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Mixability is Bayes Risk Curvature Relative to Log Loss
Published on Aug 02, 20113518 Views
Mixability of a loss governs the best possible performance when aggregating expert predictions with respect to that loss. The determination of the mixability constant for binary losses is straightforw
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Mixability is Bayes Risk Curvature Relative to Log Loss - 100:00
Mixability is Bayes Risk Curvature Relative to Log Loss - 200:06
Mixability00:24
The set-up01:25
Merging Strategies02:02
Mixability Performance Bound02:35
Multiclass Losses for Class Probability Estimation03:52
Properness05:34
n or n - 1 dimensions?06:56
Stationarity condition08:02
Superprediction Set09:27
Defining Mixability09:57
Mixability via Concavity of a f10:34
Differentiable Binary Losses11:08
Mixability via weight functions11:53
Tools for the The Multiclass Case12:36
Multiclass Characterisation of Mixability13:34
Main Result14:08
Relaxing the Restriction to Proper Losses14:56
Connection with Abernethy et al (2009)15:49
Conclusions17:12