Abstract-Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications.
Regression problems provide some of the most challenging research opportunities in the area of machine learning, and more broadly intelligent systems, where the predictions of some target variables are critical to a specific application. Rainfall is a prime example, as it exhibits unique characteristics of high volatility and chaotic patterns that do not exist in other time series data. This work's main impact is to show the benefit machine learning algorithms, and more broadly intelligent systems have over the current state-of-the-art techniques for rainfall prediction within rainfall derivatives. We apply and compare the predictive performance of the current state-of-the-art (Markov chain extended with rainfall prediction) and six other popular machine learning algorithms, namely: Genetic Programming, Support Vector Regression, Radial Basis Neural Networks, M5 Rules, M5 Model trees, and k-Nearest Neighbours. To assist in the extensive evaluation, we run tests using the rainfall time series across data sets for 42 cities, with very diverse climatic features. This thorough examination shows that the machine learning methods are able to outperform the current state-of-the-art. Another contribution of this work is to detect correlations between different climates and predictive accuracy. Thus, these results show the positive effect that machine learning-based intelligent systems have for predicting rainfall based on predictive accuracy and with minimal correlations existing across climates.
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Abstract-Rainfall is one of the most challenging variables to predict, as it exhibits very unique characteristics that do not exist in other time series data. Moreover, rainfall is a major component and is essential for applications that surround water resource planning. In particular, this paper is interested in the prediction of rainfall for rainfall derivatives. Currently in the rainfall derivatives literature, the process of predicting rainfall is dominated by statistical models, namely using a Markovchain extended with rainfall prediction (MCRP). In this paper we outline a new methodology to be carried out by predicting rainfall with Genetic Programming (GP). This is the first time in the literature that GP is used within the context of rainfall derivatives. We have created a new tailored GP to this problem domain and we compare the performance of the GP and MCRP on 21 different data sets of cities across Europe and report the results. The goal is to see whether GP can outperform MCRP, which acts as a benchmark. Results indicate that in general GP significantly outperforms MCRP, which is the dominant approach in the literature.
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