Consistency of losses for learning from weak labels

Jesús Cid-Sueiro, Darío García-García, Raúl Santos-Rodríguez

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

7 Citations (Scopus)

Abstract

In this paper we analyze the consistency of loss functions for learning from weakly labelled data, and its relation to properness. We show that the consistency of a given loss depends on the mixing matrix, which is the transition matrix relating the weak labels and the true class. A linear transformation can be used to convert a conventional classification-calibrated (CC) loss into a weak CC loss. By comparing the maximal dimension of the set of mixing matrices that are admissible for a given CC loss with that for proper losses, we show that classification calibration is a much less restrictive condition than properness. Moreover, we show that while the transformation of conventional proper losses into a weak proper losses does not preserve convexity in general, conventional convex CC losses can be easily transformed into weak and convex CC losses. Our analysis provides a general procedure to construct convex CC losses, and to identify the set of mixing matrices admissible for a given transformation. Several examples are provided to illustrate our approach.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages197-210
Number of pages14
Volume8724 LNAI
EditionPART 1
ISBN (Print)9783662448472
DOIs
Publication statusPublished - 1 Jan 2014
EventEuropean Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014 - Nancy, France
Duration: 15 Sep 201419 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8724 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

ConferenceEuropean Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014
CountryFrance
CityNancy
Period15/09/1419/09/14

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