Integrating simulated annealing and delta technique for constructing optimal prediction intervals

This paper aims at developing a new criterion for quantitative assessment of prediction intervals. The proposed criterion is developed based on both key measures related to quality of prediction intervals: length and coverage probability. This criterion is applied as a cost function for optimizing prediction intervals constructed using delta technique for neural network model. Optimization seeks out to minimize length of prediction intervals without compromising their coverage probability. Simulated Annealing method is employed for readjusting neural network parameters for minimization of the new cost function. To further ameliorate search efficiency of the optimization method, parameters of the network trained using weight decay method are considered as the initial set in Simulated Annealing algorithm. Implementation of the proposed method for a real world case study shows length and coverage probability of constructed prediction intervals are better than those constructed using traditional techniques.

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.

Construction and optimisation of prediction intervals for neural network models

This thesis makes contributions to basic and fundamental research in the field of prediction interval construction using neural network models. It proposes novel methods for objective assessment, rapid construction, and optimisation of neural network-based prediction intervals for uncertainty quantification.

Optimizing the quality of bootstrap-based prediction intervals

The bootstrap method is one of the most widely used methods in literature for construction of confidence and prediction intervals. This paper proposes a new method for improving the quality of bootstrap-based prediction intervals. The core of the proposed method is a prediction interval-based cost function, which is used for training neural networks. A simulated annealing method is applied for minimization of the cost function and neural network parameter adjustment. The developed neural networks are then used for estimation of the target variance. Through experiments and simulations it is shown that the proposed method can be used to construct better quality bootstrap-based prediction intervals. The optimized prediction intervals have narrower widths with a greater coverage probability compared to traditional bootstrap-based prediction intervals.

Prediction intervals to account for uncertainties in travel time prediction

The accurate prediction of travel times is desirable but frequently prone to error. This is mainly attributable to both the underlying traffic processes and the data that are used to infer travel time. A more meaningful and pragmatic approach is to view travel time prediction as a probabilistic inference and to construct prediction intervals (PIs), which cover the range of probable travel times travelers may encounter. This paper introduces the delta and Bayesian techniques for the construction of PIs. Quantitative measures are developed and applied for a comprehensive assessment of the constructed PIs. These measures simultaneously address two important aspects of PIs: 1) coverage probability and 2) length. The Bayesian and delta methods are used to construct PIs for the neural network (NN) point forecasts of bus and freeway travel time data sets. The obtained results indicate that the delta technique outperforms the Bayesian technique in terms of narrowness of PIs with satisfactory coverage probability. In contrast, PIs constructed using the Bayesian technique are more robust against the NN structure and exhibit excellent coverage probability.

A point-based representation for intervals

Information about time or space is often expressed in terms of points or intervals, and the relations between points and intervals. The interval based representations fall into two distinct classes based on: (i) closure and (ii) minimal representation of the domain. The advantage of closure based representation is the minimal search time at the expense of time to construct the representation, and the storage requirement. Minimal representation optimises storage required, at the expense of construction and search time. Intervals can be represented in terms of their end points. The information about points can be effectively represented using the closure approach but intervals cannot be represented with their endpoints using a point algebra system.

This paper proposes a point based system of representation for interval relations that does not perform closure. Point information is represented in terms of the known relationships between points. The costs of such a representation lies between the expense of closure and minimisation. The time taken for search and construction is better than for minimisation but not as good as for closure. Respectively, the space used is better than for closure but not as good as for minimisation

Construction of neural network-based prediction intervals using particle swarm optimization

Prediction intervals (PIs) are excellent tools for quantification of uncertainties associated with point forecasts and predictions. This paper adopts and develops the lower upper bound estimation (LUBE) method for construction of PIs using neural network (NN) models. This method is fast and simple and does not require calculation of heavy matrices, as required by traditional methods. Besides, it makes no assumption about the data distribution. A new width-based index is proposed to quantitatively check how much PIs are informative. Using this measure and the coverage probability of PIs, a multi-objective optimization problem is formulated to train NN models in the LUBE method. The optimization problem is then transformed into a training problem through definition of a PI-based cost function. Particle swarm optimization (PSO) with the mutation operator is used to minimize the cost function. Experiments with synthetic and real-world case studies indicate that the proposed PSO-based LUBE method can construct higher quality PIs in a simpler and faster manner.