regression
در نشریات گروه ریاضی-
In this article, we introduce a novel approach by presenting separate ratio and regression estimators in the context of neutrosophic stratified sampling for the very first time, incorporating auxiliary variables. We have conducted a thorough analysis to estimate these newly proposed estimators' bias and Mean Square Error (MSE) up to the first-order approximation. Theoretically using efficiency comparison criteria, our findings demonstrate the superior performance of these estimators compared to traditional unbiased estimators. Also, numerically based on real-life and artificial data, we have shown the supremacy of the neutrosophic stratified sampling over neutrosophic simple random sampling along with the supremacy of our proposed neutrosophic separate stratified estimators over neutrosophic stratified unbiased estimator. Moreover, our research highlights the enhanced reliability of neutrosophic stratified estimators when contrasted with classical stratified estimators.Keywords: Neutrosophic Variables, Neutrosophic Stratified Sampling, Regression, Ratio Estimator, Monte-Carlo Simulation, Mean Square Error
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 12, Dec 2023, PP 241 -252One of the important applications of data envelopment analysis is to determine the progress and regress of the units under evaluation at two different times, which has been addressed in many papers. Also, one of the distinctions of data coverage analysis technique with other methods is the introduction of achievable and flexible benchmarks. In the present paper, we intend to study the progress and regress of Iranian regional electricity companies during two consecutive years of 2015 and 2016. Since some of the evaluated indicators are semi-positive and semi-negative indicators, in this study we will develop Emrooznejad et al. [7] to determine the productivity index of Malmquist for semi-positive and semi-negative indicators. Finally, for further explanation, we have used the proposed models to determine the progress and regression of 16 regional electricity companies in Iran with 3 semi-positive and semi-negative indices in the presence of the limitation on the benchmark, an undesirable index and 11 completely positive indices in the nature of input with constant scale returns as a black box.Keywords: Progress, Regression, Semi-oriented radial measure, Malmquist Productivity Index, Regional Electricity Companies, Data Envelopment Analysis
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Nolan and Ojeda-Revah (2013) proposed a regression model with heavy-tailed stable errors. In this paper we extend this method for multivariate heavy-tailed errors. Furthermore, A likelihood ratio test (LRT) for testing significant of regression coefficients is proposed. Also, confidence intervals based on Fisher information for Nolan and Ojeda-Revah (2013) method, called NOR, and LRT are computed and compared with well-known methods. At the end we provide some guidance for various error distributions in heavy-tailed cases.Keywords: Regression, Quantile regression, Stable distribution, Ordinary least squares, Maximum likelihood
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International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 2, Summer-Autumn 2021, PP 2263 -2267
Ferritin is a key organizer of protected deregulation, particularly below risky hyperferritinemia, by straight immune-suppressive and pro-inflammatory things. We conclude that there is a significant association between levels of ferritin and the harshness of COVID-19. In this paper, we introduce a semi-parametric method for prediction by making a combination of NN and regression models. So, two methodologies are adopted, Neural Network (NN) and regression model in designing the model; the data was collected from a nursing home hospital for period 11/7/2021- 23/7/2021, the sample size is 100 covid positive patients with 12 females & 38 males out of 50, while 26 female & 24 male are non-COVID out of 50. The input variables of the NN model are identified as the ferritin and a gender variable. The higher results precision is attained by the multilayer perceptron (MLP) networks when we applied the explanatory variables as the inputs with one hidden layer, which covers 3 neurons, as the planned many hidden layers are with one output of the fitting NN model which is used in stages of training and validation beside the actual data. We used a portion of the actual data to verify the behavior of the developed models, we find out that only one observation is a false predictive value. This means that the estimation model has significant parameters to forecast the type of Covid cases (Covid or no Covid).
Keywords: Semi-parametric method, Neural Network models (NN), regression, Ferritin level, COVID 19, multilayer perceptron (MLP) -
Increasing globalization trends, information and Communication technologies developments including the network community expands, new media and educational innovations have enabled us to use technology to learn more as well as more efficiency and management on knowledge. However, in recent years, knowledge management has become a familiar word for today's societies and industries, and knowledge management has gained popularity, especially in the education and business sectors but its effects on new educational systems has not been much studied. Systems such as the Learning Management System (LMS), which play an important role in learning employees and employees of corporations and industrial societies, and even banks and educational centers. In this study, considering the positive and negative effects of the LMS learning system on learning, we examine its effects on knowledge sharing and then knowledge management. Using the questionnaire, we collect the data and analyze the effects by regression analysis.
Keywords: LMS, Knowledge sharing, Regression, Knowledge Management -
موضوع اصلی این مقاله، بررسی پایه مرزی برای یک ایده آل نقاط است. برای این منظور ابتدا الگوریتمی برای محاسبه ایده آل مرتب و پایه مرزی نظیر آن برای یک ایده آل نقاط (که دارای چندگانگی هستند) می پردازیم. ایده آل نقاط از کاربردهای مختلفی در علوم و مهندسی برخوردار است که در این مقاله ما به کاربرد آن در یافتن مدل آماری بهینه اشاره می کنیم. در پایان، پس از بیان مطالب مورد نیاز، با استفاده از روش های ارایه شده در این مقاله، به محاسبه مدل های مختلف برای مثالی بر مبنای داده های واقعی و توضیح کارآیی مدل های ارایه شده می پردازیم.
کلید واژگان: پایه مرزی، ایده آل نقاط، الگوریتم بوخبرگر-مولر، طرح آزمایش ها، رگرسیون رده بندی ریاضی (2010): 13P10، 14Q99، .68W30IntroductionBorder bases are a generalization of Gröbner bases for zero-dimensional ideals which have attracted the interest of many researchers recently. More precisely, border bases provide a new method to find a structurally stable monomial basis for the residue class ring of a polynomial ideal and this yields a special generating set for the ideal possessing many nice properties.Given a finite set of points, finding the set of all polynomials vanishing on it (so-called either ideal of points or vanishing ideal of the set of points) has numerous applications in several fields in Mathematics and other sciences. In 1982, Buchberger and Möller proposed an algorithm to compute a Gröbner basis for an ideal of points. This algorithm proceeds by performing Gaussian elimination on a generalized Vandermonde matrix. In 2006, Farr and Gao presented an incremental algorithm to compute a Gröbner basis for an ideal of points. The main goal of their paper is to calculate a Gröbner basis for the vanishing ideal of any finite set of points under any monomial ordering, and for points with nontrivial multiplicities they adapt their algorithm to compute the vanishing ideal via Taylor expansions.The method of border bases is a beneficial tool to obtain a set of polynomial models identified by experimental design and regression. The utilization of Gröbner bases theory in experimental design was introduced by Pistone and Wynn. However, using Gröbner bases we cannot find all possible models which form structure of an order ideal for an experiment. For example, if we consider the design {(-1,1),(1,1),(0,0),(1,0),(0,-1)}, the model {} cannot be computed by Gröbner bases method. This fact is expected this method relies on monomial orderings.
Material and methodsIn this paper, we first present the Buchberger-Möller and Farr-Gao algorithms and then by applying these algorithms, we describe an algorithm which computes a border basis for the ideal of points corresponding to the input set of points with nontrivial multiplicity. In addition, we focus on presenting different models related to an experiment by using the concept of monomial bases for the residue class ring of a polynomial ideal.
Results and discussionAs we mentioned earlier, Buchberger-Möller algorithm is an efficient algorithm to compute a Gröbner basis for an ideal of points. We describe a simpler presentation of this algorithm in which we use the function NormalForm which receives as input a linear polynomial p and a Grbner basis G = { , . . . , } of linear polynomials in , . . . , and returns f and q=[, . . . , ] where f is the remainder of the division of p by G and p=+· · ·++r. Furthermore, we compare the efficiency of this algorithm with the function VanishingIdeal of Maple. Given a finite set of points, we consider the case in which some points in the set have nontrivial multiplicity. Based on the Farr-Gao algorithm, we prepare an algorithm that computes a border basis for the vanishing ideal of the finite set of points by using Taylor expansions. Suppose that n is the number of factors in an experiment. An experimental design is a finite set of points. The set of all polynomials vanishing at the design is called a design ideal. Regression analysis is a useful statistical process for the investigation of relationships between a response (or dependent) variable and one or more predictor (or independent) variables. When there is more than one predictor variable in a regression model, the model is a multiple linear regression model which we can call polynomial model. Suppose a random sample of size n is given (then we have exactly n data points are observed from (Y,X). The expession error? is the model for multiple linear regression where chr('39')s are called slopes or regression coefficients. Also, representing the merged effects of the predictor variables on the response variable is called interaction effect. By using multiple linear regression, we can analyze models containing interaction effects. For example, let us consider the following model +error. By substituting and , we have a multiple linear regression as follows +error. In addition, multiple R-squared or R2 is a statistical measure that states the square of the relationship between the predicted response value and response value. It should be noted that multiple R-squared is always any value between 0 and 1, where a value closer to 1 informing that a greater proportion of variance is computed for the model. Statistically, a high multiple R-squared shows a well-fitting regression model. Also in multiple regression, tolerance is used as an indicator of multicollinearity. Tolerance may be said to be the opposite of the coefficient of determination and is obtained as . All other things equal, researchers desire higher levels of tolerance, as low levels of tolerance are known to affect adversely the results associated with a multiple regression analysis. The smaller the tolerance of a variable, the more redundant is its contribution to the regression (i.e., it is redundant with the contribution of other independent variables). In the regression equation, if the tolerance of any of the variables is equal to zero (or very close to zero), the regression equation cannot be evaluated (the matrix is said to be ill-conditioned in this case, and it cannot be inverted).
ConclusionThe following conclusions were drawn from this research.We present a simpler variant of Buchberger- Möller algorithm (which seems to be easier for the implementation issue) for computing a border basis for an ideal of points.
We present an algorithm that incrementally computes a border basis for the vanishing ideal of any finite set of points in which some points have multiplicity.We provide good statistical polynomial models which are more suitable for practical applications due to the stability of border bases models compared with Gröbner bases models.Keywords: Border basis, Ideal of points, Buchberger-Möller algorithm, Experimental design, Regression -
The nature and importance of user’s comments in various social media systems play an important role in creating or changing people's perceptions of certain topics or popularizing them. It has now an important place in various fields, including education, sales, prediction, and so on. In this paper, Facebook social network has been considered as a case study. The purpose of this study is to predict the volume of Facebook users' comments on the published content called post. Therefore, the existing problem is classified as a regression problem. In the method presented in this paper, three regression models called elastic network, M5P model, and radial basis function regression model are combined and an ensemble model is made to predict the volume of comments. In order to combine these base models, a strategy called stack generalization is used, based on which the output of the base models is provided to a linear regression model as new features. This linear regression model combines the outputs of the 3 base models and determines the final output of the system. To evaluate the performance of the proposed model, a database of the UCI dataset, which has 5 training sets and 10 test sets, has been used. Each test set in this database has 100 records. In the present study, the efficiency of the base models and the proposed ensemble model is evaluated on all these sets. Finally, it is concluded that the use of the ensemble model can reduce the average correlation coefficient (as one of the evaluation criteria of the model) to 74.4 ± 16.4, which is an acceptable result.
Keywords: regression, Ensemble Model, Facebook, Comment Volume Prediction -
International Journal Of Nonlinear Analysis And Applications, Volume:11 Issue: 1, Winter-Spring 2020, PP 433 -444
A primary aspect of human aging is progressive neurological dysfunction. Due to the fundamental variations in aging in mice and humans, it is difficult to obtain and research effective mouse models. There are two types of tissue phenotypes that are distinct; one is the tissue for retina and one for the hippocampus. Each form has three strains. A variational formulation for sparse approximations is introduced in this work, inferring both the kernel hyper-parameters and inducing inputs by maximising a lower bound of probability of true log marginal. In order to account for more complexity with the time series, a model is built on this series with a correlated human model performance. The molecular senescence of the hippocampus and retina, both with accelerated neurological senescence (SAMP10 and SAMP8) models were presented. The purpose of the study is to specify the relationship between these genes or pathways that would provide insight into the mechanism for this phenotype which will be superior to the current incomplete state-of-the-art approximations. Furthermore, the combined study of the essential features of inbred strains and profiling of gene expression can help determine which genes are essential for complex phenotypes. However, the identification, sequencing and gene expression of full-genome polymorphism of inbred mouse strains with intermediate.
Keywords: Sparse Gaussian Process (Classification, Regression), Puma Package, Coregionalisation Model, Senescence-Accelerated Mice strains
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