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Part 2 New Techniques

5 Microchoice Bounds (the algebra of choices)
 5.1.  A Motivating Observation
 5.2.  The Simple Microchoice Bound
 5.3.  Combining Microchoice with Freund’s Query Tree approach
 5.4.  Microchoice discussion
6 PAC-Bayes bounds
 6.1.  PAC-Bayes Basics
 6.2.  A Tighter PAC-Bayes Bound
 6.3.  PAC-Bayes Approximations
 6.4.  Application of the PAC-Bayes bound
7 Averaging Bounds (Improved margin)
 7.1.  Earlier Results
 7.2.  A generalized averaging bound
 7.3.  Proof of main theorem
 7.4.  Methods for tightening
 7.5.  Final thoughts for Averaging Bounds
8 Computable Shell bounds
 8.1.  The Discrete Shell Bound
 8.2.  Sampling Shell Bound
 8.3.  Lower Bounds
 8.4.  Shell Bounds for Continuous Spaces
 8.5.  Conclusion
9 Tight covering number bounds
 9.1.  Introduction
 9.2.  The Setting and Prior Results
 9.3.  Bracketing Covering Number Bound
 9.4.  Covering number calculations
 9.5.  Conclusion and Future Work
10 Holdout bounds: Progressive Validation
 10.1.  Progressive Validation Technique
 10.2.  Variance Analysis
 10.3.  Deviation Analysis
 10.4.  A Quick Experiment
 10.5.  Conclusion
11 Combining sample complexity and holdout bounds
 11.1.  Combination Possibilities
 11.2.  General Approaches for Combined Bounds
 11.3.  Approximations in Combinations
 11.4.  Conclusion

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