Parameter identification in Markov chain choice models

Arushi Gupta, Daniel Hsu
Proceedings of the 28th International Conference on Algorithmic Learning Theory, PMLR 76:330-340, 2017.

Abstract

This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. The underlying parameters of the model were previously shown to be identifiable from the choice probabilities for the all-products assortment, together with choice probabilities for assortments of all-but-one products. Obtaining and estimating choice probabilities for such large assortments is not desirable in many settings. The main result of this work is that the parameters may be identified from assortments of sizes two and three, regardless of the total number of products. The result is obtained via a simple and efficient parameter recovery algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v76-gupta17a, title = {Parameter identification in Markov chain choice models}, author = {Gupta, Arushi and Hsu, Daniel}, booktitle = {Proceedings of the 28th International Conference on Algorithmic Learning Theory}, pages = {330--340}, year = {2017}, editor = {Hanneke, Steve and Reyzin, Lev}, volume = {76}, series = {Proceedings of Machine Learning Research}, month = {15--17 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v76/gupta17a/gupta17a.pdf}, url = {https://proceedings.mlr.press/v76/gupta17a.html}, abstract = {This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. The underlying parameters of the model were previously shown to be identifiable from the choice probabilities for the all-products assortment, together with choice probabilities for assortments of all-but-one products. Obtaining and estimating choice probabilities for such large assortments is not desirable in many settings. The main result of this work is that the parameters may be identified from assortments of sizes two and three, regardless of the total number of products. The result is obtained via a simple and efficient parameter recovery algorithm.} }
Endnote
%0 Conference Paper %T Parameter identification in Markov chain choice models %A Arushi Gupta %A Daniel Hsu %B Proceedings of the 28th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2017 %E Steve Hanneke %E Lev Reyzin %F pmlr-v76-gupta17a %I PMLR %P 330--340 %U https://proceedings.mlr.press/v76/gupta17a.html %V 76 %X This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. The underlying parameters of the model were previously shown to be identifiable from the choice probabilities for the all-products assortment, together with choice probabilities for assortments of all-but-one products. Obtaining and estimating choice probabilities for such large assortments is not desirable in many settings. The main result of this work is that the parameters may be identified from assortments of sizes two and three, regardless of the total number of products. The result is obtained via a simple and efficient parameter recovery algorithm.
APA
Gupta, A. & Hsu, D.. (2017). Parameter identification in Markov chain choice models. Proceedings of the 28th International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 76:330-340 Available from https://proceedings.mlr.press/v76/gupta17a.html.

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