## Rademacher and Gaussian Complexities: Risk Bounds and Structural Results

*Peter L. Bartlett, Shahar Mendelson*;
3(Nov):463-482, 2002.

### Abstract

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.

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