21. However, in contrast to boosting algorithms that analytically minimize a convex loss function ( e . g. 22. The quadratic penalty term makes the loss function strictly convex, and it therefore has a unique minimum. 23. Two very commonly used loss functions are the absolute loss, L ( a ) = | a |. 24. As long as the loss function is continuously differentiable, the classifier will always be driven toward purer solutions. 25. By construction of the optimization problem, other values of w would give larger values for the loss function . 26. Other loss functions can be conceived, although the mean squared error is the most widely used and validated. 27. BrownBoost uses a non-convex potential loss function , thus it does not fit into the AnyBoost framework. 28. While the above is the most common form, other smooth approximations of the Huber loss function also exist. 29. However, this loss function is not convex, which makes the regularization problem very difficult to minimize computationally. 30. Loss functions need not be explicitly stated for statistical theorists to prove that a statistical procedure has an optimality property.
