Assessing the Impact of Model Complexity on Overfitting Risk and Predictive Performance in Statistical Learning

Posted: Nov 08, 2018

• Charlotte Morales
• Claire Cook
• Daniel Wood

Abstract

The fundamental challenge in statistical learning involves balancing model complexity with generalization capability. While complex models can capture intricate patterns in training data, they often suffer from overfitting, where they memorize noise rather than learning underlying relationships. The classical bias-variance tradeoff provides a theoretical foundation for understanding this phenomenon, but practical applications reveal limitations in existing complexity metrics and their relationship to overfitting risk. Traditional approaches to model selection typically rely on parameter counts or degrees of freedom as proxies for complexity, yet these measures often fail to capture the true capacity of modern learning algorithms to overfit. This research addresses critical gaps in our understanding of how different dimensions of model complexity contribute to overfitting across varying data conditions. We propose that complexity should be conceptualized as a multifaceted construct encompassing not only the number of parameters but also the functional flexibility, interaction depth, regularization sensitivity, and architectural constraints of learning algorithms. Our investigation seeks to answer several fundamental questions: How do different complexity dimensions interact to influence overfitting risk? What are the optimal complexity thresholds for various data characteristics? Can we develop more robust complexity metrics that better predict generalization performance? Our work makes several novel contributions to the field. First, we introduce a comprehensive framework for quantifying model complexity across multiple dimensions, moving beyond traditional single-metric approaches. Second, we systematically evaluate how these complexity dimensions interact with dataset characteristics to influence overfitting patterns. Third, we identify specific complexity thresholds and interaction effects that have practical implications for model selection and regularization strategies. Finally, we provide empirical evidence challenging conventional assumptions about the linear relationship between complexity and overfitting risk.