Data complexity in machine learning

Li, Ling and Abu-Mostafa, Yaser S. (2006) Data complexity in machine learning. Technical Report. California Institute of Technology, Pasadena, USA. [CaltechCSTR:2006.004]

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Abstract

We investigate the role of data complexity in the context of binary classification problems. The universal data complexity is defined for a data set as the Kolmogorov complexity of the mapping enforced by the data set. It is closely related to several existing principles used in machine learning such as Occam's razor, the minimum description length, and the Bayesian approach. The data complexity can also be defined based on a learning model, which is more realistic for applications. We demonstrate the application of the data complexity in two learning problems, data decomposition and data pruning. In data decomposition, we illustrate that a data set is best approximated by its principal subsets which are Pareto optimal with respect to the complexity and the set size. In data pruning, we show that outliers usually have high complexity contributions, and propose methods for estimating the complexity contribution. Since in practice we have to approximate the ideal data complexity measures, we also discuss the impact of such approximations.

EPrint Type:	Monograph (Technical Report)
Subjects:	All Records
ID Code:	557
Deposited By:	Ling Li
Deposited On:	31 May 2006
Record Number:	CaltechCSTR:2006.004
Official Persistent URL:	http://resolver.caltech.edu/CaltechCSTR:2006.004
Official Citation:	L. Li and Y. S. Abu-Mostafa. Data complexity in machine learning. Computer Science Technical Report CaltechCSTR:2006.004, California Institute of Technology, May 2006.
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

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