The Vapnik-Chervonenkis (VC) dimension is an important concept in the field of computational learning theory that provides a measure for the complexity of a model or system. It was developed by Vladimir Vapnik and Alexey Chervonenkis in the early 1970s and used in the development of the Support Vector Machine (SVM) and related algorithms. The VC dimension is typically used to measure the capacity of a machine learning algorithm; that is, its ability to “learn” from a training set and generalize to unseen data. It is an important feature both for understanding the capabilities of a system prior to use and for assessing the accuracy and reliability of results.
The VC dimension is defined as the number of distinct patterns that a model can classify correctly, and is determined by the number of parameters used within the model. For instance, a linear model with two free parameters can accurately classify up to three distinct patterns. A model with three free parameters can accurately classify up to seven distinct patterns, and so on. This simple relationship is described by the VC dimension formula which is usually expressed as:
d_{vc} = m + 1, where m is the number of parameters used in the model.
The VC dimension is most often used to analyze the performance of supervised learning algorithms, but it is also applicable to other types of models and systems. In particular, it is useful for analyzing the capabilities and limitations of a neural network, which, due to its complexities, is typically difficult to analyze. Because of its versatility and ubiquity, the VC dimension is considered a fundamental concept in computational learning theory and is a central tool used to evaluate and compare the accuracy and performance of machine learning algorithms.
The VC dimension is sometimes referred to as the needlestack dimension or complexity dimension.
