# Rademacher Complexity

**See:** Statistical Learning Theory; Function.

## References

### 2011

- (Sammut & Webb, 2011) ⇒ Claude Sammut, and Geoffrey I. Webb. (2011). “Rademacher Complexity.” In: (Sammut & Webb, 2011) p.823

### 2009

- http://en.wikipedia.org/wiki/Rademacher_complexity
- In statistics and machine learning,
**Rademacher complexity**, named after Hans Rademacher, measures richness of a class of real-valued functions with respect to a probability distribution.

- In statistics and machine learning,

### 2003

- (Bartlett & Mendelson, 2003) ⇒ Peter L. Bartlett, and Shahar Mendelson. (2003). “Rademacher and Gaussian Complexities: risk bounds and structural results.” In: The Journal of Machine Learning Research, 3.
- We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.