Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

A forward constrained selection algorithm for probabilistic neural network

A new probabilistic neural network (PNN) learning algorithm based on forward constrained selection (PNN-FCS) is proposed. An incremental learning scheme is adopted such that at each step, new neurons, one for each class, are selected from the training samples arid the weights of the neurons are estimated so as to minimize the overall misclassification error rate. In this manner, only the most significant training samples are used as the neurons. It is shown by simulation that the resultant networks of PNN-FCS have good classification performance compared to other types of classifiers, but much smaller model sizes than conventional PNN.

Trade-off associated with selection for increased ability to resist parasitoid attack in Drosophila melanogaster

Costs of resistance are widely assumed to be important in the evolution of parasite and pathogen defence in animals, but they have been demonstrated experimentally on very few occasions. Endoparasitoids are insects whose larvae develop inside the bodies of other insects where they defend themselves from attack by their hosts' immune systems (especially cellular encapsulation). Working with Drosophila melanogaster and its endoparasitoid Leptopilina boulardi, we selected for increased resistance in four replicate populations of flies. The percentage of flies surviving attack increased from about 0.5% to between 40% and 50% in five generations, revealing substantial additive genetic variation in resistance in the field population from which our culture was established. In comparison with four control lines, flies from selected lines suffered from lower larval survival under conditions of moderate to severe intraspecific competition.

Cross-resistance following artificial selection for increased defense against parasitoids in Drosophila melanogaster

An increase in resistance to one natural enemy may result in no correlated change, a positive correlated change, or a negative correlated change in the ability of the host or prey to resist other natural enemies. The type of specificity is important in understanding the evolutionary response to natural enemies and was studied here in a Drosaphila-parasitoid system. Drosophila melanogaster lines selected for increased larval resistance to the endoparasitoid wasps Asobara tabida or Leptopilina boulardi were exposed to attack by A. tabida, L. boulardi and Leptopilina heterotama at 15 degrees C, 20 degrees C, and 25 degrees C. In general, encapsulation ability increased with temperature, with the exception of the lines selected against L. boulardi, which showed the opposite trend. Lines selected against L, boulardi showed large increases in resistance against all three parasitoid species, and showed similar levels of defense against A. tabida to the lines selected against that parasitoid. In contrast, lines selected against A. tabida showed a large increase in resistance to A. tabida and generally to L. heterotoma, but displayed only a small change in their ability to survive attack by L. boulardi. Such asymmetries in correlated responses to selection for increased resistance to natural enemies may influence host-parasitoid community structure.

Radial basis function classifier construction using particle swarm optimisation aided orthogonal forward regression

We develop a particle swarm optimisation (PSO) aided orthogonal forward regression (OFR) approach for constructing radial basis function (RBF) classifiers with tunable nodes. At each stage of the OFR construction process, the centre vector and diagonal covariance matrix of one RBF node is determined efficiently by minimising the leave-one-out (LOO) misclassification rate (MR) using a PSO algorithm. Compared with the state-of-the-art regularisation assisted orthogonal least square algorithm based on the LOO MR for selecting fixednode RBF classifiers, the proposed PSO aided OFR algorithm for constructing tunable-node RBF classifiers offers significant advantages in terms of better generalisation performance and smaller model size as well as imposes lower computational complexity in classifier construction process. Moreover, the proposed algorithm does not have any hyperparameter that requires costly tuning based on cross validation.

To 'be', and not to 'have': auxiliary selection in unaccusative verbs in Italian

This paper investigates the characteristics of unaccusative verbs in Italian with respect to the consistency with which these verbs select the auxiliaries ‘be’ (essere) and ‘have’ (avere) in compound tense forms. The study builds on the gradient approach to split intransitivity (Sorace 2000) by exploring the behaviour of 29 intransitive Italian verbs with respect to their core-peripheral features: auxiliary selection acceptability ratings and associated variance measures. Although there is clear support for the gradient approach in relation to the general order of semantic categories along the unaccusativity gradient, the results reveal that the ordering of subclasses within the Change group conflict with that currently proposed in the literature. In addition, the findings demonstrate the aspectual and lexical semantic characteristics of internally-caused change-of-state verbs in Italian require further investigation before their auxiliary selection behaviour can be properly understood. Furthermore, contrary to the gradient account, Existence verbs, the most stative and therefore the most peripheral subclass in the unaccusativity hierarchy, exhibit behaviour more characteristic of core unaccusative verbs. This study examines a wider range of semantic subclasses of unaccusative verbs than has hitherto been reported and identifies the core-peripheral boundary for Italian.1

Mean-tracking clustering algorithm for radial basis function centre selection

Radial basis functions can be combined into a network structure that has several advantages over conventional neural network solutions. However, to operate effectively the number and positions of the basis function centres must be carefully selected. Although no rigorous algorithm exists for this purpose, several heuristic methods have been suggested. In this paper a new method is proposed in which radial basis function centres are selected by the mean-tracking clustering algorithm. The mean-tracking algorithm is compared with k means clustering and it is shown that it achieves significantly better results in terms of radial basis function performance. As well as being computationally simpler, the mean-tracking algorithm in general selects better centre positions, thus providing the radial basis functions with better modelling accuracy

Selection of funding schemes by a borrowing decision model: a Hong Kong case study

In financial decision-making, a number of mathematical models have been developed for financial management in construction. However, optimizing both qualitative and quantitative factors and the semi-structured nature of construction finance optimization problems are key challenges in solving construction finance decisions. The selection of funding schemes by a modified construction loan acquisition model is solved by an adaptive genetic algorithm (AGA) approach. The basic objectives of the model are to optimize the loan and to minimize the interest payments for all projects. Multiple projects being undertaken by a medium-size construction firm in Hong Kong were used as a real case study to demonstrate the application of the model to the borrowing decision problems. A compromise monthly borrowing schedule was finally achieved. The results indicate that Small and Medium Enterprise (SME) Loan Guarantee Scheme (SGS) was first identified as the source of external financing. Selection of sources of funding can then be made to avoid the possibility of financial problems in the firm by classifying qualitative factors into external, interactive and internal types and taking additional qualitative factors including sovereignty, credit ability and networking into consideration. Thus a more accurate, objective and reliable borrowing decision can be provided for the decision-maker to analyse the financial options.

Variable selection algorithm for the construction of MIMO operating point dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm.

On the utility of input selection and pruning for financial distress prediction models

Analyzes the use of linear and neural network models for financial distress classification, with emphasis on the issues of input variable selection and model pruning. A data-driven method for selecting input variables (financial ratios, in this case) is proposed. A case study involving 60 British firms in the period 1997-2000 is used for illustration. It is shown that the use of the Optimal Brain Damage pruning technique can considerably improve the generalization ability of a neural model. Moreover, the set of financial ratios obtained with the proposed selection procedure is shown to be an appropriate alternative to the ratios usually employed by practitioners.