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 classificationcalibrated (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 language  English 

Title of host publication  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 
Publisher  Springer Verlag 
Pages  197210 
Number of pages  14 
Volume  8724 LNAI 
Edition  PART 1 
ISBN (Print)  9783662448472 
DOIs  
Publication status  Published  1 Jan 2014 
Event  European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014  Nancy, France Duration: 15 Sep 2014 → 19 Sep 2014 
Publication series
Name  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 

Number  PART 1 
Volume  8724 LNAI 
ISSN (Print)  03029743 
ISSN (Electronic)  16113349 
Conference
Conference  European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014 

Country  France 
City  Nancy 
Period  15/09/14 → 19/09/14 
Fingerprint
Dive into the research topics of 'Consistency of losses for learning from weak labels'. Together they form a unique fingerprint.Profiles

Dr Raul SantosRodriguez
 Department of Engineering Mathematics  Associate Professor of Data Science and Intelligent Systems
Person: Academic