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Choice Computation - Correlated Utilities

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Karthik Natarajan

on 16 June 2015

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Transcript of Choice Computation - Correlated Utilities

A Convex Optimization Approach for Computing Correlated Choice Probabilities with Many Alternatives
MNL



Choice Probability
Cross Moment Model
CMM
New Results
Computational Results




Closed form, numerical integration or simulation







Convex optimization formulation
Simplex
Random utility maximization




Representative agent model
MNP



i.i.d. Gumbel random error term






Entropy maximization
Random utility maximization



Representative agent model
Random utility maximization


Representative agent model
Multivariate normal random error terms with
zero mean and given covariance matrix

Several simulation based methods



No simple form that is amenable for computation

Multinomial Logit & Probit Models
Distribution that maximizes the expected agent utility given first two moments:



Previous works shows that this reduces to solving a semidefinite program (SDP):
Choice probability in CMM
A representative agent model for CMM:



Efficiently computable gradient that makes a simple gradient ascent method suitable for CMM:
Selin Damla Ahipasaoglu (SUTD), Xiaobo Li (University of Minnesota), Karthik Natarajan (SUTD)
Full transcript