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UID:www.tcs.tifr.res.in/event/395
DTSTAMP:20230914T125923Z
SUMMARY:A Markov Chain Approximation for Choice Modeling
DESCRIPTION:Speaker: Vineet Goyal (Columbia University\nIndustrial Engineer
 ing and Operations Research\n500 West\, 120th Street\nNew York\, NY 10027\
 nUnited States of America)\n\nAbstract: \nAssortment planning is an import
 ant problem that arises in many industries such as retailing and airlines.
  One of the key challenges in an assortment planning problem is to identif
 y the ``right model'' for the substitution behavior of customers from the 
 data. Error in model selection can lead to highly sub-optimal decisions. I
 n this paper\, we present a new choice model that is a simultaneous approx
 imation for all random utility based discrete choice models including the 
 multinomial logit\, the nested logit and mixtures of multinomial logit mod
 els. Our model is based on a new primitive for substitution behavior where
  substitution from one product to another is modeled as a state transition
  of a Markov chain.\n \nWe show that the choice probabilities computed by
  our model are a good approximation to the true choice probabilities of an
 y random utility discrete based choice model under mild conditions. Moreov
 er\, they are exact if the underlying model is a Multinomial logit model. 
 We also give a procedure to estimate the parameters of the Markov chain mo
 del that does not require any knowledge of the latent choice model. Furthe
 rmore\, we show that the assortment optimization problem under our choice 
 model can be solved efficiently in polynomial time. This is quite surprisi
 ng as we can not even express the choice probabilities using a functional 
 form. Our numerical experiments show that the average maximum relative er
 ror between the estimates of the Markov chain choice probability and the t
 rue choice probability is less than $3\\%$ (the average being taken over d
 ifferent offer sets). Therefore\, our model provides a tractable data-driv
 en approach to choice modeling and assortment optimization that is robust 
 to model selection errors.\n\n \n
URL:https://www.tcs.tifr.res.in/web/events/395
DTSTART;TZID=Asia/Kolkata:20130820T143000
DTEND;TZID=Asia/Kolkata:20130820T153000
LOCATION:AG-69
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