Journal of Engineering Mathematics & Statistics ISSN: 3139-1222 (Online)

Authors: Surender Venkatesh, Ranjeet Prasad, Neha Kulkarni

Abstract: The rapid growth of data across engineering, science, economics, and social domains has increased the need for advanced statistical models capable of handling multiple interrelated variables simultaneously. Multivariate statistical models have long served as a core analytical framework for understanding complex dependency structures among variables. In recent years, learning-based statistical models, particularly those inspired by machine learning, have significantly expanded the scope and performance of traditional multivariate approaches. This paper presents a comprehensive review of multivariate and learning-based statistical models, highlighting their theoretical foundations, methodological developments, and practical applications. Classical techniques such as multivariate regression, principal component analysis, and factor analysis are discussed alongside modern learning-based models including neural networks, support vector machines, and ensemble methods. The paper also examines hybrid frameworks that integrate probabilistic modeling with data-driven learning strategies. Challenges such as high dimensionality, interpretability, and computational complexity are critically analyzed. The review concludes by outlining emerging trends and open research problems in multivariate and learning-based statistical modeling.

Keywords: Multivariate analysis, statistical learning, high-dimensional data, machine learning models, probabilistic modeling, data-driven methods