Sharpening Occam's Razor: A Kolmogorov Complexity-Based Approach

Title: Sharpening Occam's Razor: A Kolmogorov Complexity-Based Approach

Abstract: This research article presents a new formulation of Occam's razor theorem, based on Kolmogorov complexity. This formulation allows for better sample complexity than both length-based and VC-based versions of Occam's razor theorem in many applications, and achieves a sharper reverse of Occam's razor theorem. The authors weaken the assumptions made in a previous study [5] and extend the reverse to superpolynomial running times.

Keywords: Analysis of algorithms, pac-learning, Kolmogorov complexity, Occam's razor-style theorems

Main Research Question: Can a representation-independent formulation of Occam's razor theorem improve the sample complexity and provide a sharper reverse of the theorem?

Methodology: The authors use a new formulation of Occam's razor theorem based on Kolmogorov complexity. This approach allows for a more precise definition of the theorem and enables the authors to achieve better sample complexity and a sharper reverse of the theorem.

Results: The authors provide results that show that their KC-based Occam's razor theorem is convenient to use, provides better sample complexity than the length-based version, and is representation-independent. They also demonstrate that their formulation allows for a sharper reverse of Occam's razor theorem than previously proved.

Implications: The new formulation of Occam's razor theorem presented in this research article has significant implications for the field of machine learning and data analysis. It provides a more accurate and efficient method for determining the optimal complexity of learning algorithms and offers a sharper reverse of Occam's razor theorem. Additionally, the results of this study may have implications for other areas of computer science and mathematics that rely on Occam's razor theorem.

Link to Article: https://arxiv.org/abs/0201005v2 Authors: arXiv ID: 0201005v2