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Generalization Bounds and Consistency for Latent Structural Probit and Ramp Loss
Published on Jan 25, 20123444 Views
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 dimensi
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Chapter list
Generalization Bounds and Consistency for Latent-Structural Probit and Ramp Loss00:00
Why Surrogate Loss Functions00:14
Structural Surrogate Loss Functions03:08
Surrogate Loss in the Binary Case05:57
Basic Properties07:02
Empirical Studies12:20
Some Notation13:04
Consistency of Probit Loss13:29
PAC - Bayesian Bounds14:04
Consistency of Ramp Loss15:09
Main Lemma15:26
Proof of Main Lemma Part I15:27
Proof of Main Lemma Part II15:28
Using the Main Lemma15:29
A Comparison of Convergence Rates15:30