Wavelet Neural Networks: A Practical Guide

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

Constructing Prediction Intervals with Neural Networks: An Empirical Evaluation of Bootstrapping and Conformal Inference Methods

Artificial neural networks (ANNs) are popular tools for accomplishing many machine learning tasks, including predicting continuous outcomes. However, the general lack of confidence measures provided with ANN predictions limit their applicability, especially in military settings where accuracy is paramount. Supplementing point predictions with prediction intervals (PIs) is common for other learning algorithms, but the complex structure and training of ANNs renders constructing PIs difficult. This work provides the network design choices and inferential methods for creating better performing PIs with ANNs to enable their adaptation for military use. A two-step experiment is executed across 11 datasets, including an imaged-based dataset. Two non-parametric methods for constructing PIs, bootstrapping and conformal inference, are considered. The results of the first experimental step reveal that the choices inherent to building an ANN affect PI performance. Guidance is provided for optimizing PI performance with respect to each network feature and PI method. In the second step, 20 algorithms for constructing PIs—each using the principles of bootstrapping or conformal inference—are implemented to determine which provides the best performance while maintaining reasonable computational burden. In general, this trade-off is optimized when implementing the cross-conformal method, which maintained interval coverage and efficiency with decreased computational burden

Construction of optimal prediction intervals for load forecasting problems

Short-term load forecasting is fundamental for the reliable and efficient operation of power systems. Despite its importance, accurate prediction of loads is problematic and far remote. Often uncertainties significantly degrade performance of load forecasting models. Besides, there is no index available indicating reliability of predicted values. The objective of this study is to construct prediction intervals for future loads instead of forecasting their exact values. The delta technique is applied for constructing prediction intervals for outcomes of neural network models. Some statistical measures are developed for quantitative and comprehensive evaluation of prediction intervals. According to these measures, a new cost function is designed for shortening length of prediction intervals without compromising their coverage probability. Simulated annealing is used for minimization of this cost function and adjustment of neural network parameters. Demonstrated results clearly show that the proposed methods for constructing prediction interval outperforms the traditional delta technique. Besides, it yields prediction intervals that are practically more reliable and useful than exact point predictions. <br /

Uncertainty Quantification in Neural-Network Based Pain Intensity Estimation

Improper pain management can lead to severe physical or mental consequences, including suffering, and an increased risk of opioid dependency. Assessing the presence and severity of pain is imperative to prevent such outcomes and determine the appropriate intervention. However, the evaluation of pain intensity is challenging because different individuals experience pain differently. To overcome this, researchers have employed machine learning models to evaluate pain intensity objectively. However, these efforts have primarily focused on point estimation of pain, disregarding the inherent uncertainty and variability present in the data and model. Consequently, the point estimates provide only partial information for clinical decision-making. This study presents a neural network-based method for objective pain interval estimation, incorporating uncertainty quantification. This work explores three algorithms: the bootstrap method, lower and upper bound estimation (LossL) optimized by genetic algorithm, and modified lower and upper bound estimation (LossS) optimized by gradient descent algorithm. Our empirical results reveal that LossS outperforms the other two by providing a narrower prediction interval. As LossS outperforms, we assessed its performance in three different scenarios for pain assessment: (1) a generalized approach (single model for the entire population), (2) a personalized approach (separate model for each individual), and (3) a hybrid approach (separate model for each cluster of individuals). Our findings demonstrate the hybrid approach's superior performance, with notable practicality in clinical contexts. It has the potential to be a valuable tool for clinicians, enabling objective pain intensity assessment while taking uncertainty into account. This capability is crucial in facilitating effective pain management and reducing the risks associated with improper treatment.Comment: 26 pages, 5 figures, 9 table