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# Mixability is Bayes Risk Curvature Relative to Log Loss

Published on Aug 02, 20113515 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