On Discriminative Learning of Prediction Uncertainty Vojtch Franc, - PowerPoint PPT Presentation

On Discriminative Learning of Prediction Uncertainty Vojtěch Franc, Daniel Průša Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague

On Discriminative Learning of Prediction Uncertainty � h ( x ) 2/2 with probability c ( x ) Selective classifier: ( h, c )( x ) = reject with probability 1 − c ( x ) where h : X → Y is a classifier and c : X → [0 , 1] is a selection function

On Discriminative Learning of Prediction Uncertainty � h ( x ) 2/2 with probability c ( x ) Selective classifier: ( h, c )( x ) = reject with probability 1 − c ( x ) where h : X → Y is a classifier and c : X → [0 , 1] is a selection function Example: Linear SVM h ( x ) = sign( � φ ( x ) , w � + b ) c ( x ) = [ [ |� φ ( x ) , w � + b | ≥ θ ] ]

On Discriminative Learning of Prediction Uncertainty � h ( x ) 2/2 with probability c ( x ) Selective classifier: ( h, c )( x ) = reject with probability 1 − c ( x ) where h : X → Y is a classifier and c : X → [0 , 1] is a selection function 8 Example: Linear SVM SVM + distance to hyperplane h ( x ) = sign( � φ ( x ) , w � + b ) 6 selective risk [%] c ( x ) = [ [ |� φ ( x ) , w � + b | ≥ θ ] ] 4 Coverage: � � R S = 2.1% φ ( c ) = E x ∼ p c ( x ) 2 Selective risk: � � 0 ℓ ( y,h ( x )) c ( x ) E ( x,y ) ∼ p R S ( h, c ) = 0 20 40 60 80 100 φ ( x ) coverage [%]

On Discriminative Learning of Prediction Uncertainty � h ( x ) 2/2 with probability c ( x ) Selective classifier: ( h, c )( x ) = reject with probability 1 − c ( x ) where h : X → Y is a classifier and c : X → [0 , 1] is a selection function 8 Example: Linear SVM SVM + distance to hyperplane h ( x ) = sign( � φ ( x ) , w � + b ) 6 selective risk [%] c ( x ) = [ [ |� φ ( x ) , w � + b | ≥ θ ] ] 4 R S = 2.1% 2 In our paper we show: 1) What is the optimal c ( x ) 0 0 20 40 60 80 100 2) How to learn c ( x ) discriminatively coverage [%]

On Discriminative Learning of Prediction Uncertainty � h ( x ) 2/2 with probability c ( x ) Selective classifier: ( h, c )( x ) = reject with probability 1 − c ( x ) where h : X → Y is a classifier and c : X → [0 , 1] is a selection function 8 Example: Linear SVM SVM + distance to hyperplane SVM + learned selection function h ( x ) = sign( � φ ( x ) , w � + b ) 6 selective risk [%] c ( x ) = [ [ |� φ ( x ) , w � + b | ≥ θ ] ] 4 R S = 2.1% 2 In our paper we show: R S = 0.2% 1) What is the optimal c ( x ) 0 0 20 40 60 80 100 2) How to learn c ( x ) discriminatively coverage [%]

On Discriminative Learning of Prediction Uncertainty Vojtch Franc, - PowerPoint PPT Presentation

On Discriminative Learning of Prediction Uncertainty Vojtch Franc, Daniel Pra Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague On Discriminative Learning of Prediction Uncertainty h ( x

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