Structured Output Learning with High Order Loss Functions

Daniel Tarlow, Richard Zemel
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1212-1220, 2012.

Abstract

Often when modeling structured domains, it is desirable to leverage information that is not naturally expressed as simply a label. Examples include knowledge about the evaluation measure that will be used at test time, and partial (weak) label information. When the additional information has structure that factorizes according to small subsets of variables (i.e., is \emphlow order, or \emphdecomposable), several approaches can be used to incorporate it into a learning procedure. Our focus in this work is the more challenging case, where the additional information does not factorize according to low order graphical model structure; we call this the \emphhigh order case. We propose to formalize various forms of this additional information as high order loss functions, which may have complex interactions over large subsets of variables. We then address the computational challenges inherent in learning according to such loss functions, particularly focusing on the loss-augmented inference problem that arises in large margin learning; we show that learning with high order loss functions is often practical, giving strong empirical results, with one popular and several novel high-order loss functions, in several settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-tarlow12a, title = {Structured Output Learning with High Order Loss Functions}, author = {Tarlow, Daniel and Zemel, Richard}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {1212--1220}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/tarlow12a/tarlow12a.pdf}, url = {https://proceedings.mlr.press/v22/tarlow12a.html}, abstract = {Often when modeling structured domains, it is desirable to leverage information that is not naturally expressed as simply a label. Examples include knowledge about the evaluation measure that will be used at test time, and partial (weak) label information. When the additional information has structure that factorizes according to small subsets of variables (i.e., is \emphlow order, or \emphdecomposable), several approaches can be used to incorporate it into a learning procedure. Our focus in this work is the more challenging case, where the additional information does not factorize according to low order graphical model structure; we call this the \emphhigh order case. We propose to formalize various forms of this additional information as high order loss functions, which may have complex interactions over large subsets of variables. We then address the computational challenges inherent in learning according to such loss functions, particularly focusing on the loss-augmented inference problem that arises in large margin learning; we show that learning with high order loss functions is often practical, giving strong empirical results, with one popular and several novel high-order loss functions, in several settings.} }
Endnote
%0 Conference Paper %T Structured Output Learning with High Order Loss Functions %A Daniel Tarlow %A Richard Zemel %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-tarlow12a %I PMLR %P 1212--1220 %U https://proceedings.mlr.press/v22/tarlow12a.html %V 22 %X Often when modeling structured domains, it is desirable to leverage information that is not naturally expressed as simply a label. Examples include knowledge about the evaluation measure that will be used at test time, and partial (weak) label information. When the additional information has structure that factorizes according to small subsets of variables (i.e., is \emphlow order, or \emphdecomposable), several approaches can be used to incorporate it into a learning procedure. Our focus in this work is the more challenging case, where the additional information does not factorize according to low order graphical model structure; we call this the \emphhigh order case. We propose to formalize various forms of this additional information as high order loss functions, which may have complex interactions over large subsets of variables. We then address the computational challenges inherent in learning according to such loss functions, particularly focusing on the loss-augmented inference problem that arises in large margin learning; we show that learning with high order loss functions is often practical, giving strong empirical results, with one popular and several novel high-order loss functions, in several settings.
RIS
TY - CPAPER TI - Structured Output Learning with High Order Loss Functions AU - Daniel Tarlow AU - Richard Zemel BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-tarlow12a PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 1212 EP - 1220 L1 - http://proceedings.mlr.press/v22/tarlow12a/tarlow12a.pdf UR - https://proceedings.mlr.press/v22/tarlow12a.html AB - Often when modeling structured domains, it is desirable to leverage information that is not naturally expressed as simply a label. Examples include knowledge about the evaluation measure that will be used at test time, and partial (weak) label information. When the additional information has structure that factorizes according to small subsets of variables (i.e., is \emphlow order, or \emphdecomposable), several approaches can be used to incorporate it into a learning procedure. Our focus in this work is the more challenging case, where the additional information does not factorize according to low order graphical model structure; we call this the \emphhigh order case. We propose to formalize various forms of this additional information as high order loss functions, which may have complex interactions over large subsets of variables. We then address the computational challenges inherent in learning according to such loss functions, particularly focusing on the loss-augmented inference problem that arises in large margin learning; we show that learning with high order loss functions is often practical, giving strong empirical results, with one popular and several novel high-order loss functions, in several settings. ER -
APA
Tarlow, D. & Zemel, R.. (2012). Structured Output Learning with High Order Loss Functions. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:1212-1220 Available from https://proceedings.mlr.press/v22/tarlow12a.html.

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