## A Hybrid System for Probability Estimation in Multiclass Problems Combining SVMs and Neural Networks

- Cristián Bravo, Jose Luis Lobato, Richard Weber, Gaston L'Huillier
- 2008 Eighth International Conference on Hybrid…
- 2008

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5 Excerpts

- Published 1999 in IEEE Trans. Neural Networks

The problem of designing cost functions to estimate a posteriori probabilities in multiclass problems is addressed in this paper. We establish necessary and sufficient conditions that these costs must satisfy in one-class one-output networks whose outputs are consistent with probability laws. We focus our attention on a particular subset of the corresponding cost functions; those which verify two usually interesting properties: symmetry and separability (well-known cost functions, such as the quadratic cost or the cross entropy are particular cases in this subset). Finally, we present a universal stochastic gradient learning rule for single-layer networks, in the sense of minimizing a general version of these cost functions for a wide family of nonlinear activation functions.

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@article{CidSueiro1999CostFT,
title={Cost functions to estimate a posteriori probabilities in multiclass problems},
author={Jes{\'u}s Cid-Sueiro and Juan Ignacio Arribas and Sebastian Urban-Munoz and An{\'i}bal R. Figueiras-Vidal},
journal={IEEE transactions on neural networks},
year={1999},
volume={10 3},
pages={645-56}
}