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