Search results for: regression method

Authors: Autcha Araveeporn

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This paper presents a study about a nonparametric regression model consisting of a smoothing spline method and a penalized spline regression method. We also compare the techniques used for estimation and prediction of nonparametric regression model. We tried both methods with crude oil prices in dollars per barrel and the Stock Exchange of Thailand (SET) index. According to the results, it is concluded that smoothing spline method performs better than that of penalized spline regression method.

Keywords: nonparametric regression model, penalized spline regression method, smoothing spline method, Stock Exchange of Thailand (SET)

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Authors: Yi-Cheng Tian, Miin-Shen Yang

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The mixture likelihood approach to clustering is a popular clustering method where the expectation and maximization (EM) algorithm is the most used mixture likelihood method. In the literature, the EM algorithm had been used for mixture regression models. However, these EM mixture regression algorithms are sensitive to initial values with a priori number of clusters. In this paper, to resolve these drawbacks, we construct a learning-based schema for the EM mixture regression algorithm such that it is free of initializations and can automatically obtain an approximately optimal number of clusters. Some numerical examples and comparisons demonstrate the superiority and usefulness of the proposed learning-based EM mixture regression algorithm.

Keywords: clustering, EM algorithm, Gaussian mixture model, mixture regression model

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: Byung Ho Jung, Dong Hoon Lim

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Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. Logistic regression is used extensively in numerous disciplines, including the medical and social science fields. In this paper, we address the problem of estimating parameters in the logistic regression based on MapReduce framework with RHadoop that integrates R and Hadoop environment applicable to large scale data. There exist three learning algorithms for logistic regression, namely Gradient descent method, Cost minimization method and Newton-Rhapson's method. The Newton-Rhapson's method does not require a learning rate, while gradient descent and cost minimization methods need to manually pick a learning rate. The experimental results demonstrated that our learning algorithms using RHadoop can scale well and efficiently process large data sets on commodity hardware. We also compared the performance of our Newton-Rhapson's method with gradient descent and cost minimization methods. The results showed that our newton's method appeared to be the most robust to all data tested.

Keywords: big data, logistic regression, MapReduce, RHadoop

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Authors: Suparman

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Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Keywords: regression, piecewise, Bayesian, reversible Jump MCMC

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Authors: Suparman

Abstract:

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: piecewise regression, bayesian, reversible jump MCMC, segmentation

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Jude Opara, Esemokumo Perewarebo Akpos

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This paper is on non-parametric linear regression over its parametric counterparts with large sample size. Data set on anthropometric measurement of primary school pupils was taken for the analysis. The study used 50 randomly selected pupils for the study. The set of data was subjected to normality test, and it was discovered that the residuals are not normally distributed (i.e. they do not follow a Gaussian distribution) for the commonly used least squares regression method for fitting an equation into a set of (x,y)-data points using the Anderson-Darling technique. The algorithms for the nonparametric Theil’s regression are stated in this paper as well as its parametric OLS counterpart. The use of a programming language software known as “R Development” was used in this paper. From the analysis, the result showed that there exists a significant relationship between the response and the explanatory variable for both the parametric and non-parametric regression. To know the efficiency of one method over the other, the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) are used, and it is discovered that the nonparametric regression performs better than its parametric regression counterparts due to their lower values in both the AIC and BIC. The study however recommends that future researchers should study a similar work by examining the presence of outliers in the data set, and probably expunge it if detected and re-analyze to compare results.

Keywords: Theil’s regression, Bayesian information criterion, Akaike information criterion, OLS

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Authors: Gianna Zou

Abstract:

Propensity score matching (PSM), introduced by Paul R. Rosenbaum and Donald Rubin in 1983, is a popular statistical matching technique which tries to estimate the treatment effects by taking into account covariates that could impact the efficacy of study medication in clinical trials. PSM can be used to reduce the bias due to confounding variables. However, PSM assumes that the response values are normally distributed. In some cases, this assumption may not be held. In this paper, a machine learning method - Bayesian Additive Regression Tree (BART), is used as a more robust method of matching. BART can work well when models are misspecified since it can be used to model heterogeneous treatment effects. Moreover, it has the capability to handle non-linear main effects and multiway interactions. In this research, a BART Matching Method (BMM) is proposed to provide a more reliable matching method over PSM. By comparing the analysis results from PSM and BMM, BMM can perform well and has better prediction capability when the response values are not normally distributed.

Keywords: BART, Bayesian, matching, regression

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Authors: Y. H. Wu, Ji-Yuan Lin, Yu-Ming Liou

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This study aims to set up the landslide susceptibility map of County Route 89 at Ren-Ai Township in Nantou County using the Instability Index Method and Logistic regression. Seven susceptibility factors including Slope Angle, Aspect, Elevation, Distance to fold, Distance to River, Distance to Road and Accumulated Rainfall were obtained by GIS based on the Typhoon Toraji landslide area identified by Industrial Technology Research Institute in 2001. To calculate the landslide percentage of each factor and acquire the weight and grade the grid by means of Instability Index Method. In this study, landslide susceptibility can be classified into four grades: high, medium high, medium low and low, in order to determine the advantages and disadvantages of the two models. The precision of this model is verified by classification error matrix and SRC curve. These results suggest that the logistic regression model is a preferred method than instability index in the assessment of landslide susceptibility. It is suitable for the landslide prediction and precaution in this area in the future.

Keywords: instability index method, logistic regression, landslide susceptibility, SRC curve

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Authors: Shahadut Hossain, Jacek Wesolowski, Zahirul Hoque

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In many epidemiological and environmental studies covariate measurements are subject to the detection limit. In most applications, covariate measurements are usually truncated from below which is known as left-truncation. Because the measuring device, which we use to measure the covariate, fails to detect values falling below the certain threshold. In regression analyses, it causes inflated bias and inaccurate mean squared error (MSE) to the estimators. This paper suggests a response-based regression calibration method to correct the deleterious impact introduced by the covariate detection limit in the estimators of the parameters of simple logistic regression model. Compared to the maximum likelihood method, the proposed method is computationally simpler, and hence easier to implement. It is robust to the violation of distributional assumption about the covariate of interest. In producing correct inference, the performance of the proposed method compared to the other competing methods has been investigated through extensive simulations. A real-life application of the method is also shown using data from a population-based case-control study of non-Hodgkin lymphoma.

Keywords: environmental exposure, detection limit, left truncation, bias, ad-hoc substitution

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Authors: Songul Cinaroglu

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Machine learning regression methods are recommended as an alternative to classical regression methods in the existence of variables which are difficult to model. Data for health expenditure is typically non-normal and have a heavily skewed distribution. This study aims to compare machine learning regression methods by hyperparameter tuning to predict health expenditure per capita. A multiple regression model was conducted and performance results of Lasso Regression, Random Forest Regression and Support Vector Machine Regression recorded when different hyperparameters are assigned. Lambda (λ) value for Lasso Regression, number of trees for Random Forest Regression, epsilon (ε) value for Support Vector Regression was determined as hyperparameters. Study results performed by using 'k' fold cross validation changed from 5 to 50, indicate the difference between machine learning regression results in terms of R², RMSE and MAE values that are statistically significant (p < 0.001). Study results reveal that Random Forest Regression (R² ˃ 0.7500, RMSE ≤ 0.6000 ve MAE ≤ 0.4000) outperforms other machine learning regression methods. It is highly advisable to use machine learning regression methods for modelling health expenditures.

Keywords: machine learning, lasso regression, random forest regression, support vector regression, hyperparameter tuning, health expenditure

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Authors: Zhou Jianhong

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Model averaging is a desirable approach to deal with model uncertainty, which, however, has rarely been explored for Poisson regression. In this paper, we propose a model averaging procedure based on an unbiased estimator of the expected Kullback-Leibler distance for the Poisson regression. Simulation study shows that the proposed model average estimator outperforms some other commonly used model selection and model average estimators in some situations. Our proposed methods are further applied to a real data example and the advantage of this method is demonstrated again.

Keywords: model averaging, poission regression, Kullback-Leibler distance, statistics

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Authors: Dalia Rimawi, Walid Salameh, Amal Al-Omari, Hadeel AbdelKhaleq

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Predication of Survival time of patients with cancer, is a core factor that influences oncologist decisions in different aspects; such as offered treatment plans, patients’ quality of life and medications development. For a long time proportional hazards Cox regression (ph. Cox) was and still the most well-known statistical method to predict survival outcome. But due to the revolution of data sciences; new predication models were employed and proved to be more flexible and provided higher accuracy in that type of studies. Artificial neural network is one of those models that is suitable to handle time to event predication. In this study we aim to compare ph Cox regression with artificial neural network method according to data handling and Accuracy of each model.

Keywords: Cox regression, neural networks, survival, cancer.

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Authors: Zikiou Nadia, Lahdir Mourad, Ameur Soltane

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In this paper, we propose an effective method for image compression based on SVM Regression (SVR), with three different kernels, and biorthogonal 2D Discrete Wavelet Transform. SVM regression could learn dependency from training data and compressed using fewer training points (support vectors) to represent the original data and eliminate the redundancy. Biorthogonal wavelet has been used to transform the image and the coefficients acquired are then trained with different kernels SVM (Gaussian, Polynomial, and Linear). Run-length and Arithmetic coders are used to encode the support vectors and its corresponding weights, obtained from the SVM regression. The peak signal noise ratio (PSNR) and their compression ratios of several test images, compressed with our algorithm, with different kernels are presented. Compared with other kernels, Gaussian kernel achieves better image quality. Experimental results show that the compression performance of our method gains much improvement.

Keywords: image compression, 2D discrete wavelet transform (DWT-2D), support vector regression (SVR), SVM Kernels, run-length, arithmetic coding

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Authors: Hyon I. Paek, Sang Rim Kim, Hyon A. Ryu

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In functional linear regression, one typical problem is to reduce dimension. Compared with multivariate linear regression, functional linear regression is regarded as an infinite-dimensional case, and the main task is to reduce dimensions of functional response and functional predictors. One common approach is to adapt functional principal component analysis (FPCA) on functional predictors and then use a few leading functional principal components (FPC) to predict the functional model. The leading FPCs estimated by the typical FPCA explain a major variation of the functional predictor, but these leading FPCs may not be mostly correlated with the functional response, so they may not be significant in the prediction for response. In this paper, we propose a supervised functional principal component analysis method for a functional response model with FPCs obtained by considering the correlation of the functional response. Our method would have a better prediction accuracy than the typical FPCA method.

Keywords: supervised, functional principal component analysis, functional response, functional linear regression

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Authors: Rajeshwar Singh

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The presence of multicollinearity is common in handling with several explanatory variables simultaneously due to exhibiting a linear relationship among them. A great problem arises in understanding the impact of explanatory variables on the dependent variable. Thus, the method of least squares estimation gives inexact estimates. In this case, it is advised to detect its presence first before proceeding further. Using the ridge regression degree of its occurrence is reduced but principal components regression gives good estimates in this situation. This paper discusses well-known techniques of the ridge and principal components regressions and applies to get the estimates of coefficients by both techniques. In addition to it, this paper also discusses the conflicting claim on the discovery of the method of ridge regression based on available documents.

Keywords: conflicting claim on credit of discovery of ridge regression, multicollinearity, principal components and ridge regressions, variance inflation factor

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Authors: Yina F. Muñoz, Alexander Paz, Hanns De La Fuente-Mella, Joaquin V. Fariña, Guilherme M. Sales

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The primary approach for estimating bridge deterioration uses Markov-chain models and regression analysis. Traditional Markov models have problems in estimating the required transition probabilities when a small sample size is used. Often, reliable bridge data have not been taken over large periods, thus large data sets may not be available. This study presents an important change to the traditional approach by using the Small Data Method to estimate transition probabilities. The results illustrate that the Small Data Method and traditional approach both provide similar estimates; however, the former method provides results that are more conservative. That is, Small Data Method provided slightly lower than expected bridge condition ratings compared with the traditional approach. Considering that bridges are critical infrastructures, the Small Data Method, which uses more information and provides more conservative estimates, may be more appropriate when the available sample size is small. In addition, regression analysis was used to calculate bridge deterioration. Condition ratings were determined for bridge groups, and the best regression model was selected for each group. The results obtained were very similar to those obtained when using Markov chains; however, it is desirable to use more data for better results.

Keywords: concrete bridges, deterioration, Markov chains, probability matrix

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Authors: Georgios Charizanos, Haydar Demirhan, Duygu Icen

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Two of the most impactful issues in classical logistic regression are class imbalance and complete separation. These can result in model predictions heavily leaning towards the imbalanced class on the binary response variable or over-fitting issues. Fuzzy methodology offers key solutions for handling these problems. However, most studies propose the transformation of the binary responses into a continuous format limited within [0,1]. This is called the possibilistic approach within fuzzy logistic regression. Following this approach is more aligned with straightforward regression since a logit-link function is not utilized, and fuzzy probabilities are not generated. In contrast, we propose a method of fuzzifying binary response variables that allows for the use of the logit-link function; hence, a probabilistic fuzzy logistic regression model with the Monte Carlo method. The fuzzy probabilities are then classified by selecting a fuzzy threshold. Different combinations of fuzzy and crisp input, output, and coefficients are explored, aiming to understand which of these perform better under different conditions of imbalance and separation. We conduct numerical experiments using both synthetic and real datasets to demonstrate the performance of the fuzzy logistic regression framework against seven crisp machine learning methods. The proposed framework shows better performance irrespective of the degree of imbalance and presence of separation in the data, while the considered machine learning methods are significantly impacted.

Keywords: fuzzy logistic regression, fuzzy, logistic, machine learning

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Authors: Monika Chuchro

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This paper presents a preliminary attempt to apply classification of time series using meta-clusters in order to improve the quality of regression models. In this case, clustering was performed as a method to obtain a subgroups of time series data with normal distribution from inflow into waste water treatment plant data which Composed of several groups differing by mean value. Two simple algorithms: K-mean and EM were chosen as a clustering method. The rand index was used to measure the similarity. After simple meta-clustering, regression model was performed for each subgroups. The final model was a sum of subgroups models. The quality of obtained model was compared with the regression model made using the same explanatory variables but with no clustering of data. Results were compared by determination coefficient (R2), measure of prediction accuracy mean absolute percentage error (MAPE) and comparison on linear chart. Preliminary results allows to foresee the potential of the presented technique.

Keywords: clustering, data analysis, data mining, predictive models

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Authors: Luh Eka Suryani, Purhadi

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Poisson regression is a non-linear regression model with response variable in the form of count data that follows Poisson distribution. Modeling for a pair of count data that show high correlation can be analyzed by Poisson Bivariate Regression. Data, the number of infant mortality and maternal mortality, are count data that can be analyzed by Poisson Bivariate Regression. The Poisson regression assumption is an equidispersion where the mean and variance values are equal. However, the actual count data has a variance value which can be greater or less than the mean value (overdispersion and underdispersion). Violations of this assumption can be overcome by applying Generalized Poisson Regression. Characteristics of each regency can affect the number of cases occurred. This issue can be overcome by spatial analysis called geographically weighted regression. This study analyzes the number of infant mortality and maternal mortality based on conditions in East Java in 2016 using Geographically Weighted Bivariate Generalized Poisson Regression (GWBGPR) method. Modeling is done with adaptive bisquare Kernel weighting which produces 3 regency groups based on infant mortality rate and 5 regency groups based on maternal mortality rate. Variables that significantly influence the number of infant and maternal mortality are the percentages of pregnant women visit health workers at least 4 times during pregnancy, pregnant women get Fe3 tablets, obstetric complication handled, clean household and healthy behavior, and married women with the first marriage age under 18 years.

Keywords: adaptive bisquare kernel, GWBGPR, infant mortality, maternal mortality, overdispersion

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Authors: Kamna Solanki, Yudhvir Singh, Sandeep Dalal

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Software testing is a time and cost intensive process. A scrutiny of the code and rigorous testing is required to identify and rectify the putative bugs. The process of bug identification and its consequent correction is continuous in nature and often some of the bugs are removed after the software has been launched in the market. This process of code validation of the altered software during the maintenance phase is termed as Regression testing. Regression testing ubiquitously considers resource constraints; therefore, the deduction of an appropriate set of test cases, from the ensemble of the entire gamut of test cases, is a critical issue for regression test planning. This paper presents a novel method for designing a suitable prioritization process to optimize fault detection rate and performance of regression test on predefined constraints. The proposed method for test case prioritization m-ACO alters the food source selection criteria of natural ants and is basically a modified version of Ant Colony Optimization (ACO). The proposed m-ACO approach has been coded in 'Perl' language and results are validated using three examples by computation of Average Percentage of Faults Detected (APFD) metric.

Keywords: regression testing, software testing, test case prioritization, test suite optimization

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Authors: Kajingulu Malandala, Ranganai Edmore

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The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

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Authors: Retius Chifurira

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Logistic regression model is the most used regression model to predict meteorological drought probabilities. When the dependent variable is extreme, the logistic model fails to adequately capture drought probabilities. In order to adequately predict drought probabilities, we use the generalized linear model (GLM) with the quantile function of the generalized extreme value distribution (GEVD) as the link function. The method maximum likelihood estimation is used to estimate the parameters of the generalized extreme value (GEV) regression model. We compare the performance of the logistic and the GEV regression models in predicting drought probabilities for Zimbabwe. The performance of the regression models are assessed using the goodness-of-fit tests, namely; relative root mean square error (RRMSE) and relative mean absolute error (RMAE). Results show that the GEV regression model performs better than the logistic model, thereby providing a good alternative candidate for predicting drought probabilities. This paper provides the first application of GLM derived from extreme value theory to predict drought probabilities for a drought-prone country such as Zimbabwe.

Keywords: generalized extreme value distribution, general linear model, mean annual rainfall, meteorological drought probabilities

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Authors: Anastasiia Yu. Timofeeva

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Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: grade point average, orthogonal regression, penalized regression spline, locally weighted regression

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Authors: Kornelius Ronald Demu, Dewi Retno Sari Saputro, Purnami Widyaningsih

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Human Development Index (HDI) is a standard measurement for a country's human development. Several factors may have influenced it, such as life expectancy, gross domestic product (GDP) based on the province's annual expenditure, the number of poor people, and the percentage of an illiterate people. The scatter plot between HDI and the influenced factors show that the plot does not follow a specific pattern or form. Therefore, the HDI's data in Indonesia can be applied with a nonparametric regression model. The estimation of the regression curve in the nonparametric regression model is flexible because it follows the shape of the data pattern. One of the nonparametric regression's method is a truncated spline. Truncated spline regression is one of the nonparametric approach, which is a modification of the segmented polynomial functions. The estimator of a truncated spline regression model was affected by the selection of the optimal knots point. Knot points is a focus point of spline truncated functions. The optimal knots point was determined by the minimum value of generalized cross validation (GCV). In this article were applied the data of Human Development Index with a truncated spline nonparametric regression model. The results of this research were obtained the best-truncated spline regression model to the HDI's data in Indonesia with the combination of optimal knots point 5-5-5-4. Life expectancy and the percentage of an illiterate people were the significant factors depend to the HDI in Indonesia. The coefficient of determination is 94.54%. This means the regression model is good enough to applied on the data of HDI in Indonesia.

Keywords: generalized cross validation (GCV), Human Development Index (HDI), knots point, nonparametric regression, truncated spline

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Authors: J. Satya Eswari, Ch. Venkateswarlu

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The formulation of a commercial pharmaceutical product involves several composition factors and response characteristics. When the formulation requires to satisfy multiple response characteristics which are conflicting, an optimal solution requires the need for an efficient multiobjective optimization technique. In this work, a regression is combined with a non-dominated sorting differential evolution (NSDE) involving Naïve & Slow and ε constraint techniques to derive different multiobjective optimization strategies, which are then evaluated by means of a trapidil pharmaceutical formulation. The analysis of the results show the effectiveness of the strategy that combines the regression model and NSDE with the integration of both Naïve & Slow and ε constraint techniques for Pareto optimization of trapidil formulation. With this strategy, the optimal formulation at pH=6.8 is obtained with the decision variables of micro crystalline cellulose, hydroxypropyl methylcellulose and compression pressure. The corresponding response characteristics of rate constant and release order are also noted down. The comparison of these results with the experimental data and with those of other multiple regression model based multiobjective evolutionary optimization strategies signify the better performance for optimal trapidil formulation.

Keywords: pharmaceutical formulation, multiple regression model, response surface method, radial basis function network, differential evolution, multiobjective optimization

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Authors: Kang-Mo Jung

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The use of regularization for statistical methods has become popular. The least absolute shrinkage and selection operator (LASSO) framework has become the standard tool for sparse regression. However, it is well known that the LASSO is sensitive to outliers or leverage points. We consider a new robust estimation which is composed of the weighted loss function of the pairwise difference of residuals and the adaptive penalty function regulating the tuning parameter for each variable. Rank regression is resistant to regression outliers, but not to leverage points. By adopting a weighted loss function, the proposed method is robust to leverage points of the predictor variable. Furthermore, the adaptive penalty function gives us good statistical properties in variable selection such as oracle property and consistency. We develop an efficient algorithm to compute the proposed estimator using basic functions in program R. We used an optimal tuning parameter based on the Bayesian information criterion (BIC). Numerical simulation shows that the proposed estimator is effective for analyzing real data set and contaminated data.

Keywords: adaptive penalty function, robust penalized regression, variable selection, weighted rank regression

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Authors: Abdullah A. AlShaher

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In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2^nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.

Keywords: character recognition, regression curves, handwritten Arabic letters, expectation maximization algorithm

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Authors: Saeed Eskandari, Seyed Rasoul Mehdikhani

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Radiation sources have been used in many industries, such as gamma sources in medical imaging. These waves have destructive effects on humans and the environment. It is very important to detect and find the source of these waves because these sources cannot be seen by the eye. A portable robot has been designed and built with the purpose of revealing radiation sources that are able to scan the place from 5 to 20 meters away and shows the location of the sources according to the intensity of the waves on a two-dimensional digital image. The operation of the robot is done by measuring the pixels separately. By increasing the image measurement resolution, we will have a more accurate scan of the environment, and more points will be detected. But this causes a lot of time to be spent on scanning. In this paper, to overcome this challenge, we designed a method that can optimize this time. In this method, a small number of important points of the environment are measured. Hence the remaining pixels are predicted and estimated by regression algorithms in machine learning. The research method is based on comparing the actual values of all pixels. These steps have been repeated with several other radiation sources. The obtained results of the study show that the values estimated by the regression method are very close to the real values.

Keywords: regression, machine learning, scan radiation, robot

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