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The machine learning problem of classifier design is studied from the perspective of probability elicitation, in statistics. This shows that the standard approach of proceeding from the specification of a loss, to the minimization of conditional risk is overly restrictive. It is shown that a better alternative is to start from the specification of a functional form for the minimum conditional risk, and derive the loss function. This has various consequences of practical interest, such as showing that 1) the widely adopted practice of relying on convex loss functions is unnecessary, and 2) many new losses can be derived for classification problems. These points are illustrated by the derivation of a new loss which is not convex, but does not compromise the computational tractability of classifier design, and is robust to the contamination of data with outliers. A new boosting algorithm, SavageBoost, is derived for the minimization of this loss. Experimental results show that it is indeed less sensitive to outliers than conventional methods, such as Ada, Real, or LogitBoost, and converges in fewer iterations.

Experimental Results:
We compared SavageBoost to AdaBoost, RealBoost, and LogitBoost. The latter is generally considered more robust to outliers and thus a good candidate for comparison. Ten binary UCI data sets were used to explore the robustness of the algorithms to outliers. In all cases, five fold validation was used with varying levels of outlier contamination. The Figure shows the average error of the four methods on the Liver- Disorder set. Our results confirm previous studies that have noted AdaBoost sensitivity to outliers. SavageBoost produced generally better results at all contamination levels.

Publications: On the Design of Loss Functions for Classification: theory, robustness to outliers, and SavageBoost.
Hamed Masnadi-Shirazi and Nuno Vasconcelos
Proceedings of Neural Information Processing Systems (NIPS),
Vancouver, Canada, Dec 2008.

Contact: Nuno Vasconcelos, Hamed Masnadi-Shirazi


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