The basic conclusion of this thesis is that we can achieve bounds tight enough to yield useful results on real learning problems with standard learning algorithms or simple variants on standard learning algorithms. The evidence of this conclusion is reported in the last two chapters.
To accomplish this goal, considerable theoretical work was completed. This includes:
In particular, microchoice bounds (Section 5), PAC-Bayes bounds (Section 6), shell bound (Section 8), and combined bounds (Section 11) have proved useful for practical application.
It is worth emphasizing that all of the bounds reported here rest upon only an assumption of example independence implying wide applicability.