear and time-variant, dynamic system represented by a SFG, in particular any feedforward, time delay or recurrent neural network In this work, we use discrete time notation, but the same theory holds for the continuous time case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (for the BC method) or its derivative (FC method) both obtained from the first by simple transformations without the complex chain rule expansions of derivatives usually employed.The BC and FC methods are dual and the adjoint and derivative SFGs (of the same SFG) can be obtained one from the other by graph transformations. The BC method is local in space but not in time while the FC is local in time but not in space.

In the work presented in this paper an Interval Arithmetic MLP (IAMLP) is used to detect the region in the input space to which an uncertainty decision should be appropriately associated. This region may be originated both by sub-regions which are not represented in the training set and by sub-regions where the probabilities of the two classes are very similar. To train the IAMLP, an algorithm will be presented which in particular is able detect the two certainty regions and the uncertainty one. The algorithm has been used for studying a simple artificial problem and one real-world application, the Breast Cancer data base.

The aim of this paper is to investigate the behavior of neural clusterons that learn in an unsupervised fashion by means of an information-theoretic based rule. Particularly the aim is to investigate on the clusteron’s statistical estimation abilities that naturally emerge from their learning behaviors.

The purpose of this work is to outline a computational architecture for the intelligent processing of sensorimotor patterns. The focus is on the nature of the internal representations of the outside world which are necessary for planning and other goal-oriented functions. A model named N-SOBoS (new self-organizing body-schema), based on the SOBoS model [10] and on the dual Extended Topology Representing Network architecture is proposed, which integrates a number of concepts and methods partly explored in the field [15, 11, 12]. The novelty and the biological plausibility is related to the global architecture which allows to deal with sensorimotor patterns in a coordinate-free way, using population codes as internal representations and communication channels among different cortical maps.

In fMRI the key problem of data analysis is to detect the weak BOLD signal component (about 2–5%) in the MR signal. Standard approaches, that typically use cross-correlation analysis or statistical parametric mapping, imply a presumptive knowledge of the expected stimulus-response pattern, which is not available in spontaneous events like hallucinations, sleep, or epileptic seizures. To evidence the possibility of analyzing these events by means of fMRI, we investigated a computational approach based on a self-organizing neural network (Neural Gas) that detects timedependent alterations in the regional intensity of the functional signal.

Long Short-Term Memory (LSTM,[1]) can solve many tasks not solvable by previous learning algorithms for recurrent neural networks (RNNs). We identify a weakness of LSTM networks processing continual input streams without explicitly marked sequence ends. Without resets, the internal state values may grow indefinitely and eventually cause the network to break down. Our remedy is an adaptive “forget gate” that enables an LSTM cell to learn to reset itself at appropriate times, thus releasing internal resources. We review an illustrative benchmark problem on which standard LSTM outperforms other RNN algorithms. All algorithms (including LSTM) fail to solve a continual version of that problem. LSTM with forget gates, however, easily solves it in an elegant way.

We present a method for analyzing the behavior of RBFs in an on-line scenario which provides a description of the learning dynamics without invoking the thermodynamic limit. Our analysis is based on a master equation that describes the dynamics of the weight space probability density for any value of the input space dimension. Because the transition probability appearing in the master equation cannot be written in closed form, some approximate form of the dynamics is developed. We assume a arbitrary small learning rate (small noise) and we derive in this limit the dynamic evolution of the means and the variances of the net weights. The analytic results are then confirmed by simulations.

We introduce a neural network architecture based on Smolensky’s Harmony Theory in order to solve a particular form of Binding Problem in a visual scene containing 4 subpatterns. The network performance is studied through computer simulations. The results obtained evidence how Harmony Theory can be used to solve Binding Problem, but its performance, even if significatively greater than chance level, is still too low.

Almeida et al. have recently proposed online algorithms for local step size adaptation in nonlinear systems trained by gradient descent. Here we develop an alternative to their approach by extending Sutton’s work on linear systems to the general, nonlinear case. The resulting algorithms are computationally little more expensive than other acceleration techniques, do not assume statistical independence between successive training patterns, and do not require an arbitrary smoothing parameter. In our benchmark experiments, they consistently outperform other acceleration methods as well as stochastic gradient descent with fixed learning rate and momentum.

A novel approach for segmentation of color images is proposed. The approach is based on a feed-forward neural network that learns to recognize the hue range of meaningful objects. Experimental results showed that the proposed method is effective and robust even in presence of changing environmental conditions. The described technique has been tested in the framework of the Robot Soccer World Cup Initiative (RoboCup). The approach is fully general and it may be successfully employed in any intermediate level image-processing task, where the color is a meaningful descriptor.

The human cardiovascular system (CVS) is a complex dynamical system. The determination of models for individual subjects/astronauts is of particular interest in (space) medicine. CVS models complexity and the large number of free parameters cause standard system identification methods to fail. A concept named aspect is introduced. This concept represents independent components of dynamical systems. Aspects are closely related to projection pursuit, independent component analysis and model selection. Using this concept it was possible to identify individualized CVS models that reproduce the shift in cardiovascular reaction due to exposure to weightlessness. The application of MLPs to approximate single aspects of the CVS (model) allows to perform identification in real time.

In this paper a Neural Networks based approach is presented to identify the noise in the VIRGO context. VIRGO is an experiment to detect Gravitational Waves by means of a Laser Interferometer. Preliminary results appear to be very promising for data analysis of realistic Interferometer outputs.

Wavelets are a powerful tool for multi-resolution analysis as they combine spatial and frequency locality. In this paper an efficient procedure to compute the Wavelet coefficients, called lifting schema, is illustrated. It can be applied efficiently to construct Wavelet networks. Results on face reconstruction operated at different resolution are reported and discussed.

We present a novel approach for the reconstruction of coded images and video, which permits fast recovery of the data with good quality in case of limited channel bandwidth. It is based on the use of a neural network which is able to interpolate the DC components of the coded data with higher accuracy and lower artifacts with respect to standard interpolators.

A status report is presented on microcalcification clusters search in the frame of the CALMA project. CALMA’s purpose is to build a mammographic database and to develop automatic tools for the detection of breast cancers. A microcalcification is a very brilliant object, but rather small (0.1 to 1.0 mm in diameter). Some of them, either grouped in cluster or diffused may indicate the presence of a tumour. In the following 250 images with microcalcifications from our database have been analyzed, and a CAD tool has been designed to detect clusters, reaching a correct classification of 88%.

Classification problems involving signals can benefit from the application of subspace neural networks. In order to fully exploit them, a constructive approach based on learning theory is mandatory. A possible method having these characteristics is proposed in the present contribution. It yields satisfactory performances, as illustrated by the results obtained with the well-known sonar benchmark.

Face recognition is an important application of image processing and a recent paper has compared various methods of processing images of faces. The best of these methods is a complicated linear projection based system, which successfully copes with images having variable expression, pose and facial lighting. This paper considers how a simple weightless neural network, with simple preprocessing, compares with the more complicated method.

A status report is presented on the massive lesions search in the frame of the CALMA project. CALMA’s main purpose is to collect a database of mammographic images, developing CAD tools to be used as a second radiologist in the classification of breast tumoural disease. Massive lesions are rather large objects to be detected, but they show up with a faint contrast slowly increasing with time. The need for tools able to recognize such a lesion at an early stage is therefore apparent. The work performed on images collected from Italian hospitals in the last year, as well as on images available from public databases is here presented, indicating, at this stage, a number of false positives of the order of 3 per image keeping a large sensitivity on our sample. This achievement although improvable, is comparable with results obtained by other groups working on the same subject.

This paper presents a method for classification of Synthetic Aperture Radar (SAR) images [1], based on the joint exploitation of a novel Wavelet Filtering Algorithm [2] and Neural Networks [3]. An illustrative example is presented that shows how the use of the proposed technique of Wavelet Filtering allows both to mitigate negative effects of multiplicative noise (speckle) and to classify the considered image without resolution decrease. The proposed Wavelet Filtering, applied on the image, provides four images (an approximation image and three detail images); detail images have the same resolution as original image. The use of Wavelet Filtering (WF) on the detail images jointly to a Multilayer Feedforward Network allows us to reduce some of typical drawbacks of the SAR classification problems, and thus to have a more efficient tool with respect to the traditional approach. The proposed method is tested on a real SAR image, and it is compared with traditional approaches based on MLP use, and on FFT-2Dfiltering-MLP technique.

In this paper we present a neural network based estimator system which performs well the frequency extraction from unevenly sampled signals. It uses an unsupervised Hebbian nonlinear neural algorithm to extract the principal components which, in turn, are used by the MUSIC frequency estimator algorithm to extract the frequencies.We generalize this method to avoid an interpolation preprocessing step and to improve the performance by using a new stop criterion to avoid overfrtting.The experimental results are obtained comparing our methodology with the others known in literature.

A naturally structured information is typical in symbolic processing. Nonetheless, learning in connectionism is usually related to poorly organized data, like arrays or sequences. For these types of data, classical neural networks are proven to be universal approximators.Recently, recursive networks were introduced in order to deal with structured data. They also represent a universal tool to approximate mappings between graphs and real vector spaces. In this paper, an overview of the present state of the art on approximation in recursive networks is carried on. Finally, some results on generalization are reviewed, establishing the VC-dim for recursive architectures of fixed size.

This paper describes an Object Oriented software environment for ANN’s simulation. A key feature of our software is that it uses Persistence, by means of an Object Oriented Data Base. Moreiver, the simulator is Parallel: it is being developed using multithreading, so that efficiency and portability have been obtained. Some preliminary results are shown.

We present a numerical and structural comparison of three neural PCA techniques: The GHA by Sanger, the APEX by Kung and Diamataras, and the ψ-APEX first proposed by the present author in

Clustering optimization is pursued in the present work by relying on a simple imitation of a physical law: the gravitational attraction. The resulting algorithm belongs to the category of hierarchical clustering. It is based on a merging approach in a scale-space, where the given data are represented. Its performance depends on a suitable quality index that indirectly measures the compactness and isolation of the clusters. This index suggests that the “natural” partition of clusters should be stable over a considerable scale parameter interval (lifetime). The effect of this stability index on the proposed algorithm is illustrated by some clustering examples.

Usually the Hebbian learning spontaneously seems to produce associative memory behavior in the network where they are applied. The unsupervised learning performed by the Hebbian rule, automatically creates associations into the network as soon as the responses to the inputs are computed. The paradigm we are discussing here is different from the classical unsupervised learning paradigm, and it is a quite general solution for the implementation of a a Hebbian rule in a Boolean neural network. Our system may not be seen as an associative memory only, it is both a controller and a classifier.

The semiparametric Support Vector Machine (SVM) has recently been introduced as a generalization of the classical SVM to the case in which some a priori knowledge about the considered problem is available. Semiparametric SVM training requires that we solve an optimization problem very similar (it only imposes a larger number of equality constraints) to that to be solved for classical SVM training. In both cases training is usually performed by means of existing software packages. Since this black-box approach may be undesirable, with reference to the classical SVM, some simple and explicit algorithms, difficult to extend to the semiparametric case, have recently been proposed. In this paper we introduce a simple iterative algorithm for semiparametric SVM training which compares well with some typical software packages, can be simply implemented and has minimal memory requirements.

The solution of binary classification problems is obtained by employing a new learning method, called Hamming Clustering (HC). It is able to build in a constructive way a two-layer perceptron with binary weights, which can be easily implemented by means of conventional logical ports.This technique generalizes the information contained in the given training set by combining input patterns that are close each other according to the Hamming distance. The output class is assigned in a competitive way, thus allowing the treatment of ambiguous samples.The application of HC to the signal prediction in genomic sequences shows its ability to determine regularities in complex problems.

The extraction of a set of rules underlying a classification problem is performed by applying a new algorithm reconstructing the AND-OR expression of any Boolean function from a given set of samples.The basic kernel of the method, called Hamming Clustering (HC), is the generation of clusters of input patterns that belong to the same class and are close each other according to the Hamming distance. Inputs are identified and neglected, which do not influence the final output, thus automatically reducing the complexity of the final set of rules.The performances of HC are evaluated through artificial and real-world benchmarks: its application to the breast cancer prognosis leads to the derivation of a small set of rules solving the associated classification problem.

This paper begins a systematic validation for a simple and reliable artificial neural network model that can be directly related to the main behaviour of biological neural networks. The sigmoid-plus-linear filter appears to be a promising candidate if the sigmoidal function is calculated in reference to the pulse generation refractory effects. We directly compare a classical spiking neuron model with a scheme based on a sigmoidal function plus a linear filter. The filter is computed as the best least squares fit to the output of the spiking model. The results seem to confirm that FIR and IIR neural networks may be able to represent the essence of the signal processing performed by biological neurons.

In this paper it is shown that the ability of classification and the ability of approximating a function are correlated to the value (in the training points) of the gradient of the output function learned by the network.It has been designed a feedforward neural network (“αNet”) that makes use of the Hermite function regression formula to approximate its hidden unit activation functions; the Hermite algorithm leads to a smooth function approximation, hence it is obtained a low value of the gradient of the output function of each output unit.Experimental results, concerning the 5-parity and the two-spiral problems, show the better skill of classification and interpolation of ocNet with respect to a traditional feedforward network that uses sigmoids as activation function of the hidden units.

This paper is centered on the analysis of lateral connections in a network of neurons following BCM synaptic modification theory. This is a non-supervised algorithm, based on properties inspired by the behaviour of real neurons in hyppocampus and visual cortex, that allows synaptic strength to increase or decrease according to a time-varying threshold based on the previous “history” of neural activity. From a statistical point of view it represents a Projection Pursuit (PP) method based on an Objective Function that seeks “interesting” projections in input space, along those directions presenting statistical properties far from normal (gaussian). After a short introduction to BCM theory, we test various schemes of lateral connectivity between neurons receiving the same inputs, using assumptions inspired by the anatomical and functional properties of visual cortex of evolved mammals (like primates and cats). Using computer simulations, the different schemes (uniform, random, gaussian, coulombian, linearly and exponentially decaying connections) were compared in relation to their ability to improve selectivity and to form a “metric”, namely to preserve the correspondence between close inputs and the topology of the corresponding activated neurons, in the case of linearly dependent inputs.

The analog VLSI on-chip learning implementation looks attractive for a wide range of applications due to its promising performances. On the other hand, precision requirements seem to be too difficult to be satisfied through the analog circuit approach.In this paper we present the analog on-chip learning implementation of a gradient descent learning algorithm; to overcome main problems, we adopted a Weight Perturbation learning algorithm and, from the circuit implementation point of view, current mode and translinear operated circuits. The proposed architecture is very efficient in terms of speed, size and power consumption; moreover it exhibits also an augmented scalability and modularity.

This paper describes a method for the recognition of dynamic gestures using a combination Neural Network/ discrete Hidden Markov Model. This work deals with four topics. First a reliable and robust person localization task is presented. Then we focus on the view-based recognition of the user’s static gestural instructions from a predefined vocabulary based on both a skin color model and statistical normalized moment invariants. The segmentation of the postures occurs by means of the skin color model based on the Mahalanobis metric. From the resulting binary image containing only regions which have been classified as skin candidates we extract translation and scale invariant moments. Further a Kohonen Self Organizing Map (SOM) is used to cluster the feature space. After the self-organizing process we modify the SOM weight vectors using the Learning Vector Quantization (LVQ) method causing the weights to approach the decision boundaries and we quantize each of them into a symbol. Finally, the symbol sequence extracted from time-sequential images is used as input for a system of discrete Hidden Markov Models (DHMMs).To train and test the system we gathered the data from four people performing five repetitions of each of five movements from our vocabulary (stop, go to left, go to right, hello-waving left and hello-waving right). The system uses input from a color video camera and is user-independent.

This paper presents a preliminary study about the design of an intelligent on-line monitoring system to urban environment modeling and prediction. The area of interest is that of the small town of Villa San Giovanni, in Southern Italy, which experiences a very peculiar condition of practical as well as scientific appeal. NNs are used as a basis for modeling interactions among many variables in order to predict well in advance a strong pollution episode may take place. The NN model is supported by a fuzzy knowledge based system which is able to extract the underlying correlation among different types of variables. The fuzzy logic approach is also used to derive statement which may help local politicians to explain their planned actions in order to prevent acute pollution episodes.

This paper proposes the use of Fuzzy Neural Network (FNN) approaches for the early detection of disruption in tokamak plasmas. The fuzzy neural models is able to combine signals from various different plasma diagnostics in order to make an estimation of the expected time of disruption. This is, in turn, useful for having sufficient margin to initiate a disruption avoidance action. The inclusion of many diagnostic measurements results in a much more accurate prediction than that provided by traditional physical approaches. The use of fuzzy logic concept is suggested by the consideration that those previous techniques make use of expert knowledge for deciding about the onset of a disruption. In addition, learning approaches allow to tune the model. The proposed method appears to be a step forward with respect to more conventional NN approach.

This paper addresses the use of neural network methods to perform real-time quality control in industrial assembly lines of DC Permanent Magnet Motors (PM). This task can be viewed as a difficult non-linear inverse identification problem. Due to long parameter setting time, noisy environment and in some cases human supervision requirements, these methods are not adequate for realtime applications. Moreover, PM quality control requires the satisfaction of particular specifications rather than simple model parameter identification. So neural networks seem to be a promising paradigm.In this study we apply fast adaptive spline networks to perform complex model inversion and reduce the effect of noise on the data. Experimental results demonstrate the effectiveness of the proposed method.

The analysis of non linear dynamic systems is a very important field of research for a lot of real applications. Mainly for economical and financial dynamic systems, sometimes it is very difficult to define a mathematical model, both owing to the lack of knowledge relative to the input-output relationships, and the unpossibility to reproduce artificially the data with repeated experiments. On the other side, a fuzzy logic system can identify a model even from a scarce data base, with other advantages, that are robustness, adaptive, and noise filtering properties, easiness of implementation, maintenance, comprehensibility. For real financial markets we hypothyse that time series shown some characteristic dynamic behaviour that can be observed during the time evolution, the sampled values being the realisation of an unknown, and maybe complex, dynamical system generated by an unknown function f, like the following one: $$x(t +1) = f\{x(t -k + 1),...,x(t - 1),x(t)\}+ \varepsilon(t)$$ where ε(t) is the error component. This idea is the main point of all the quantitative analysing methods, like auto-regressive linear model, non linear approach, up to Artificial Intelligence methods. The efficient market hypothesis, see [20], [50], contrasts with the presence of a deterministic component, but now this point of view is supported both by theoretical and statistical consideration, partially justified by the psychological behaviour of the investors, see [18]. In this way, some typical patterns can be observed and classified. Let us point out again the difficult that we usually encounter when analysing a financial time series, which often shows complex dynamic behaviour like chaotic motion [32].

Nowdays neural networks (NN) are applied in the most various fields and are actually receiving a lot of attention among the researcher’s community. In this paper we will provide a review of some NN applications in economics. We distinguish the applications according to the main objectives achieved by NN in this field: prediction, classification and modelingeconomic theory. It is a matter of fact that NN share with statistics a lot of methodological and computational aspects [9] as well as many fields of application. In this framework we introduce a general strategy for astatistical approach to NN which allows to use NN in a statistical context taking into account typical statistical applications problems, such as the selection and coding of the variables, the sample representativeness but more the interpretation, visualization and stability of the results.

The main aim of this paper is to design the connection between economic models and new planning tools (neural networks) in a complex economy. Very interesting features of these systems are: self-organisation, learning and self-renforcing mechanisms. These properties are discussed under different points of view in the paper.

After a survey of literature, we analyse the main experiences of economic forecasting using NN. The review aims at two purposes: it provides a general summary of the work in ANN forecasting done to date and it furnishes guidelines for neural network modelling. Particular attention is given to the peculiarity of economic data (high noise, non stationary, and small sample size signals) and to the contrast between model and data driven approaches. We discuss fundamental limitations and inherent difficulties when using neural networks for the economic forecasting. Recently, the traditional analogy with biological nervous systems has been considered insufficient. A deeper understanding of theoretical foundations of these models is required. Some hints for assessing the correctness of NN implementation and their contribution to a better forecast are reported.

Becattini in his paper of 1998 [1] says that an ”industrial district”, in the Marshall sense, is a social and economic entity, placed in a fixed area, characterized by an industrious presence of population and of industrial companies. Sforzi, using the data of census of population of 1981, divides the Italian territory into 955 “local work systems. Brusco and Paba in [5], using the data of census of population from 1951 to 1991, present a mathematical algorithm which takes into account the qualifications proposed by Sforzi. This algorithm defines four indexes, which take account of different details. The first regards the manufacturer quota, the second the small (less than 100 employees) manufacturer quota, the third the specialization index, the fourth the small (less than 100 employees) sector quota. All the areas in which the four indexes are simultaneously greater than one are considered “industrial districts”. Unfortunately this algorithm is too restrictive, in the sense that, some “historical districts” don’ satisfy this algorithm. To solve this problem, we propose in this paper a Fuzzy System.[2],[16] It is composed of five input variables and one output variable. Four of the input variables are the four indexes proposed by Brusco and Paba, the fifth is the percentage of employees engaged in the territory we analyze. The output variable is an explicit score in percentage that evaluates to what extent that territory has the peculiarity typical of a district. In this score it is possible to see three things: 1) the classical districts, those which are considered by Brusco and Paba using the crisp valuation, are present; 2) the “historical districts” that were left out of the score by a too restrictive definition are recovered; 3) the new score offers a real classification of “industrial districts” whereas the classic result is “yes or no”. In this paper we have analyzed the clothing branch.

The aim of this work is to develop an equation to explain quarterly movements in personal consumption expenditure in durable goods and specifically in motor vehicles. In particular, we focus in the role of liquidity. Two sets of instruments are used. The description is done using a non-linear least squares (NLS) technique while the forecasting is done using a Neural Network. The model obtained using the NLS, even if showing a quite high goodness of fit, is quite unstable and the results are highly dependent on the starting values of some parameters. Furthermore, the high number of parameters estimated do not allow to perform a comprehensive set of econometric test. This set of reasons suggested to move to a method of forecasting able to overcome these problems. The tool used for perform the forecasting is a trained back-propagation MLP neural network.

In this paper a method is described for using neural networks to estimate the conditional mean of a non linear time series. Assuming a non constant conditional variance, the procedure allows to consider directly its estimation. The performance of the proposed approach is evaluated. A comparison with the standard technique is also presented using simulated data sets and financial time series representing daily prices of equities from the Italian stock market.