Mean Absolute Error Criterion Research Articles

Urban Water Demand Forecasting and Comparative Analysis by Artificial Neural Networks, Support Vector Machines and Box-Jenkins Methods

Water demand forecasting is currently being used in many fields such as the investment planning, the design of the water systems (treatment plants, storage, transmission and distribution lines), the operation of existing systems at optimal capacity, calculation of operation and investment costs, and determination of urban water management policies (pricing policy, water conservation, etc.). Therefore, it can be said that an accurate water demand forecast has a key role in the planning, design, operation, and management of water systems. In this study, it is aimed to forecast Diyarbakir city centre drinking water demand by using Artificial Neural Networks method and Winters’s Seasonal Exponential Smoothing and Box-Jenkins methods based on time series analysis, and to compare forecasts obtained. For this purpose, firstly the data related to the variables affecting the water demand of Diyarbakir city centre for the time interval of 2003 – 2013 has been collected and analyzed. Then, a drinking water demand forecast has been made on the basis of this data by using Artificial Neural Network, Winters’s Seasonal Exponential Smoothing, and Box-Jenkins methods. The forecasts obtained from these three methods have been compared according to Productivity, The Mean Square Error, The Root Mean Square Error and The Mean Absolute Percentage Error criteria. In comparison results, it was seen that, in all performance criteria, Artificial Neural Networks method has better forecast results than those methods based on time series analysis.

In silico prediction of the developmental toxicity of diverse organic chemicals in rodents for regulatory purposes.

The experimental determination of the developmental toxicity potential (LEL) of chemicals is not only tedious, time and resource intensive, but it also involves unethical tests on animals. In this study, we have established quantitative structure activity relationship (QSAR) models for predicting the developmental toxicity potential of chemicals in rodents following the OECD guidelines. Accordingly, decision tree forest (DTF) and decision tree boost (DTB) based local (L-QSAR), global (G-QSAR) and interspecies quantitative structure activity-activity relationship (ISC QSAAR) models were developed for estimating the LEL (lowest effective level) dose of chemicals for developmental toxicity in rats and rabbits. The structural features of chemicals responsible for developmental toxicity in rodents were extracted and used in QSAR/QSAAR analysis. The external predictive power of the developed models was evaluated through the internal and external validation procedures. In test data, the L-QSAR models (DTF, DTB) yielded R2 values of >0.846 (rat) and >0.906 (rabbit), whereas in G-QSAR, the correlation value was >0.870 between the measured and predicted endpoint values. In ISC QSAAR models, the R2 values in test data were 0.830 (DTF) and 0.927 (DTB), respectively. Values of various statistical validation coefficients derived from the test data (except rm2 in DTF based rat L-QSAR and ISC QSAAR models) were above their respective threshold limits, thus putting a high confidence in this analysis. The prediction quality of the developed QSAR/QSAAR models was also assessed using the mean absolute error (MAE) criteria and found good. The applicability domains of the constructed models were defined using the descriptor range, leverage, and standardization approaches. The results suggest that the developed QSAR/QSAAR models can reliably predict the developmental toxicity potential of structurally diverse chemicals in rodents, generating useful toxicity data for risk assessment in humans.

Neural network models for software development effort estimation: a comparative study

Software development effort estimation (SDEE) is one of the main tasks in software project management. It is crucial for a project manager to efficiently predict the effort or cost of a software project in a bidding process, since overestimation will lead to bidding loss and underestimation will cause the company to lose money. Several SDEE models exist; machine learning models, especially neural network models, are among the most prominent in the field. In this study, four different neural network models: Multilayer Perceptron, General Regression Neural Network, Radial Basis Function Neural Network, and Cascade Correlation Neural Network are compared with each other based on: (1) predictive accuracy centered on the Mean Absolute Error criterion, (2) whether such a model tends to overestimate or underestimate, and (3) how each model classifies the importance of its inputs. Industrial datasets from the International Software Benchmarking Standards Group (ISBSG) are used to train and validate the four models. The main ISBSG dataset was filtered and then divided into five datasets based on the productivity value of each project. Results show that the four models tend to overestimate in 80percent of the datasets, and the significance of the model inputs varies based on the selected model. Furthermore, the Cascade Correlation Neural Network outperforms the other three models in the majority of the datasets constructed on the Mean Absolute Residual criterion.

The Role of Auxiliary Variables in Deterministic and Deterministic-Stochastic Spatial Models of Air Temperature in Poland

Our study examines the role of auxiliary variables in the process of spatial modelling and mapping of climatological elements, with air temperature in Poland used as an example. The multivariable algorithms are the most frequently applied for spatialization of air temperature, and their results in many studies are proved to be better in comparison to those obtained by various one-dimensional techniques. In most of the previous studies, two main strategies were used to perform multidimensional spatial interpolation of air temperature. First, it was accepted that all variables significantly correlated with air temperature should be incorporated into the model. Second, it was assumed that the more spatial variation of air temperature was deterministically explained, the better was the quality of spatial interpolation. The main goal of the paper was to examine both above-mentioned assumptions. The analysis was performed using data from 250 meteorological stations and for 69 air temperature cases aggregated on different levels: from daily means to 10-year annual mean. Two cases were considered for detailed analysis. The set of potential auxiliary variables covered 11 environmental predictors of air temperature. Another purpose of the study was to compare the results of interpolation given by various multivariable methods using the same set of explanatory variables. Two regression models: multiple linear (MLR) and geographically weighted (GWR) method, as well as their extensions to the regression-kriging form, MLRK and GWRK, respectively, were examined. Stepwise regression was used to select variables for the individual models and the cross-validation method was used to validate the results with a special attention paid to statistically significant improvement of the model using the mean absolute error (MAE) criterion. The main results of this study led to rejection of both assumptions considered. Usually, including more than two or three of the most significantly correlated auxiliary variables does not improve the quality of the spatial model. The effects of introduction of certain variables into the model were not climatologically justified and were seen on maps as unexpected and undesired artefacts. The results confirm, in accordance with previous studies, that in the case of air temperature distribution, the spatial process is non-stationary; thus, the local GWR model performs better than the global MLR if they are specified using the same set of auxiliary variables. If only GWR residuals are autocorrelated, the geographically weighted regression-kriging (GWRK) model seems to be optimal for air temperature spatial interpolation.

Interest rate next-day variation prediction based on hybrid feedforward neural network, particle swarm optimization, and multiresolution techniques

Multiresolution analysis techniques including continuous wavelet transform, empirical mode decomposition, and variational mode decomposition are tested in the context of interest rate next-day variation prediction. In particular, multiresolution analysis techniques are used to decompose interest rate actual variation and feedforward neural network for training and prediction. Particle swarm optimization technique is adopted to optimize its initial weights. For comparison purpose, autoregressive moving average model, random walk process and the naive model are used as main reference models. In order to show the feasibility of the presented hybrid models that combine multiresolution analysis techniques and feedforward neural network optimized by particle swarm optimization, we used a set of six illustrative interest rates; including Moody’s seasoned Aaa corporate bond yield, Moody’s seasoned Baa corporate bond yield, 3-Month, 6-Month and 1-Year treasury bills, and effective federal fund rate. The forecasting results show that all multiresolution-based prediction systems outperform the conventional reference models on the criteria of mean absolute error, mean absolute deviation, and root mean-squared error. Therefore, it is advantageous to adopt hybrid multiresolution techniques and soft computing models to forecast interest rate daily variations as they provide good forecasting performance.

A variant of K nearest neighbor quantile regression

Compared with local polynomial quantile regression, K nearest neighbor quantile regression (KNNQR) has many advantages, such as not assuming smoothness of functions. The paper summarizes the research of KNNQR and has carried out further research on the selection of k, algorithm and Monte Carlo simulations. Additionally, simulated functions are Blocks, Bumps, HeaviSine and Doppler, which stand for jumping, volatility, mutagenicity slope and high frequency function. When function to be estimated has some jump points or catastrophe points, KNNQR is superior to local linear quantile regression in the sense of the mean squared error and mean absolute error criteria. To be mentioned, even high frequency, the superiority of KNNQR could be observed. A real data is analyzed as an illustration.

Pan evaporation modeling using least square support vector machine, multivariate adaptive regression splines and M5 model tree

Summary Pan evaporation (Ep) modeling is an important issue in reservoir management, regional water resources planning and evaluation of drinking-water supplies. The main purpose of this study is to investigate the accuracy of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 Model Tree (M5Tree) in modeling Ep. The first part of the study focused on testing the ability of the LSSVM, MARS and M5Tree models in estimating the Ep data of Mersin and Antalya stations located in Mediterranean Region of Turkey by using cross-validation method. The LSSVM models outperformed the MARS and M5Tree models in estimating Ep of Mersin and Antalya stations with local input and output data. The average root mean square error (RMSE) of the M5Tree and MARS models was decreased by 24–32.1% and 10.8–18.9% using LSSVM models for the Mersin and Antalya stations, respectively. The ability of three different methods was examined in estimation of Ep using input air temperature, solar radiation, relative humidity and wind speed data from nearby station in the second part of the study (cross-station application without local input data). The results showed that the MARS models provided better accuracy than the LSSVM and M5Tree models with respect to RMSE, mean absolute error (MAE) and determination coefficient (R2) criteria. The average RMSE accuracy of the LSSVM and M5Tree was increased by 3.7% and 16.5% using MARS. In the case of without local input data, the average RMSE accuracy of the LSSVM and M5Tree was respectively increased by 11.4% and 18.4% using MARS. In the third part of the study, the ability of the applied models was examined in Ep estimation using input and output data of nearby station. The results reported that the MARS models performed better than the other models with respect to RMSE, MAE and R2 criteria. The average RMSE of the LSSVM and M5Tree was respectively decreased by 54% and 3.4% using MARS. The overall results indicated that the LSSVM could be successfully used in estimating Ep by using local input and output data while the MARS model performed better than the LSSVM in the case of without local input and outputs.

Multiple seasonal cycles forecasting model: the Italian electricity demand

Forecasting energy load demand data based on high frequency time series has become of primary importance for energy suppliers in nowadays competitive electricity markets. In this work, we model the time series of Italian electricity consumption from 2004 to 2014 using an exponential smoothing approach. Data are observed hourly showing strong seasonal patterns at different frequencies as well as some calendar effects. We combine a parsimonious model representation of the intraday and intraweek cycles with an additional seasonal term that captures the monthly variability of the series. Irregular days, such as public holidays, are modelled separately by adding a specific exponential smoothing seasonal term. An additive ARMA error term is then introduced to lower the volatility of the estimated trend component and the residuals’ autocorrelation. The forecasting exercise demonstrates that the proposed model performs remarkably well, in terms of lower root mean squared error and mean absolute percentage error criteria, in both short term and medium term forecasting horizons.

Linearization Method of Carrier Catalytic Gas Sensor Characteristics Using High-Order Polynomial

To improve detecting performance of gas concentration in coal-mine, a new linearization method of carrier cat- alytic gas sensor characteristics based on high-order polynomials was introduced. Firstly, the calibration data of sensor was used to establish the training sample set. Then, the high-order polynomial was employed to establish nonlinear re- gression inverse model of sensor characteristics. Finally, the polynomial coefficients were intelligently tuned by improved clone selection algorithm (ICSA) and the criteria of mean absolute error (MAE) minimization. Experimental results showed the the method proposed in this paper is effective, and the performance of inearization model is superior to that of the traditional least square method.

Development of Hybrid Models for Forecasting Time-Series Data Using Nonlinear SVR Enhanced by PSO

Real-world time-series are rarely purely linear or nonlinear and often contain both these patterns. Therefore, in this article, we have developed four hybrid models by combining linear seasonal autoregressive integrated moving average (SARIMA) and nonlinear support vector regression (NLSVR) models for time-series forecasting. Further, particle swarm optimization (PSO), which is a very efficient population-based global stochastic optimization technique, is employed to estimate the hyperparameters of resultant models. A relevant computer program is written in MATLAB function (m file). The SAS and MATLAB software packages are used for carrying out data analysis. Subsequently, as an illustration, the models are applied to all-India monthly marine products export time-series data. Superiority of hybrid models over individual SARIMA and NLSVR models is demonstrated for the data under consideration using root mean square error (RMSE) and mean absolute error (MAE) criteria.

Time series forecasting based on wavelet filtering

Forecasting time series data is one of the most important issues involved in numerous applications in real life. Time series data have been analyzed in either the time or frequency domains. The objective of this study is to propose a forecasting method based on wavelet filtering. The proposed method decomposes the original time series into the trend and variation parts and constructs a separate model for each part. Simulation and real case studies were conducted to examine the properties of the proposed method under various scenarios and compare its performance with time series forecasting models without wavelet filtering. The results from both simulated and real data showed that the proposed method based on wavelet filtering yielded more accurate results than the models without wavelet filtering in terms of mean absolute percentage error criterion.

Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method

This paper examines the effect of varying stepsizes in finding the approximate solution of stochastic differential equations (SDEs). One step Milstein method (MLSTM) for solution of general first order stochastic differential equations (SDEs) has been derived using Ito Lemma and Euler-Maruyama Method as supporting tools. Two problems in the form of first order SDEs have been considered. The method of solution used is one step Milstein method. The absolute errors were calculated using the exact solution and numerical solution. Comparison of varying the stepsizes was achieved using mean absolute error criterion. The results showed that the mean absolute error due to approximation decreases as the stepsizes decreases. The order of convergence is approximately 1, which indicates the accuracy of the method. Also, the effect of varying stepsizes can also be identified using graphical method constructed for various stepsizes.

Time Series Forecasting using Least Square Support Vector Machine for Canadian Lynx Data

Time series analysis and forecasting is an active research area over the last few decades. There are various kinds of forecasting models have been developed and researchers have relied on statistical techniques to predict the future. This paper discusses the application of Least Square Support Vector Machine (LSSVM) models for Canadian Lynx forecasting. The objective of this paper is to examine the flexibility of LSSVM in time series forecasting by comparing it with other models in previous research such as Artificial Neural Networks (ANN), Auto-Regressive Integrated Moving Average (ARIMA), Feed-Forward Neural Networks (FNN), Self-Exciting Threshold Auto-Regression (SETAR), Zhang’s model, Aladang’s hybrid model and Support Vector Regression (SVR) model. The experiment results show that the LSSVM model outperforms the other models based on the criteria of Mean Absolute Error (MAE) and Mean Square Error (MSE). It also indicates that LSSVM provides a promising alternative technique in time series forecasting.

Using a logistic growth regression model to forecast the demand for tourism in Las Vegas

For many years significant attention has been devoted to the application of forecasting models, both causal and time series, to the demand for tourism. However, most studies use national data and only a few are destination specific. The present paper applies a logistic growth forecasting model to tourist demand for Las Vegas and the empirical results indicate a superiority of logistic growth model when compared to the benchmark seasonal autoregressive integrated moving average (SARIMA) and Naïve 1 models. Based on the accuracy criteria of mean absolute percentage error and root mean square percentage error, the present study demonstrates that forecasts of tourism demand obtained by logistic growth forecasting model are more accurate (and hence more useful to tourism managers and planners) than forecasts obtained through any of the two benchmark models.

A multi-scale relevance vector regression approach for daily urban water demand forecasting

Water is one of the most important resources for economic and social developments. Daily water demand forecasting is an effective measure for scheduling urban water facilities. This work proposes a multi-scale relevance vector regression (MSRVR) approach to forecast daily urban water demand. The approach uses the stationary wavelet transform to decompose historical time series of daily water supplies into different scales. At each scale, the wavelet coefficients are used to train a machine-learning model using the relevance vector regression (RVR) method. The estimated coefficients of the RVR outputs for all of the scales are employed to reconstruct the forecasting result through the inverse wavelet transform. To better facilitate the MSRVR forecasting, the chaos features of the daily water supply series are analyzed to determine the input variables of the RVR model. In addition, an adaptive chaos particle swarm optimization algorithm is used to find the optimal combination of the RVR model parameters. The MSRVR approach is evaluated using real data collected from two waterworks and is compared with recently reported methods. The results show that the proposed MSRVR method can forecast daily urban water demand much more precisely in terms of the normalized root-mean-square error, correlation coefficient, and mean absolute percentage error criteria.

HIDDEN MARKOV MODELS WITH COVARIATES FOR ANALYSIS OF DEFECTIVE INDUSTRIAL MACHINE PARTS

Monthly counts of industrial machine part errors are modeled using a two-state Hidden Markov Model (HMM) in order to describe the effect of machine part error correction and the amount of time spent on the error correction on the likelihood of the machine part to be in a &#34defective&#34 or &#34non-defective&#34 state. The number of machine parts errors were collected from a thermo plastic injection molding machine in a car bumper auto parts manufacturer in Liberec city, Czech Republic from January 2012 to November 2012. A Bayesian method is used for parameter estimation. The results of this study indicate that the machine part error correction and the amount of time spent on the error correction do not improve the machine part status of the individual part, but there is a very strong month-to-month dependence of the machine part states. Using the Mean Absolute Error (MAE) criterion, the performance of the proposed model (MAE = 1.62) and the HMM including machine part error correction only (MAE = 1.68), from our previous study, is not significantly different. However, the proposed model has more advantage in the fact that the machine part state can be explained by both the machine part error correction and the amount of time spent on the error correction.

An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China

In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO–NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt–Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt–Winters exponential smoothing method.

Modeling of Dissolved Oxygen in River Water Using Artificial Intelligence Techniques

The accuracy of artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming (GEP) in modeling dissolved oxygen (DO) concentration was investigated in this study. Water temperature, specific conductance, pH, discharge and DO concentration data from South Platte River at Englewood, Colorado were used. Various input combinations of these data were tried as inputs to the ANN and ANFIS methods. The ANN and ANFIS models with the water temperature, specific conductance, pH and discharge input parameters performed the best. The optimal GEP model was obtained for the best input combination and compared with the ANN and ANFIS models with respect to correlation coefficient, root mean square error, mean absolute error and mean absolute relative error criteria. Results revealed that the GEP model performed better than the ANN and ANFIS models in modeling DO concentration.

Multicriteria Robust Fitting of Elliptical Primitives

Geometric fitting is present in different fields of science, engineering and astronomy. In particular, ellipse shapes are some of the most commonly employed geometric features in digital image analysis and visual pattern recognition. Most geometric and algebraic methods are sensitive to noise and outlier points and so the results are not usually acceptable. In this paper, a robust geometric multicriteria method based on the mean absolute geometric error and the eccentricity to fit an ellipse to set of points is proposed. It is well known that the least mean absolute error criterion leads to robust estimations. The experimental results on different real and synthetic data have shown that the proposed algorithm is robust to outliers. Moreover, it allows us to identify outliers and remove them.

English

  The data were taken from the “Enhancing of Mutton Production through goat breeding” a Project run at Livestock Production Research Institute Bahadurnagar (Okara); the growth performance of Beetal goats were compared by statistical non-linear models, like Exponential, Gompertz and Logistic models. These models were based to obtain the best fitted model by following the criteria of mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE). Run test were used to check the independence and normality of the models and residuals were checked by Shapiro - Wilk test. Errors were found to be normal and independently distributed. Body weights of Beetal goats and Bucks were examined by shape of the curves and it revealed that the values of α, β and γ of Gompertz model were higher than that of exponential and logistics in both the district of Okara and Sahiwal. Also, values of MAE, RMSE and MAPE of Gompertz model were lower than the logistic and exponential.   Key words: Bodyweight of Beetal, Gompertz, least value.