Personalized Recommendations using Discrete Choice Models with Inter- and Intra-Consumer Heterogeneity Moshe Ben-Akiva With Felix Becker, Mazen Danaf,

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Presentation transcript:

Personalized Recommendations using Discrete Choice Models with Inter- and Intra-Consumer Heterogeneity Moshe Ben-Akiva With Felix Becker, Mazen Danaf, and Bilge Atasoy Intelligent Transportation Systems Lab Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Contents Objective Flexible Mobility on Demand (FMOD) The Model Model Estimation Online Application Conclusion Appendix Making public transportation competitive App based mobility service Customer requests for trips (original, destination, time of travel) App displays a menu of travel options Customer makes a choice Complements mass transit Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Objective Estimate consumer preferences for an app based recommendation system which predicts user responses to options: - Stored user preferences, identified upon login. - Online updates as more choices are made. - Offline updates to account for population trends. Apply method for a Flexible Mobility on Demand (FMOD) system. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

FMOD (1) Flexible Mobility on Demand1 aims at making public transportation competitive by: Personalization: tailoring options to individual preferences Optimization: maximizing operator profit and user satisfaction Flexibility: offering a variety of travel options Making public transportation competitive App based mobility service Customer requests for trips (original, destination, time of travel) App displays a menu of travel options Customer makes a choice Complements mass transit 1Atasoy, B., Ikeda, T., Song, X., and Ben-Akiva, M. (2015). The Concept and Impact Analysis of a Flexible Mobility on Demand System. Transportation Research Part C: Emerging Technologies, 56, 373-392. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Para-transit with Flexible Route and Schedule FMOD (2) Para-transit with Flexible Route and Schedule Taxi: door-to-door, private Shared-taxi: door-to-door, shared Mini-bus: fixed stops, shared Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

FMOD (3) An app-based personalized para-transit service whereby: A customer requests a trip (origin, destination, time of travel) The app displays a menu of options The customer makes a choice Making public transportation competitive App based mobility service Customer requests for trips (original, destination, time of travel) App displays a menu of travel options Customer makes a choice Complements mass transit Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Optimization and Preferences FMOD (4) User Experience FMOD Server Optimization and Preferences Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

FMOD (5) FMOD Algorithms Dynamic allocation of vehicles taxi shared mini-bus FMOD server choice Fleet offer request allocate Customer Maximizing Profit / Welfare Dynamic allocation of vehicles Optimized assortment of modes Based on individual level preferences Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

FMOD (6) Individual level preferences are estimated and continuously updated through two interacting and repeated steps: Online estimation: users’ preferences are updated in real-time as they make more choices. Offline estimation: data are pooled periodically and used to update individual as well as population level parameters. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

The Model (1) Discrete choice models that account for random taste variations on two levels: Inter-consumer heterogeneity: random taste variations among individuals. Intra-consumer heterogeneity: random taste variations among menus for a given individual. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

The Model (2) McFadden’s hierarchical mixture model1 accounts for intra and inter-consumer heterogeneity by three levels of parameters: Population-level parameters µ and Ωb: average tastes/preferences in the population and the inter-consumer variance-covariance matrix respectively. Individual-level parameters ζn and Ωw: average tastes/preferences of a specific individual and the intra-consumer variance-covariance matrix respectively. Menu-level parameters ηmn: to reflect menu-specific (choice specific) taste perturbations. 1Ben-Akiva, M., McFadden, D., and Train, K. (2015). Foundations of stated preference elicitation, consumer choice behavior and choice-based conjoint analysis. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

The Model (3) Where: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

The Model (4) Where: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (1) The model is estimated using Hierarchical Bayes (HB) and Monte Carlo Markov Chain (MCMC) with Gibbs sampling with an embedded Metropolis–Hastings (MH) algorithm 1,2. 1 Train, K. (2009), Discrete Choice Methods with Simulation, Cambridge University Press, Chapter 12. 2Ben-Akiva, M., McFadden, D., and Train, K. (2015). Foundations of stated preference elicitation, consumer choice behavior and choice-based conjoint analysis, pp. 57. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (2) Unconditional posterior defined as: Where: Draws from posterior distribution obtained by Gibbs sampling from five conditional posteriors. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (3) Step I: Normal Bayesian update of µ with a diffuse prior and ζn as the data. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (4) Step II: Normal Bayesian update of Ωb with a diffuse prior and ζn as the data. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (5) Step III: Normal Bayesian update of Ωw with a diffuse prior and ηmn as the data. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (6) Step IV: Normal Bayesian update of ζn with µ as a prior and ηmn as the data. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (7) Step V: MH algorithm. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (8) Model is tested using the Swissmetro data set1. Nine stated choices of travel mode for each respondents offering as alternatives rail, Swissmetro, and car. Estimation using choices 1-8 and testing on choice 9. Random parameters used for travel cost, travel time, and headway Money-metric utility specification. 1Bierlaire, M., Axhausen, K. and Abay, G. (2001). Acceptance of modal innovation: the case of the Swissmetro, Proceedings of the 1st Swiss Transportation Research Conference, Ascona, Switzerland. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (9) Probability of Chosen Alternative in Menus 1-8 Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (10) Market Shares in Menus 1-8 Observed Predicted (same dataset) Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (11) Distribution of Random Parameters ζTime Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (12) Distribution of Random Parameters ζHeadway Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (13) Distribution of Random Parameters Scale parameter Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (14) Comparison of Single and Double Mixture Model: Probability of Chosen Alternative in Menus 1-8 Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Model Estimation (15) Probability of Chosen Alternative in Menu 9 Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Online Application (1) Continuously running MCMC: Offline: periodically (e.g. Overnight or once every week), update all the parameters (µ, Ωb, ζn, Ωw , and ηmn) by iterating steps I through V. Online: in real time, once a choice is made, update individual specific parameters (ζn and ηmn) using steps IV and V. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Online Application (2) Compare three models: Double mixture model estimation using menus 1-7 (representing periodical update) Online procedure on menu 8 after double mixture model estimation on menus 1-7 (representing online update once a choice is made) Double mixture model estimation using menus 1-8 (representing full offline procedure) Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Online Application (3) Probability of Chosen Alternative in Menu 9 Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Conclusion Demonstrated the application of a discrete choice model with both intra and inter-consumer heterogeneity. Results showed significant improvements over the single mixture. Preliminary results show the benefit from a process that combines online and offline updating. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015 THANK YOU!

APPENDIX A: Gibbs Sampling Procedure Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015 APPENDIX A: Gibbs Sampling Procedure

APPENDIX A (1) Step I-a: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX A (2) Step I-b: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX A (3) Step II: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX A (4) Step III: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX A (5) Step IV: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX A (6) Step V: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX A (7) Step V: Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX B: Parameter Estimates in the Online Procedure Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015 APPENDIX B: Parameter Estimates in the Online Procedure

APPENDIX B (1) Distribution of Random Parameters (Offline run on choices 1-7, online applied for 8th choice) ζTime Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX B (2) Distribution of Random Parameters (Offline run on choices 1-7, online applied for 8th choice) ζHeadway Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

APPENDIX B (3) Distribution of Random Parameters (Offline run on choices 1-7, online applied for 8th choice) Scale parameter Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015