Learning Nonparametric Choice Models with Discrete Fourier Analysis

Published Online:https://doi.org/10.1287/moor.2024.0439

References

  • [1] Akchen Y-C, Mišić V (2025a) Assortment optimization under the decision forest model. Preprint, submitted December 16, https://arxiv.org/abs/2103.14067.Google Scholar
  • [2] Akchen Y-C, Mišić VV (2025b) Column-randomized linear programs: Performance guarantees and applications. Oper. Res. 73(3):1366–1383.LinkGoogle Scholar
  • [3] Amrollahi A, Zandieh A, Kapralov M, Krause A (2019) Efficiently learning Fourier sparse set functions. Adv. Neural Inform. Processing Systems, vol. 32 (Neural Information Processing Systems, La Jolla, CA), 15094–15103.Google Scholar
  • [4] Ben-Akiva M, Bierlaire M (1999) Discrete choice methods and their applications to short term travel decisions. Hall RW, ed. Handbook of Transportation Science (Springer, Boston), 5–33.CrossrefGoogle Scholar
  • [5] Blanchet J, Gallego G, Goyal V (2016) A Markov chain approximation to choice modeling. Oper. Res. 64(4):886–905.LinkGoogle Scholar
  • [6] Block H, Marshak J (1959) Random orderings and stochastic theories of response. Technical report, Cowles Foundation for Research in Economics, Yale University, New Haven, CT.Google Scholar
  • [7] Blum A (1994) Relevant examples and relevant features: Thoughts from computational learning theory. Papers 1994 AAAI Fall Sympos. Relevance (Association for the Advancement of Artificial Intelligence, Washington, DC), 14–18.Google Scholar
  • [8] Chen Y-C, Mišić VV, (2022) Decision forest: A nonparametric approach to modeling irrational choice. Management Sci. 68(10):7090–7111.Google Scholar
  • [9] Chen N, Gallego G, Tang Z (2019) The use of binary choice forests to model and estimate discrete choices. Preprint, submitted August 3, https://arxiv.org/abs/1908.01109v1.Google Scholar
  • [10] Chierichetti F, Kumar R, Tomkins A (2018) Discrete choice, permutations, and reconstruction. SODA’18 Proc. Twenty-Ninth Annual ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 576–586.Google Scholar
  • [11] Désir A, Goyal V, Jagabathula S, Segev D (2021) Mallows-smoothed distribution over rankings approach for modeling choice. Oper. Res. 69(4):1206–1227.LinkGoogle Scholar
  • [12] Farias VF, Jagabathula S, Shah D (2013) A nonparametric approach to modeling choice with limited data. Management Sci. 59(2):305–322.LinkGoogle Scholar
  • [13] Francisca S, Golrezaei N, Emamjomeh-Zadeh E, Kempe D (2022) Active learning for non-parametric choice models. Preprint, submitted August 5, https://arxiv.org/abs/2208.03346v1.Google Scholar
  • [14] Goldreich O, Levin LA (1989) A hard-core predicate for all one-way functions. Proc. Twenty-First Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 25–32.Google Scholar
  • [15] Hauser J (2014) Consideration-set heuristics. J. Bus. Res. 67(8):1688–1699.CrossrefGoogle Scholar
  • [16] Haviv I, Regev O (2017) The restricted isometry property of subsampled Fourier matrices. Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis (Springer, Cham, Switzerland), 163–179.CrossrefGoogle Scholar
  • [17] Hayes TP (2005) A large-deviation inequality for vector-valued martingales. Combinatorics Probab. Comput. (July 26), https://www.cs.unm.edu/~hayes/papers/VectorAzuma/.Google Scholar
  • [18] Jagabathula S, Rusmevichientong P (2017) A nonparametric joint assortment and price choice model. Management Sci. 63(9):3128–3145.LinkGoogle Scholar
  • [19] Jagabathula S, Rusmevichientong P (2019) The limit of rationality in choice modeling: Formulation, computation, and implications. Management Sci. 65(5):2196–2215.AbstractGoogle Scholar
  • [20] Jagabathula S, Venkataraman A (2022) Nonparametric estimation of choice models. Chen X, Jasin S, Shi C, eds. The Elements of Joint Learning and Optimization in Operations Management (Springer, Cham, Switzerland), 177–209.CrossrefGoogle Scholar
  • [21] Kamishima T, Kazawa H, Akaho S (2005) Supervised ordering—An empirical survey. Fifth IEEE Internat. Conf. Data Mining ICDM’05 (IEEE, Piscataway, NJ), 673–676.Google Scholar
  • [22] Kolountzakis MN, Markakis E, Mehta A (2005) Learning symmetric k-juntas in time no(k). Preprint, submitted April 12, https://arxiv.org/abs/math/0504246.Google Scholar
  • [23] Kushilevitz E, Mansour Y (1993) Learning decision trees using the Fourier spectrum. SIAM J. Comput. 22(6):1331–1348.CrossrefGoogle Scholar
  • [24] Linial N, Mansour Y, Nisan N (1993) Constant depth circuits, Fourier transform, and learnability. J. ACM 40(3):607–620.CrossrefGoogle Scholar
  • [25] Luce R (1959) Individual Choice Behavior: A Theoretical Analysis (Wiley, Hoboken, NJ).Google Scholar
  • [26] Mattei N, Walsh T (2013) PREFLIB: A library for preferences HTTP://WWW.PREFLIB.ORG. Algorithmic Decision Theory ADT 2013 (Springer, Berlin), 259–270.CrossrefGoogle Scholar
  • [27] McFadden D (1972) Conditional logit analysis of qualitative choice behavior. Zarembka P ed. Frontiers in Econometrics (Academy Press, New York), 105–142.Google Scholar
  • [28] Mišić VV (2016) Data, models and decisions for large-scale stochastic optimization problems. Doctoral thesis, Massachusetts Institute of Technology, Cambridge.Google Scholar
  • [29] Mossel E, O’Donnell R, Servedio RP (2003) Learning juntas. Proc. Thirty-Fifth Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 206–212.Google Scholar
  • [30] O’Donnell R (2014) Analysis of Boolean Functions (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [31] Stobbe P, Krause A (2012) Learning Fourier sparse set functions. Proc.15th Internat. Conf. Artificial Intelligence Statist. (PMLR, New York), 1125–1133.Google Scholar
  • [32] van Ryzin G, Vulcano G (2015) A market discovery algorithm to estimate a general class of nonparametric choice models. Management Sci. 61(2):281–300.LinkGoogle Scholar
  • [33] Vitelli V, Sorensen O, Crispino M, Frigessi A, Arjas E (2014) Probabilistic preference learning with the Mallows rank model. Foundations Trends® Machine Learn. 18(1):5796–5844.Google Scholar
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