A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)

The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.Comment: 20 pages, Chapter 1 of The Paradox of Overfitting, Master's thesis, Rijksuniversiteit Groningen, 200

Quantifying Overfitting: Introducing the Overfitting Index

In the rapidly evolving domain of machine learning, ensuring model generalizability remains a quintessential challenge. Overfitting, where a model exhibits superior performance on training data but falters on unseen data, is a recurrent concern. This paper introduces the Overfitting Index (OI), a novel metric devised to quantitatively assess a model's tendency to overfit. Through extensive experiments on the Breast Ultrasound Images Dataset (BUS) and the MNIST dataset using architectures such as MobileNet, U-Net, ResNet, Darknet, and ViT-32, we illustrate the utility and discernment of the OI. Our results underscore the variable overfitting behaviors across architectures and highlight the mitigative impact of data augmentation, especially on smaller and more specialized datasets. The ViT-32's performance on MNIST further emphasizes the robustness of certain models and the dataset's comprehensive nature. By providing an objective lens to gauge overfitting, the OI offers a promising avenue to advance model optimization and ensure real-world efficacy

Replica analysis of overfitting in regression models for time-to-event data

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox's proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. In this paper we present a mathematical theory of overfitting in regression models for time-to-event data, which aims to increase our quantitative understanding of the problem and provide practical tools with which to correct regression outcomes for the impact of overfitting. It is based on the replica method, a statistical mechanical technique for the analysis of heterogeneous many-variable systems that has been used successfully for several decades in physics, biology, and computer science, but not yet in medical statistics. We develop the theory initially for arbitrary regression models for time-to-event data, and verify its predictions in detail for the popular Cox model.Comment: 37 pages, 9 figure