Mallows-Smoothed Distribution over Rankings Approach for Modeling Choice

References

• Adamaszek A , Wiese A (2015) A quasi-PTAS for the two-dimensional geometric knapsack problem. Proc. 26th Annual ACM-SIAM Sympos. Discrete Algorithms (SIAM, Philadelphia), 1491–1505.Google Scholar
• Aouad A , Levi R , Segev D (2019) Approximation algorithms for dynamic assortment optimization models. Math. Oper. Res. 44(2):487–511.Link, Google Scholar
• Aouad A , Farias V , Levi R , Segev D (2018) The approximability of assortment optimization under ranking preferences. Oper. Res. 66(6):1661–1669.Link, Google Scholar
• Awasthi P , Blum A , Sheffet O , Vijayaraghavan A (2014) Learning mixtures of ranking models. Adv. Neural Inform. Processing Systems 27:2609–2617.Google Scholar
• Bansal N , Chakrabarti A , Epstein A , Schieber B (2006) A quasi-PTAS for unsplittable flow online graphs. Proc. 38th Annual ACM Sympos. Theory Comput. (ACM, New York), 721–729.Google Scholar
• Bertsimas D , Mišić VV (2019) Exact first-choice product line optimization. Oper. Res. 67(3):651–670.Link, Google Scholar
• Blanchet JH , Gallego G , Goyal V (2016) A Markov chain approximation to choice modeling. Oper. Res. 64(4):886–905.Link, Google Scholar
• Brightwell GR , Winkler P (1991) Counting linear extensions is #P-complete. Proc. 23rd Annual ACM Sympos. Theory Comput. (ACM, New York), 175–181.Google Scholar
• Bront JJM , Méndez-Díaz I , Vulcano G (2009) A column generation algorithm for choice-based network revenue management. Oper. Res. 57(3):769–784.Link, Google Scholar
• Chaffey D (2019) E-commerce conversion rates—How do yours compare? Accessed April 20, 2018, https://www.smartinsights.com/ecommerce/ecommerce-analytics/ecommerce-conversion-rates/.Google Scholar
• Chan T-HH , Elbassioni KM (2011) A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics. Discrete Comput. Geometry 46(4):704–723.Crossref, Google Scholar
• Davis JM , Gallego G , Topaloglu H (2014) Assortment optimization under variants of the nested logit model. Oper. Res. 62(2):250–273.Link, Google Scholar
• Désir A , Goyal V , Segev D , Ye C (2020) Constrained assortment optimization under the Markov chain–based choice model. Management Sci. 66(2):698–721.Link, Google Scholar
• Doignon J-P , Pekeč A , Regenwetter M (2004) The repeated insertion model for rankings: Missing link between two subset choice models. Psychometrika 69(1):33–54.Crossref, Google Scholar
• Dwork C , Kumar R , Naor M , Sivakumar D (2001) Rank aggregation methods for the web. Proc. 10th Internat. Conf. World Wide Web (ACM, New York), 613–622.Google Scholar
• Farias VF , Jagabathula S , Shah D (2013) A nonparametric approach to modeling choice with limited data. Management Sci. 59(2):305–322.Link, Google Scholar
• Feldman JB , Topaloglu H (2017) Revenue management under the Markov chain choice model. Oper. Res. 65(5):1322–1342.Link, Google Scholar
• Frank M , Wolfe P (1956) An algorithm for quadratic programming. Naval Res. Logist. 3(1–2):95–110.Crossref, Google Scholar
• Gallego G , Topaloglu H (2014) Constrained assortment optimization for the nested logit model. Management Sci. 60(10):2583–2601.Link, Google Scholar
• Guiver J , Snelson E (2009) Bayesian inference for Plackett-Luce ranking models. Proc. 26th Annual Internat. Conf. Machine Learn. (ACM, New York), 377–384.Google Scholar
• Honhon D , Jonnalagedda S , Pan XA (2012) Optimal algorithms for assortment selection under ranking-based consumer choice models. Manufacturing Service Oper. Management 14(2):279–289.Link, Google Scholar
• Jagabathula S . (2014) Assortment optimization under general choice. Submitted October 21, 2014, http://dx.doi.org/10.2139/ssrn.2512831.Google Scholar
• Jagabathula S , Rusmevichientong P (2017) A nonparametric joint assortment and price choice model. Management Sci. 63(9):3128–3145.Link, Google Scholar
• Jagabathula S , Rusmevichientong P (2019) The limit of rationality in choice modeling: Formulation, computation, and implications. Management Sci. 65(5):2196–2215.Abstract, Google Scholar
• Kamishima T (2003) Nantonac collaborative filtering: Recommendation based on order responses. Proc. Ninth ACM SIGKDD Internat. Conf. Knowledge Discovery Data Mining (ACM, New York), 583–588.Google Scholar
• Kamishima T , Kazawa H , Akaho S (2005) Supervised ordering—An empirical survey. Proc. 5th IEEE Internat. Conf. Data Mining (IEEE, New York), 673–676.Google Scholar
• Lebanon G , Mao Y (2008) Non-parametric modeling of partially ranked data. J. Machine Learn. Res. 9:2401–2429.Google Scholar
• Lu T , Boutilier C (2014) Effective sampling and learning for Mallows models with pairwise-preference data. J. Machine Learn. Res. 15(1):3783–3829.Google Scholar
• Luce RD (1959) Individual Choice Behavior: A Theoretical Analysis (Wiley, New York).Google Scholar
• Mallows CL (1957) Non-null ranking models. Biometrika 44(1):114–130.Crossref, Google Scholar
• Marden JI (1995) Analyzing and Modeling Rank Data (Chapman and Hall, London).Google Scholar
• McFadden D (1978) Modeling the choice of residential location. Transportation Res. Rec. (673):72–77.Google Scholar
• Meila M , Phadnis K , Patterson A , Bilmes JA (2012) Consensus ranking under the exponential model. Preprint, submitted June 20, https://arxiv.org/abs/1206.5265.Google Scholar
• Méndez-Díaz I , Miranda-Bront JJ , Vulcano G , Zabala P (2010) A branch-and-cut algorithm for the latent class logit assortment problem. Electronic Notes Discrete Math. 36:383–390.Crossref, Google Scholar
• Murphy TB , Martin D (2003) Mixtures of distance-based models for ranking data. Comput. Statist. Data Anal. 41(3):645–655.Crossref, Google Scholar
• Mustafa NH , Raman R , Ray S (2015) Quasi-polynomial time approximation scheme for weighted geometric set cover on pseudodisks and halfspaces. SIAM J. Comput. 44(6):1650–1669.Crossref, Google Scholar
• Plackett RL (1975) The analysis of permutations. J. Roy. Statist. Soc. Ser. C. Appl. Statist. 24(2):193–202.Google Scholar
• Segev D (2019) Assortment planning with nested preferences: Dynamic programming with distributions as states? Algorithmica 81(1):393–417.Crossref, Google Scholar
• Sherali HD , Adams WP (2013) A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems , vol. 31 (Springer Science & Business Media, Boston).Google Scholar
• Talluri K , van Ryzin G (2004a) Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50(1):15–33.Link, Google Scholar
• van Ryzin G , Vulcano G (2014) A market discovery algorithm to estimate a general class of nonparametric choice models. Management Sci. 61(2):281–300.Link, Google Scholar
• van Ryzin G , Vulcano G (2017) An expectation-maximization method to estimate a rank-based choice model of demand. Oper. Res. 65(2):396–407.Link, Google Scholar
• Yellott JI (1977) The relationship between Luce’s choice axiom, Thurstone’s theory of comparative judgment, and the double exponential distribution. J. Math. Psych. 15(2):109–144.Crossref, Google Scholar