Parameter Estimation for Generalized Thurstone Choice Models

Milan Vojnovic, Seyoung Yun
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:498-506, 2016.

Abstract

We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into how the estimation accuracy depends on the choice of a generalized Thurstone choice model and the structure of comparison sets. We find that for a priori unbiased structures of comparisons, e.g., when comparison sets are drawn independently and uniformly at random, the number of observations needed to achieve a prescribed estimation accuracy depends on the choice of a generalized Thurstone choice model. For a broad set of generalized Thurstone choice models, which includes all popular instances used in practice, the estimation error is shown to be largely insensitive to the cardinality of comparison sets. On the other hand, we found that there exist generalized Thurstone choice models for which the estimation error decreases much faster with the cardinality of comparison sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-vojnovic16, title = {Parameter Estimation for Generalized Thurstone Choice Models}, author = {Vojnovic, Milan and Yun, Seyoung}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {498--506}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/vojnovic16.pdf}, url = {https://proceedings.mlr.press/v48/vojnovic16.html}, abstract = {We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into how the estimation accuracy depends on the choice of a generalized Thurstone choice model and the structure of comparison sets. We find that for a priori unbiased structures of comparisons, e.g., when comparison sets are drawn independently and uniformly at random, the number of observations needed to achieve a prescribed estimation accuracy depends on the choice of a generalized Thurstone choice model. For a broad set of generalized Thurstone choice models, which includes all popular instances used in practice, the estimation error is shown to be largely insensitive to the cardinality of comparison sets. On the other hand, we found that there exist generalized Thurstone choice models for which the estimation error decreases much faster with the cardinality of comparison sets.} }
Endnote
%0 Conference Paper %T Parameter Estimation for Generalized Thurstone Choice Models %A Milan Vojnovic %A Seyoung Yun %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-vojnovic16 %I PMLR %P 498--506 %U https://proceedings.mlr.press/v48/vojnovic16.html %V 48 %X We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into how the estimation accuracy depends on the choice of a generalized Thurstone choice model and the structure of comparison sets. We find that for a priori unbiased structures of comparisons, e.g., when comparison sets are drawn independently and uniformly at random, the number of observations needed to achieve a prescribed estimation accuracy depends on the choice of a generalized Thurstone choice model. For a broad set of generalized Thurstone choice models, which includes all popular instances used in practice, the estimation error is shown to be largely insensitive to the cardinality of comparison sets. On the other hand, we found that there exist generalized Thurstone choice models for which the estimation error decreases much faster with the cardinality of comparison sets.
RIS
TY - CPAPER TI - Parameter Estimation for Generalized Thurstone Choice Models AU - Milan Vojnovic AU - Seyoung Yun BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-vojnovic16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 498 EP - 506 L1 - http://proceedings.mlr.press/v48/vojnovic16.pdf UR - https://proceedings.mlr.press/v48/vojnovic16.html AB - We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into how the estimation accuracy depends on the choice of a generalized Thurstone choice model and the structure of comparison sets. We find that for a priori unbiased structures of comparisons, e.g., when comparison sets are drawn independently and uniformly at random, the number of observations needed to achieve a prescribed estimation accuracy depends on the choice of a generalized Thurstone choice model. For a broad set of generalized Thurstone choice models, which includes all popular instances used in practice, the estimation error is shown to be largely insensitive to the cardinality of comparison sets. On the other hand, we found that there exist generalized Thurstone choice models for which the estimation error decreases much faster with the cardinality of comparison sets. ER -
APA
Vojnovic, M. & Yun, S.. (2016). Parameter Estimation for Generalized Thurstone Choice Models. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:498-506 Available from https://proceedings.mlr.press/v48/vojnovic16.html.

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