Abstract
This statistical learning theory frameworks that are used when the examples are not provided sequentially are discussed. A new PAC Bound framework for Intersection-Closed Concepts Classes is introduced that will provide a number of examples that are needed for an algorithm to achieve a given accuracy in its prediction. The framework provide an improved bound for inspection closed concept classes of binary valued functions closed by product of a combinatorial parameter describing the effectiveness of the class. Model selection by Bootstrap Penalization for Classification derives the finite sample error bounds for model selection, that is a problem of automatically choosing the best class of concepts in a collection of such classes. Machine learning theories are becoming important as many of the problems, such as multiclass extension and realistic setting binary classification remain largely under-investigated.