Statistics, Optimization & Information Computing

Least square estimation of non-linear structural models

Reinhard Oldenburg — 2023-12-18

A new method for estimating a wide class of structural equation models (SEM) is proposed and evaluated. A weighted least squares approach is used that estimates parameters and latent variables. This new approach is flexible enough to handle non-linear and non-smooth models and allows us to model various constraints. The method includes various strategies to deal with the problem of choosing weights. The principle strengths and weaknesses of this approach are discussed, and simulation studies are performed to reveal the problems and potential of this approach.

Stochastic differential equations mixed model for individual growth with the inclusion of genetic characteristics

Nelson T. Jamba — 2023-12-19

In early work we have studied a class of stochastic differential equation (SDE) models, for which the Gompertz and the Bertalanffy-Richards stochastic models are particular cases, to describe individual growth in random environments, and applied it to model cattle weight evolution using real data. We have started to work on these type of models considering that the model parameters are fixed, i.e. the same for all the animals. Aiming to incorporate variability among individuals, we consider that the model parameters can be random variables, resulting in SDE mixed models. In additon, here we consider SDE mixed models, allowing the parameters to be random and propose to incorporate each animal's genetic characteristics considering the transformed animal's weight at maturity to be a function of its genetic values. The main objective is to extend the SDE mixed model to the more realistic case where the individual genetic value becomes an important component in the estimated growth curve. For the estimation of the model parameters we have used maximum likelihood estimation theory. Estimates and asymptotic confidence intervals of the parameters are presented. A comparison with SDE non-mixed model and SDE mixed model without the inclusion of genetic characteristics is shown with the conclusion that the incorporation of some genetic characteristics in the model parameters improves the estimation of the animal's growth curve.

Solving a Typical Small Sample Size MRSM Dataset Problem Using a Flexible Hybrid Ensemble Approach for Credibility

Delson Chikobvu — 2024-01-05

Multiresponse surface methodology often involves small data analytics which, statistically, have regression modelling credibility problems. This is worsened by dataset, model selection and solution methodology uncertainties. It is difficult for solution methodologies which select and use single best models per response at simultaneous optimisation to effectively deal with these problems. This paper exploited the fact that model selection criteria choose differently, in a flexible hybrid ensemble system, to generate several solutions for integration and comparison. Mean square prediction error, with bias-variance-covariance decomposition values, was computed and analysed at simultaneous optimisation. Results suggest that the credibility of the final solution is enhanced when working with multiple models, solution methodologies and results. However, the results do not show any significance of small sample size correction to model selection criteria and analysis of bias-variance-covariance decompositions at simultaneous optimisation does not encourage dependence on theoretical optimality for best results.

Proposed Two-Steps Procedure of Classification High Dimensional Data with Regularized Logistic Regression

Omar Alshebly — 2023-11-29

The field of Bioinformatics has developed in response to the rapid increase in biological data, particularly high-dimensional gene expression data. Bioinformatics utilizes optimization, computational science, and statistical methods to effectively address challenges in the field of molecular biology. Numerous genes (variables) in gene expression are irrelevant to their study. Gene selection has been demonstrated to be an effective means of enhancing the performance of numerous methods of classification. The job of acquiring significant variables via the use of ranking variable selection (RVS) techniques and then picking the most effective classifier is an enormous challenge in the context of high-dimensional data. in this study, we proposed a new ranking filter method using smooth clipped absolute deviation depending on the resampling technique (RSVS) to obtain a proficient subset of genes with strong classification abilities. This is achieved by merging A screening technique employed as a filtering method in conjunction with Regularized Logistic Regression, such as LASSO,ALASSO,ENET, and MCP. The study involved the utilization of both simulated and real datasets to conduct an empirical evaluation of the proposed approach. The findings indicated that the proposed method outperformed other established methods. it was tested using three publicly data sets about Cancer. The Results demonstrate that the suggested approach is highly effective and viable, thus showing a strong level of performance with regards to accuracy, geometric mean, and the area under the curve. Furthermore, The findings suggest that the genes most often chosen are physiologically associated with the specific form of cancer. Therefore, the method that has been suggested has potential advantages for the classification of cancer via the use of DNA gene expression data within a clinical setting.

Filtering problem for sequences with periodically stationary multi-seasonal increments with spectral densities allowing canonical factorizations

Maksym Luz — 2023-12-03

We consider a stochastic sequence $\xi(m)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. The filtering problem is solved for this type of sequences based on observations with a periodically stationary noise. When spectral densities are known and allow the canonical factorizations, we derive the mean square error and the spectral characteristics of the optimal estimate of the functional $A{\xi}=\sum_{k=0}^{\infty}{a}(k) {\xi}(-k)$. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral
characteristics of the optimal linear estimate of the functional are proposed in the case where the spectral densities are not known, but some sets of admissible spectral densities are given.

Truncated Cauchy Power Kumaraswamy Generalized family of distributions: Theory and Applications

Ibrahim Elbatal — 2023-12-19

A new family called the Truncated Cauchy Power Kumaraswamy -G family of distributions is proposed. Some special models of this family are introduced. Statistical properties of the family such as expansion of density function, moments, incomplete moments, mean deviation, bonferroni and Lorenz curves are proposed. We discuss the method of maximum likelihood to estimate the model parameters and study its performance by simulation. Real data sets are modeled to illustrate the importance and exibility of the proposed model in comparison to some known ones yielded favourable results.

The Type II Exponentiated Half Logistic-Gompertz-G Power Series Class of Distributions: Properties and Applications

Simbarashe Chamunorwa — 2024-02-17

We propose and study a new generalized class of distributions called the Type II Exponentiated Half Logistic-
Gompertz-G Power Series (TIIEHL-Gom-GPS) distribution. Some structural properties including expansion of density,
ordinary and conditional moments, generating function, order statistics and entropy are derived. We present some special
cases of the proposed distribution. The maximum likelihood method is used for estimating the model parameters. The
importance of the new class of distributions are illustrated by means of two applications to real data sets.

On the Jajte Law of Large Numbers for Exchangeable Random Variables

Habib Naderi — 2023-12-19

In this paper, we prove an extension of the Jajte strong law of large numbers for exchangeable random variables, we make a simulation study for the asymptotic behavior in the sense of convergence almost surly for weighted sums of exchangeable weighted random variables.

An Algorithm for Solving Quadratic Programming Problems with an M-matrix

Katia Hassaini — 2024-02-18

In this study, we propose an approach for solving a quadratic
programming problem with an M-matrix and simple constraints (QPs). It is
based on the algorithms of Luk-Pagano and Stachurski. These methods use
the fact that an M-matrix possesses a nonnegative inverse which allows to
have a sequence of feasible points monotonically increasing. Introducing the
concept of support for an objective function developed by Gabasov et al., our
approach leads to a more general condition which allows to have an initial
feasible solution, related to a coordinator support and close to the optimal
solution. The programming under MATLAB of our method and that of Luk
and Pagano has allowed us to make a comparison between them, with an
illustration on two numerical examples.

Bayesian Estimation of the Odd Lindley Exponentiated Exponential Distribution : Applications in-Reliability

Nour El houda Djemoui — 2024-01-29

In this work, we investigate the estimation of the unknown parameters and the reliability characteristics of
the Odd Lindley Exponentiated Exponential distribution. The Bayes estimators and corresponding risks are derived using
various loss functions with complete data and a gamma prior distribution. A simulation study was carried out to calculate all
the results. We used Pitman’s closeness criterion and the integrated mean squared error to compare the performance of the
Bayesian and maximum likelihood estimators. Finally, we illustrate our techniques by analysing a real-life data set.

Comparative Study between Partial Bayes and Empirical Bayes Method in Gamma Distribution

Babulal Seal — 2023-12-19

Though the name Partial Bayes was used earlier in a different context, but in statistics this is started from 2021, (Banerjee and Seal, 2021). Also, we know that empirical Bayes method was studied extensively for several decades. In this paper, these two methods are compared in two parameter gamma distribution having shape and scale parameter. As expected, it is found that empirical Bayes method is good in some cases. However, partial Bayes method performs even better in some cases where the shape parameter is sufficiently small, i.e. variation in the data is small. Even, overall performances of these two methods do not differ too much. But whenever we have information that shape parameter is small, then in that case partial Bayes method performs well. These results are also found by extensive simulation technique. The performances of these two estimators are also compared using two real datasets.

An Enhanced Genetic Algorithm using Directional-Based Crossover and normal mutation For Global Optimization Problems

Ahmed M.Abdelkhalek — 2023-12-29

Global optimization has been employed in many practical modeling processes. Using gradient methods to solve optimization problems may be computationally inefficient and time-consuming, particularly when convexity or differentiability is not guaranteed. On the other hand, nature-inspired techniques offer an effective gradient-free approach for solving complex, non-convex, or non-differentiable problems. Genetic algorithms are one of the most effective and widely used nature-inspired techniques. However, canonical genetic algorithms do not always guarantee convergence to the optimum point owing to the stochastic nature of the genetic operators, and typically require more work to ensure convergence and increase performance. Improving the genetic operators remains an open issue and usually involves a trade-off between the speed of convergence and searchability. In this study, we propose an enhanced genetic algorithm that relies on directional-based crossover and normal mutation operators to increase the speed of convergence while preserving searchability. The proposed algorithm is evaluated using a set of 40 typical benchmark functions in two dimensions. In addition, to examine its performance at higher dimensions, 16 functions from the test set were tested at 10 and 100 dimensions. The evaluation results of the proposed algorithm are compared to the outcomes of three modern optimization algorithms, namely (Whale optimization algorithm, Teacher-Learner based algorithm, and Covariance matrix adaptation evolution strategy). The results revealed that the proposed algorithm outperformed the conventional algorithms at lower dimensions in all test functions and showed a relatively better performance than the other algorithms at higher dimensions.

Risk assessment in cryptocurrency portfolios: a composite hidden Markov factor analysis framework

Mohamed Saidane — 2024-01-05

In this paper, we deal with the estimation of two widely used risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES) in a cryptocurrency context. To face the presence of regime switching in the cryptocurrency volatilities and the dynamic interconnection between them, we propose a Monte Carlo-based approach using heteroskedastic factor analysis and hidden Markov models (HMM) combined with a structured variational Expectation-Maximization (EM) learning approach. This composite approach allows the construction of a diversified portfolio and determines an optimal allocation strategy making it possible to minimize the conditional risk of the portfolio and maximize the return. The out-of-sample prediction experiments show that the composite factorial HMM approach performs better, in terms of prediction accuracy, than some other baseline methods presented in the literature. Moreover, our results show that the proposed methodology provides the best performing crypto-asset allocation strategies and it is also clearly superior to the existing methods in VaR and ES predictions.

On Probabilistic Cooperative Search Model to Detect a Lost Target in N-Disjoint Areas

Mohamed El-Hadidy — 2024-01-17

This paper presents a new probabilistic coordinated search technique for finding a randomly located target in n-disjoint known regions by using n-searchers. Each region contains one searcher. The searchers use advanced technology to communicate with each other. The purpose of this paper is to obtain the candidate utility function namely the expected value of the time for detecting the target. Additionally, to minimize this expected value given a restricted amount of time. We present a special case when the target has a multinomial distribution. This important for searching about a valuable target missing at sea or lost at wilderness area.

Unemployment Rates in Vocational Education in Indonesia Using Economic and Statistical Analysis

Suryadi — 2024-01-05

The linear regression model is used in this research to study the influence of the independent variable on the dependent variable. The dependent variable Y is the unemployment rate in vocational education, while the independent variables are X₁ in the form of Job Opportunities, X₂ in the form of Policy and X₃ in the form of Area. To estimate model parameters, the Ordinary Least Square method is used. The research results show that the three independent variables have a significant effect on the dependent variable. Variable X1 has a significant positive effect on the unemployment rate, variables X₂ and X₃ have a significant negative effect on the unemployment rate in vocational higher education in Indonesia. From the results of this research, there has been an oversupply of labor in vocational higher education in Indonesia.

Statistical Models to Measure the Impact of Intellectual Property Rights Protection on Foreign Trade in Egypt

Hanaa Hussein Ali — 2024-01-29

This study aims to estimate the relationship between the Protection of intellectual property rights indices and the foreign trade index in Egypt from 1995 to 2022. The comparison has been made between many models such as full modified ordinary least squares (FMOLS) model, dynamic ordinary least squares (DOLS) model , canonical co-integration regression (CCR) model and autoregressive distributed lag (ARDL) model. The results of the study showed that the best model was the ARDL model to increase its interpretive capacity. The study also showed that the most important property rights protection indicators affecting the foreign trade index are the number of applications and registrations of brands, the number of patents registered and granted, the number of applications and registrations of industrial designs, and the proportion of expenditure on research and development as a proportion of gross domestic product (GDP). The estimated model also passed all diagnostic tests and showed that there was no autocorrelation, no Heteroskedasticity. In addition, it was found to follow a normal distribution and to be stable.

Using transfer adaptation method for dynamic features expansion in multi-label deep neural network for recommender systems

Fargana Abdullayeva — 2024-02-17

In this paper, we propose to use a convertible deep neural network (DNN) model with a transfer adaptation mechanism to deal with varying input and output numbers of neurons. The flexible DNN model serves as a multi-label classifier for the recommender system as part of the retrieval systems’ push mechanism, which learns the combination of tabular features and proposes the number of discrete offers (targets). Our retrieval system uses the transfer adaptation, mechanism, when the number of features changes, it replaces the input layer of the neural network then freezes all gradients on the following layers, trains only replaced layer, and unfreezes the entire model. The experiments show that using the transfer adaptation technique impacts stable loss decreasing and learning speed during the training process.

An Effective Randomized Algorithm for Hyperspectral Image Feature Extraction

Jinhong Feng — 2024-02-18

Analyzing the spectral and spatial characteristics of Hyperspectral Imaging (HSI) in a three-dimensional space is a challenging task. Recently, there have been developments in 3D feature extraction methods based on tensor decomposition, which allow for the effective utilization of both global and local information in HSI. These methods also explore the inherent low-rank properties of HSI through tensor decomposition. In this paper, we propose a new approach called variable randomized T-product decomposition (Vrt-SVD), which is a variation of Tensor Singular Spectral Analysis. The goal of this approach is to improve the efficiency of tensor methods for feature extraction and reduce artifacts of image processing. By using a randomized algorithm based on the variable t-SVD, we are able to capture both global and local spatial and spectral information in HSI efficiently, which enables us to explore its low-rank characteristics. To evaluate the effectiveness of the extracted features, we use a Support Vector Machine (SVM) classifier to assess the accuracy of image classification. By conducting numerous numerical experiments, we provide strong evidence to show that the proposed method outperforms several advanced feature extraction techniques.

Comparative Evaluation of Imbalanced Data Management Techniques for Solving Classification Problems on Imbalanced Datasets

Tanawan Watthaisong — 2024-02-18

Dealing with imbalanced data is crucial and challenging when developing effective machine-learning models for data classification purposes. It significantly impacts the classification model's performance without proper data management, leading to suboptimal results. Many methods for managing imbalanced data have been studied and developed to improve data balance. In this paper, we conduct a comparative study to assess the influence of a ranking technique on the evaluation of the effectiveness of 66 traditional methods for addressing imbalanced data. The three classification models, i.e., Decision Tree, Random Forest, and XGBoost, act as classification models. The experimental settings have been divided into two segments. The first part evaluates the performance of various imbalanced dataset handling methods, while the second part compares the performance of the top 4 oversampling methods. The study encompasses 50 separate datasets: 20 retrieved from the UCI repository and 30 sourced from the OpenML repository. The evaluation is based on F-Measure and statistical methods, including the Kruskal-Wallis test and Borda Count, to rank the data imbalance handling capabilities of the 66 methods. The SMOTE technique is the benchmark for comparison due to its popularity in handling imbalanced data. Based on the experimental results, the MCT, Polynom-fit-SMOTE, and CBSO methods were identified as the top three performers, demonstrating superior effectiveness in managing imbalanced datasets. This research could be beneficial and serve as a practical guide for practitioners to apply suitable techniques for data management.

Review of Reinforcement Learning for Robotic Grasping: Analysis and Recommendations

Hiba Sekkat — 2023-12-19

This review paper provides a comprehensive analysis of over 100 research papers focused on the challenges of robotic grasping and the effectiveness of various machine learning techniques, particularly those utilizing Deep Neural Networks (DNNs) and Reinforcement Learning (RL). The objective of this review is to simplify the research process for others by gathering different forms of Deep Reinforcement Learning (DRL) grasping tasks in one place. Through a thorough analysis of the literature, the study emphasizes the critical nature of grasping for robots and how DRL techniques, particularly the Soft-Actor-Critic (SAC) strategy, have demonstrated high efficiency in handling the task. The results of this study hold significant implications for the development of more advanced and efficient grasping systems for robots. Continued research in this area is crucial to further enhance the capabilities of robots in handling complex and challenging tasks, such as grasping.