2011. Generalization bounds and consistency for latent structural probit and ramp loss

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2011. Generalization bounds and consistency for latent structural probit and ramp loss

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by David Mcallester , Joseph Keshet

Venue:	In Proc. of NIPS
Citations:	24 - 1 self

BibTeX

@INPROCEEDINGS{Mcallester_2011.generalization,
    author = {David Mcallester and Joseph Keshet},
    title = {2011. Generalization bounds and consistency for latent structural probit and ramp loss},
    booktitle = {In Proc. of NIPS},
    year = {}
}

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Abstract

We consider latent structural versions of probit loss and ramp loss. We show that these surrogate loss functions are consistent in the strong sense that for any feature map (finite or infinite dimensional) they yield predictors approaching the infimum task loss achievable by any linear predictor over the given features. We also give finite sample generalization bounds (convergence rates) for these loss functions. These bounds suggest that probit loss converges more rapidly. However, ramp loss is more easily optimized on a given sample. 1

Keyphrases

ramp loss latent structural probit generalization bound probit loss finite sample generalization bound linear predictor latent structural version loss function convergence rate infimum task loss strong sense surrogate loss function feature map infinite dimensional

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