In this paper we investigate connections between statistical learning<br />theory and data compression on the basis of support vector machine<br />(SVM) model selection. Inspired by several generalization bounds we<br />construct ``compression coefficients'' for SVMs, which measure the<br />amount by which the training labels can be compressed by some<br />classification hypothesis. The main idea is to relate the coding<br />precision of this hypothesis to the width of the margin of the<br />SVM. The compression coefficients connect well known quantities such<br />as the radius-margin ratio R\verb=^=2/rho\verb=^=2, the eigenvalues of the kernel<br />matrix and the number of support vectors. To test whether they are<br />useful in practice we ran model selection experiments on several real<br />world datasets. As a result we found that compression coefficients can<br />fairly accurately predict the parameters for which the test error is<br />minimized.
Luxburg Scholkopf, B. (2004). A Compression Approach to Support Vector Model Selection. Journal of Machine Learning Research, 5, 293–323. https://doi.org/10.1080/1369118X.2012.678878