High-Dimensional Data and the Bias Variance Tradeoff in Model Selection

Abstract

The exploration of function estimation from a specific dataset was primarily theoretical until the 1990s, despite the development of statistical learning theory in the late 1960s. This shift allowed statistical learning theory to be applied in practical multidimensional function estimation methods alongside theoretical evaluations. Statistical learning represents a contemporary approach to machine learning that employs mathematical models, algorithms, and statistical techniques to detect patterns and make predictions from large datasets. The extensive use of statistical learning in fields ranging from genetics and biology to economics and social datasets is clear from a thorough examination of the literature. This methodology has recently been used in a number of disciplines, including computer science, biology, finance, and social science. Model selection is one of the main obstacles to solving each of these studies' problems. Because the influence of bias-variance tradeoff in model selection plays a vital role especially in analyzing high-dimensional data. This comprehensive scientific review aims to investigate the role of the bias-variance tradeoff in model selection for high-dimensional datasets. We examine the concepts of bias and variance, their interrelationship, and their effects on model performance regarding prediction accuracy and generalization. Additionally, we highlight numerous strategies and techniques used to balance the bias-variance tradeoff during model selection. This review provides insights into the importance of understanding and managing the bias-variance tradeoff for effective model selection in high-dimensional data analysis.