Predicting student outcomes is an essential task and a central challenge among artificial intelligence-based personalised learning applications. Despite several studies exploring student performance prediction, there is a notable lack of comprehensive and comparative research that methodically evaluates and compares multiple machine learning models alongside deep learning architectures. In response, our research provides a comprehensive comparison to evaluate and improve ten different machine learning and deep learning models, either well-established or cutting-edge techniques, namely, random forest, decision tree, support vector machine, K-nearest neighbours classifier, logistic regression, linear regression, and state-of-the-art extreme gradient boosting (XGBoost), as well as a fully connected feed-forward neural network, a convolutional neural network, and a gradient-boosted neural network. We implemented and fine-tuned these models using Python 3.9.5. With a keen emphasis on prediction accuracy and model performance optimisation, we evaluate these methodologies across two benchmark public student datasets. We employ a dual evaluation approach, utilising both k-fold cross-validation and holdout methods, to comprehensively assess the models’ performance. Our research focuses primarily on predicting student outcomes in final examinations by determining their success or failure. Moreover, we explore the importance of feature selection using the ubiquitous Lasso for dimensionality reduction to improve model efficiency, prevent overfitting, and examine its impact on prediction accuracy for each model, both with and without Lasso. This study provides valuable guidance for selecting and deploying predictive models for tabular data classification like student outcome prediction, which seeks to utilise data-driven insights for personalised education.

In this work, we obtain a new formula for Fibonacci’s family m-step sequences. We use our formula to find the nth term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence m-step relations with constant coefficients by using the last few terms of its corresponding Fibonacci’s family m-step sequence. As a computational number theory application, we develop a method to estimate the square roots.

Handling high-dimensional datasets presents substantial computational challenges, particularly when the number of features far exceeds the number of observations and when features are highly correlated. A modern approach to mitigate these issues is feature screening. In this work, the High-dimensional Ordinary Least-squares Projection (HOLP) feature screening method is advanced by employing adaptive ridge regularization. The impact of the ridge tuning parameter on the Ridge-HOLP method is examined and Adaptive iterative ridge-HOLP (Air-HOLP) is proposed, a data-adaptive advance to Ridge-HOLP where the ridge-regularization tuning parameter is selected iteratively and optimally for better feature screening performance. The proposed method addresses the challenges of tuning parameter selection in high dimensions by offering a computationally efficient and stable alternative to traditional methods like bootstrapping and cross-validation. Air-HOLP is evaluated using simulated data and a prostate cancer genetic dataset. The empirical results demonstrate that Air-HOLP has improved performance over a large range of simulation settings. We provide R codes implementing the Air-HOLP feature screening method and integrating it into existing feature screening methods that utilize the HOLP formula.

In this work, we develop a new method for estimating the mean and standard deviation of normally distributed populations when errors exist in the sample. Our estimators are asymptotically unbiased if all errors are outlying errors (i.e. all errors lie outside a region defined by the parameters of normal distribution). However, the proposed method requires having an upper bound for the percentage of errors in the sample. The proposed method is compared with the already existing and commonly used estimators in terms of bias, mean square error, and Pitman closeness criterion. The proposed method is found to be superior to the others when the sample size is not too small. A simulation study is designed to test the performance of our estimators when most but not all errors are outlying errors. The findings of the simulation study also indicate the superiority of the proposed method when the sample size is moderately large. As an application, we use our method in Phase I of designing a control chart to improve its performance. We apply the method on a dataset where the robustness of our proposed method is tested (and compared with the other estimators) against the presence of outlying errors in Phase I data. In the findings of the application, we notice that our estimators were the only ones that identified out of control data points in Phase II when Phase I samples are contaminated with the outliers.

Implements two complementary high-dimensional feature screening methods, Adaptive Iterative Ridge High-dimensional Ordinary Least-squares Projection (Air-HOLP, suitable when the number of predictors p is greater than or equal to the sample size n) and Adaptive Iterative Ridge Ordinary Least Squares (Air-OLS, for n greater than p). Also provides helper functions to generate compound-symmetry and AR(1) correlated data, plus a unified Air() front end and a summary method. For methodological details see Joudah, Muller and Zhu (2025) .