Lower-Bounded Proper Losses for Weakly Supervised Classification
This work addresses the challenge of reliable class-probability estimation in weakly supervised learning, which is incremental as it builds on existing theoretical frameworks for proper losses.
The paper tackles the problem of weakly supervised classification by deriving conditions for loss functions to be proper and lower-bounded, and proposes a novel regularization scheme called generalized logit squeezing that ensures these properties, with experimental results demonstrating its effectiveness compared to improper or unbounded losses.
This paper discusses the problem of weakly supervised classification, in which instances are given weak labels that are produced by some label-corruption process. The goal is to derive conditions under which loss functions for weak-label learning are proper and lower-bounded -- two essential requirements for the losses used in class-probability estimation. To this end, we derive a representation theorem for proper losses in supervised learning, which dualizes the Savage representation. We use this theorem to characterize proper weak-label losses and find a condition for them to be lower-bounded. From these theoretical findings, we derive a novel regularization scheme called generalized logit squeezing, which makes any proper weak-label loss bounded from below, without losing properness. Furthermore, we experimentally demonstrate the effectiveness of our proposed approach, as compared to improper or unbounded losses. The results highlight the importance of properness and lower-boundedness.