5. Randomized estimators and empirical complexity
5.1. A pseudo-Bayesian approach to adaptive inference 
 
 
5.1.1. General framework 
 
 
5.1.2. Some pervading ideas 
 
 
 
 
 
 
5.2. A randomized rule for pattern recognition 
 
 
5.3. Generalizations of theorem 5.2.3 
 
 
5.4. The non-ambiguous case 
 
 
5.5. Empirical complexity bounds for the Gibbs estimator 
 
 
5.6. Non randomized classification rules 
 
 
5.7. Application to classification trees 
 
 
5.8. The regression setting 
 
 
5.9. Links with penalized least square regression 
 
 
5.9.1. The general case 
 
 
5.9.2. Adaptive linear least square regression estimation 
 
 
 
 
 
 
5.10. Some elementary bounds 
 
 
5.11. Some refinements about the linear regression case