Variable modeling of fuzzy phenomena with industrial applications

Includes abstract. Includes bibliographical references (leaves 98-100)

Contributions to statistical machine learning algorithm

This thesis's research focus is on computational statistics along with DEAR (abbreviation of differential equation associated regression) model direction, and that in mind, the journal papers are written as contributions to statistical machine learning algorithm literature

Oil price forecasting using gene expression programming and artificial neural networks

This study aims to forecast oil prices using evolutionary techniques such as gene expression programming (GEP) and artificial neural network (NN) models to predict oil prices over the period from January 2, 1986 to June 12, 2012. Autoregressive integrated moving average (ARIMA) models are employed to benchmark evolutionary models. The results reveal that the GEP technique outperforms traditional statistical techniques in predicting oil prices. Further, the GEP model outperforms the NN and the ARIMA models in terms of the mean squared error, the root mean squared error and the mean absolute error. Finally, the GEP model also has the highest explanatory power as measured by the R-squared statistic. The results of this study have important implications for both theory and practice

Statistical-grey consistent grey differential equation modelling

Includes abstract. Includes bibliographical references (p. 152-156)

Modeling Boundaries of Influence among Positional Uncertainty Fields

Within a CIS environment, the proper use of information requires the identification of the uncertainty associated with it. As such, there has been a substantial amount of research dedicated to describing and quantifying spatial data uncertainty. Recent advances in sensor technology and image analysis techniques are making image-derived geospatial data increasingly popular. Along with development in sensor and image analysis technologies have come departures from conventional point-by-point measurements. Current advancements support the transition from traditional point measures to novel techniques that allow the extraction of complex objects as single entities (e.g., road outlines, buildings). As the methods of data extraction advance, so too must the methods of estimating the uncertainty associated with the data. Not only will object uncertainties be modeled, but the connections between these uncertainties will also be estimated. The current methods for determining spatial accuracy for lines and areas typically involve defining a zone of uncertainty around the measured line, within which the actual line exists with some probability. Yet within the research community, the proper shape of this \u27uncertainty band\u27 is a topic with much dissent. Less contemplated is the manner in which such areas of uncertainty interact and influence one another. The development of positional error models, from the epsilon band and error band to the rigorous G-band, has focused on statistical models for estimating independent line features. Yet these models are not suited to model the interactions between uncertainty fields of adjacent features. At some point, these distributed areas of uncertainty around the features will intersect and overlap one another. In such instances, a feature\u27s uncertainty zone is defined not only by its measurement, but also by the uncertainty associated with neighboring features. It is therefore useful to understand and model the interactions between adjacent uncertainty fields. This thesis presents an analysis of estimation and modeling techniques of spatial uncertainty, focusing on the interactions among fields of positional uncertainty for image-derived linear features. Such interactions are assumed to occur between linear features derived from varying methods and sources, allowing the application of an independent error model. A synthetic uncertainty map is derived for a set of linear and aerial features, containing distributed fields of uncertainty for individual features. These uncertainty fields are shown to be advantageous for communication and user understanding, as well as being conducive to a variety of image processing techniques. Such image techniques can combine overlapping uncertainty fields to model the interaction between them. Deformable contour models are used to extract sets of continuous uncertainty boundaries for linear features, and are subsequently applied to extract a boundary of influence shared by two uncertainty fields. These methods are then applied to a complex scene of uncertainties, modeling the interactions of multiple objects within the scene. The resulting boundary uncertainty representations are unique from the previous independent error models which do not take neighboring influences into account. By modeling the boundary of interaction among the uncertainties of neighboring features, a more integrated approach to error modeling and analysis can be developed for complex spatial scenes and datasets

Learning Bayesian network equivalence classes using ant colony optimisation

Bayesian networks have become an indispensable tool in the modelling of uncertain knowledge. Conceptually, they consist of two parts: a directed acyclic graph called the structure, and conditional probability distributions attached to each node known as the parameters. As a result of their expressiveness, understandability and rigorous mathematical basis, Bayesian networks have become one of the first methods investigated, when faced with an uncertain problem domain. However, a recurring problem persists in specifying a Bayesian network. Both the structure and parameters can be difficult for experts to conceive, especially if their knowledge is tacit.To counteract these problems, research has been ongoing, on learning both the structure and parameters of Bayesian networks from data. Whilst there are simple methods for learning the parameters, learning the structure has proved harder. Part ofthis stems from the NP-hardness of the problem and the super-exponential space of possible structures. To help solve this task, this thesis seeks to employ a relatively new technique, that has had much success in tackling NP-hard problems. This technique is called ant colony optimisation. Ant colony optimisation is a metaheuristic based on the behaviour of ants acting together in a colony. It uses the stochastic activity of artificial ants to find good solutions to combinatorial optimisation problems. In the current work, this method is applied to the problem of searching through the space of equivalence classes of Bayesian networks, in order to find a good match against a set of data. The system uses operators that evaluate potential modifications to a current state. Each of the modifications is scored and the results used to inform the search. In order to facilitate these steps, other techniques are also devised, to speed up the learning process. The techniques includeThe techniques are tested by sampling data from gold standard networks and learning structures from this sampled data. These structures are analysed using various goodnessof-fit measures to see how well the algorithms perform. The measures include structural similarity metrics and Bayesian scoring metrics. The results are compared in depth against systems that also use ant colony optimisation and other methods, including evolutionary programming and greedy heuristics. Also, comparisons are made to well known state-of-the-art algorithms and a study performed on a real-life data set. The results show favourable performance compared to the other methods and on modelling the real-life data

From 'tree' based Bayesian networks to mutual information classifiers : deriving a singly connected network classifier using an information theory based technique

For reasoning under uncertainty the Bayesian network has become the representation of choice. However, except where models are considered 'simple' the task of construction and inference are provably NP-hard. For modelling larger 'real' world problems this computational complexity has been addressed by methods that approximate the model. The Naive Bayes classifier, which has strong assumptions of independence among features, is a common approach, whilst the class of trees is another less extreme example. In this thesis we propose the use of an information theory based technique as a mechanism for inference in Singly Connected Networks. We call this a Mutual Information Measure classifier, as it corresponds to the restricted class of trees built from mutual information. We show that the new approach provides for both an efficient and localised method of classification, with performance accuracies comparable with the less restricted general Bayesian networks. To improve the performance of the classifier, we additionally investigate the possibility of expanding the class Markov blanket by use of a Wrapper approach and further show that the performance can be improved by focusing on the class Markov blanket and that the improvement is not at the expense of increased complexity. Finally, the two methods are applied to the task of diagnosing the 'real' world medical domain, Acute Abdominal Pain. Known to be both a different and challenging domain to classify, the objective was to investigate the optiniality claims, in respect of the Naive Bayes classifier, that some researchers have argued, for classifying in this domain. Despite some loss of representation capabilities we show that the Mutual Information Measure classifier can be effectively applied to the domain and also provides a recognisable qualitative structure without violating 'real' world assertions. In respect of its 'selective' variant we further show that the improvement achieves a comparable predictive accuracy to the Naive Bayes classifier and that the Naive Bayes classifier's 'overall' performance is largely due the contribution of the majority group Non-Specific Abdominal Pain, a group of exclusion