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Deep Gamblers: Learning to Abstain with Portfolio Theory Liu Ziyin (U. Tokyo), Zhikang T. Wang (U. Tokyo), Paul Pu Liang (CMU), Ruslan Salakhutdinov (CMU), Louis-Philippe Morency (CMU), Masahito Ueda (U. Tokyo) Classification and the Inadequacy of loss Want to find: = arg max * Pr(|) In practice, minimize ( loss): min * − log (|) Proposed Method: The Gambler’s Loss max log = max C D E DFG log( D D + J ) SOTA Performance on Selective Classification Surprising Benefit -Training with gambler’s loss reduces overfitting -Improved performance when noisy labels are present The Learned Representation is Better Separable Toy Example: Image Rotation Intuition: Prediction as Horse Race Horse Race with Reservation horses Betting strategy: ∑ D M DFG → ∑ D E DFJ Chance of winning: D Payoff if we bet on the winning horse: D Return after winning: = D D → D D + J Objective: maximize doubling rate: max = max log = max C D E DFG log( D D + J ) -Classification Problem = Betting problem with Reservation with = 1, J =0 -Classification Problem ≤ Betting problem with Reservation Toy Example: Identifying Disconfident Images Paper: Code:

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Page 1: Deep Gamblers: Learning to Abstain with Portfolio Theorypliang/posters/neurips2019_gamblers_poster.pdf · zuwmžz 100 90 80 70 60 50 40 30 20 20 2.0 acc gblers loss gblers acc nll

DeepGamblers:LearningtoAbstainwithPortfolioTheoryLiuZiyin(U.Tokyo),ZhikangT.Wang(U.Tokyo),PaulPuLiang(CMU),

RuslanSalakhutdinov(CMU),Louis-PhilippeMorency(CMU),MasahitoUeda(U.Tokyo)

ClassificationandtheInadequacyof𝒏𝒍𝒍 lossWanttofind:𝜃 = argmax

*Pr(𝑌|𝜃)

Inpractice,minimize𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑙𝑜𝑔𝑙𝑜𝑠𝑠 (𝑛𝑙𝑙 loss):min*− log 𝑝(𝑌|𝜃)

ProposedMethod:TheGambler’sLoss

max𝐸 log 𝑆 = maxC𝑝D

E

DFG

log(𝑜D𝑏D + 𝑏J)

SOTAPerformanceonSelectiveClassification

SurprisingBenefit-Trainingwithgambler’slossreducesoverfitting-Improvedperformancewhennoisylabelsarepresent

TheLearnedRepresentationisBetterSeparable

ToyExample:ImageRotation

Intuition:PredictionasHorseRaceHorseRacewithReservation

𝑚 horsesBettingstrategy:∑ 𝑏DM

DFG → ∑ 𝑏DEDFJ

Chanceofwinning:𝑝DPayoffifwebetonthewinninghorse:𝑜DReturnafterwinning:𝑆 = 𝑜D𝑏D → 𝑜D𝑏D + 𝑏J

Objective:maximizedoublingrate:

max𝑊 = max𝐸 log 𝑆 = maxC𝑝D

E

DFG

log(𝑜D𝑏D + 𝑏J)

-ClassificationProblem= BettingproblemwithReservationwith𝑜 = 1, 𝑏J = 0-ClassificationProblem≤ BettingproblemwithReservation

ToyExample:IdentifyingDisconfidentImagesPaper:

Code:

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