Statistics, Optimization & Information Computing

A Modified Inexact SARAH Algorithm with Stabilized Barzilai-Borwein Step-Size in Machine learning

Fusheng Wang — 2023-08-18

The Inexact SARAH (iSARAH) algorithm as a variant of SARAH algorithm, which does not require computation of the exact gradient, can be applied to solving general expectation minimization problems rather than only finite sum problems. The performance of iSARAH algorithm is frequently affected by the step size selection, and how to choose an appropriate step size is still a worthwhile problem for study. In this paper, we propose to use the stabilized Barzilai-Borwein (SBB) method to automatically compute step size for iSARAH algorithm, which leads to a new algorithm called iSARAH-SBB. By introducing this adaptive step size in the design of the new algorithm, iSARAH-SBB can take better advantages of both iSARAH and SBB methods. We analyse the convergence rate and complexity of the modified algorithm under the usual assumptions. Numerical experimental results on standard data sets demonstrate the feasibility and effectiveness of our proposed algorithm.

Identifying the Neurocognitive Difference Between Two Groups Using Supervised Learning

Ramchandra Rimal — 2023-08-26

Brain Imaging Analysis is a dynamic and exciting field within neuroscience. This study is conducted with two main objectives. First, to develop a classification framework to enhance predictive performance, and second, to conduct a comparative analysis of accuracy versus inference using brain imaging data. The dataset of chess masters and chess novices is utilized to identify neurocognitive differences between the two groups, based on their resting-state functional magnetic resonance imaging data. A network of connections between brain regions is created and analyzed. Standard statistical learning techniques and machine learning models are then applied to distinguish connectivity patterns between the groups. The trade-off between model precision and interpretability is also assessed. Finally, model performance measures, including accuracy, sensitivity, specificity, and AUC, are reported to demonstrate the effectiveness of the model framework.

Solution of a model for pricing options with hedging strategy through Nonlinear Filters

Luis Sanchez — 2023-08-26

A methodology is presented to estimate the solution states for a non-linear price problem, a model for pricing options with a hedging strategy in the F$\ddot{o}$llmer-Schweizer sense is defined. The problem is to determine the price of a contingent claim, that is a contract, that pays of an amount at time $t$ in a incomplete market, that is not possible to replicate a payoff by a controlled portfolio of the basic securities. Two algorithms are presented to estimate the solution of the presented problem, the nested sequential Monte Carlo (NSMC) and space-time particle filter (STPF) are defined from sequences of probability distributions. The methodology is validated to use real data from option Asian, the states in real-time are estimated, that is proposed on the basis of the a price model. The efficiency of the forecasts of the model is compared, reproducing accuracy in the estimates. Finally, one goodness-of-fit measure to validate the performance of the model are used, obtaining insignificant estimation error.

Equilibrium stacks for a non-cooperative game defined on a product of staircase-function continuous and finite strategy spaces

Vadim Romanuke — 2023-10-27

A method of finite uniform approximation of 3-person games played with staircase-function strategies is presented. A continuous staircase 3-person game is approximated to a staircase trimatrix game by sampling the player’s pure strategy value set. The set is sampled uniformly so that the resulting staircase trimatrix game is cubic. An equilibrium of the staircase trimatrix game is obtained by stacking the equilibria of the subinterval trimatrix games, each defined on an interval where the pure strategy value is constant. The stack is an approximate solution to the initial staircase game. The (weak) consistency, equivalent to the approximate solution acceptability, is studied by how much the players’ payoff and equilibrium strategy change as the sampling density minimally increases. The consistency includes the payoff, equilibrium strategy support cardinality, equilibrium strategy sampling density, and support probability consistency. The most important parts are the payoff consistency and equilibrium strategy support cardinality (weak) consistency, which are checked in the quickest and easiest way. However, it is practically reasonable to consider a relaxed payoff consistency, by which the player’s payoff change in an appropriate approximation may grow at most by epsilon as the sampling density minimally increases. The weak consistency itself is a relaxation to the consistency, where the minimal decrement of the sampling density is ignored. An example is presented to show how the approximation is fulfilled for a case of when every subinterval trimatrix game has pure strategy equilibria.

Hybrid GA–DeepAutoencoder–KNN Model for Employee Turnover Prediction

CHIN SIANG LIM — 2023-10-27

Organizations strive to retain their top talent and maintain workforce stability by predicting employee turnover and implementing preventive measures. Employee turnover prediction is a critical task, and accurate prediction models can help organizations take proactive measures to retain employees and reduce turnover rates. Therefore, in this study, we propose a hybrid genetic algorithm–autoencoder–k-nearest neighbor (GA–DeepAutoencoder–KNN) model to predict employee turnover. The proposed model combines a genetic algorithm, an autoencoder, and the KNN model to enhance prediction accuracy. The proposed model was evaluated and compared experimentally with the conventional DeepAutoencoder–KNN and k-nearest neighbor models. The results demonstrate that the GA–DeepAutoencoder–KNN model achieved a significantly higher accuracy score (90.95\%) compared to the conventional models (86.48% and 88.37% accuracy, respectively). Our findings are expected to assist HR teams identify at-risk employees and implement targeted retention strategies to improve the retention rate of valuable employees. The proposed model can be applied to various industries and organizations, making it a valuable tool for HR professionals to improve workforce stability and productivity.

The odd log- logistic Power Inverse Lindley distribution: Model, Properties and Applications

Mahmoud Eltehiwy — 2023-11-13

In this article, we introduce a new three-parameter odd log-logistic power inverse Lindley distribution and discuss some of its properties. These include the shapes of the density and hazard rate functions, mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and root mean square error of the maximum likelihood estimators of the parameters. An application of the model to three real data sets is presented finally and compared with the fit attained by some other well-known two and three-parameter distributions for illustrative purposes. It is observed that the proposed model has some advantages in analyzing lifetime data as compared to other popular models in the sense that it exhibits varying shapes and shows more flexibility than many currently available distributions.

The Topp-Leone Odd Burr X-G Family of Distributions: Properties and Applications

Broderick Oluyede — 2023-11-13

This paper proposes a new generalized family of distributions called the Topp-Leone odd Burr X-G (TLOBX-G) distribution and its special model, Topp-Leone odd Burr X-Weibull (TLOBX-W) is studied in detail. Structural properties are derived, including the hazard rate function, quantile function, density expansion, moments, R'enyi entropy, and order statistics. The maximum likelihood technique is used to estimate the parameters of the new family of distributions and a simulation study was carried out to assess the accuracy and consistency of these estimators. Finally, the applicability, usefulness, and flexibility of TLOBX-W distribution are illustrated using two real-life datasets.

Estimation of the Multicomponent Stress-Strength Reliability Model Under the Topp-Leone Distribution: Applications, Bayesian and Non-Bayesian Assessement

M. Rasekhi — 2023-11-13

The advantages of applying multicomponent stress-strength models lie in their ability to provide a comprehensive and accurate analysis of system reliability under real-world conditions. By accounting for the interactions between different stress components and identifying critical weaknesses, engineers can make informed decisions, leading to safer and more reliable designs. The primary emphasis of this research is placed on the Bayesian and classical estimations of a multicomponent stress-strength reliability model that is derived from the bounded Topp Leone distribution. It is presumable that both stress and strength follow a Topp Leone distribution, but the shape parameters of each variable differ, and the scale parameters (which determine where the variable is bounded) remain the same. Statisticians utilize approaches such as maximum likelihood paired with parametric and non-parametric bootstrap, as well as Bayesian methods, in order to evaluate the dependability of a system. Bayesian methods are also utilized. Simulation studies are carried out with the intention of establishing the degree of precision that may be achieved by employing the various methods of estimating. For the sake of this example, two genuine data sets are dissected and examined in detail.

Complexity Analysis of an Interior-point Algorithm for CQP Based on a New Parametric Kernel Function

Randa Chalekh — 2023-09-04

In this paper, we present a primal-dual interior-point algorithm for convex quadratic programming problem based on a new parametric kernel function with a hyperbolic-logarithmic barrier term. Using the proposed kernel function we show some basic properties that are essential to study the complexity analysis of the correspondent algorithm which we find coincides with the best know iteration bounds for the large-update method, namely, $O\left(\sqrt{n} \log n \log\frac{n}{\varepsilon}\right)$ by a special choice of the parameter $p>1$.

A new routing method based on ant colony optimization in vehicular ad-hoc network

Oussama Sbayti — 2023-11-13

Vehicular Ad hoc Networks (VANETs) face significant challenges in providing high-quality service. These networks enable vehicles to exchange critical information, such as road obstacles and accidents, and support various communication modes known as Vehicle-to-Everything (V2X). This research paper proposes an intelligent method to improve the quality of service by optimizing path selection between vehicles, aiming to minimize network overhead and enhance routing efficiency. The proposed approach integrates Ant Colony Optimization (ACO) into the Optimized Link State Routing (OLSR) protocol. The effectiveness of this method is validated through implementation and simulation experiments conducted using the Simulation of Urban Mobility (SUMO) and the network simulator (NS3). Simulation results demonstrate that the proposed method outperforms the traditional OLSR algorithm in terms of throughput, average packet delivery rate (PDR), end-to-end delay (E2ED), and average routing overhead.

Implementation of Fuzzy Logic Controller Algorithms with MF optimization on FPGA

Samet Ahmed — 2023-11-13

In this work, we propose the design and implementation of a parallel-structured fuzzy logic controller with integral action and anti-windup. The Grey Wolf Optimization (GWO) optimization technique is used to optimize fuzzy rules, which allows for the complicated algebraic ideas of type 1 fuzzy logic algorithms to be reduced to straightforward numerical equations for FPGA target implementation. The techniques for operating a geared DC motor are optimized by the membership function structure of our controller's data propagation. Our proposed controller was implemented in Xilinx System Generator (XSG) and co-simulated on hardware and software with VIVADO and XSG tools.

Forecasting International Stock Market Trends: XGBoost, LSTM, LSTM-XGBoost, and Backtesting XGBoost Models

HASSAN OUKHOUYA — 2023-11-03

Forecasting time series is crucial for financial research and decision-making in business. The nonlinearity of stock market prices profoundly impacts global economic and financial sectors. This study focuses on modeling and forecasting the daily prices of key stock indices - MASI, CAC 40, DAX, FTSE 250, NASDAQ, and HKEX, representing the Moroccan, French, German, British, US, and Hong Kong markets, respectively. We compare the performance of machine learning models, including Long Short-Term Memory (LSTM), eXtreme Gradient Boosting (XGBoost), and the hybrid LSTM-XGBoost, and utilize the skforecast library for backtesting. Results show that the hybrid LSTM-XGBoost model, optimized using Grid Search (GS), outperforms other models, achieving high accuracy in forecasting daily prices. This contribution offers financial analysts and investors valuable insights, facilitating informed decision-making through precise forecasts of international stock prices.

Statistical Analysis of Covid-19 Data using the Odd Log Logistic Kumaraswamy Distribution

Festus Opone — 2023-11-13

This paper presents a statistical analysis of Covid-19 data using the Odd log logistic kumaraswamy Kumaraswamy (OLLK) distribution. Some mathematical properties of the proposed OLLK distribution such as the survival and hazard functions, quantile function, ordinary and incomplete
moments, moment generating function, probability weighted moment, distribution of order
statistic and Renyi entropy were derived. Five estimators are examined for unknown model parameters. The performance of the estimators is compared using an extensive simulation study based on the bias and mean square error criteria. Two Covid-19 data sets representing the percentage of daily recoveries of Covid-19 patients are used to illustrate the applicability of the
proposed OLLK distribution. Results revealed that the OLLK distribution is a better alternative to some existing models with bounded support.

Modified Generalized Linear Exponential Distribution: Properties and applications

Hossam Radwan — 2023-08-26

In this paper, we propose a new four-parameter lifetime distribution called modified generalized linear exponential distribution. The proposed distribution is a modification of the generalized linear exponential distribution. Several important lifetime distributions in reliability engineering and survival analysis are considered as special sub-models including modified Weibull, Weibull, linear exponential and generalized linear exponential distributions, among others. We study the mathematical and statistical properties of the proposed distribution including moments, moment generating function, modes, and quantile. We then examine hazard rate, mean residual life, and variance residual life functions of the distribution. A significant property of the new distribution is that it can have a bathtub-shaped, which is very flexible for modeling reliability data.The four unknown parameters of the proposed model are estimated by the maximum likelihood. Finally, two practical real data sets are applied to show that the proposed distribution provides a superior fit than the other sub-models and some well-known distributions.

Failure rate, vitality, and residual lifetime measures: Characterizations based on stress-strength bivariate model with application to an automated life test data

M. S Eliwa — 2023-11-17

In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode.