Discrete Choice, Permutations, and Reconstruction

Chierichetti, Flavio; Kumar, Ravi; Tomkins, Andrew

doi:10.1137/1.9781611975031.38

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…This claim can be viewed as the counterpart of Theorem 4 in the paper by Chierichetti et al (2018) for feature-dependent choice models in the continuous domain, rather than the discrete domain.…”

Section: Learning Error Guarantees and Compact Representationmentioning

confidence: 83%

Representing Random Utility Choice Models with Neural Networks

Aouad¹,

Désir²

2022

Preprint

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Motivated by the successes of deep learning, we propose a class of neural network-based discrete choice models, called RUMnets, which is inspired by the random utility maximization (RUM) framework. This model formulates the agents' random utility function using the sample average approximation (SAA) method.We show that RUMnets sharply approximate the class of RUM discrete choice models: any model derived from random utility maximization has choice probabilities that can be approximated arbitrarily closely by a RUMnet. Reciprocally, any RUMnet is consistent with the RUM principle. We derive an upper bound on the generalization error of RUMnets fitted on choice data, and gain theoretical insights on their ability to predict choices on new, unseen data depending on critical parameters of the dataset and architecture. By leveraging open-source libraries for neural networks, we find that RUMnets outperform other state-of-the-art choice modeling and machine learning methods by a significant margin on two real-world datasets.

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Section: Learning Error Guarantees and Compact Representationmentioning

confidence: 83%

Representing Random Utility Choice Models with Neural Networks

Aouad¹,

Désir²

2022

Preprint

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“…Since any RUM can be approximated arbitrarily close by a latent class MNL (LC-MNL) model [Chierichetti et al, 2018], Theorem 1 shows that there is no hope for a general prophet inequality for the LC-MNL. Nevertheless, we are able to prove some interesting results for this class.…”

Section: The Latent Class Mnlmentioning

confidence: 99%

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

Gallego¹,

Berbeglia²

2021

Preprint

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Consider a clairvoyant firm that knows the products' valuations of each arriving consumer and offers them only the most profitable product they are willing to buy. How much more can such a firm make relative to a firm that offers all consumers the assortment that maximizes expected revenues? We show that for general discrete choice models, the ratio can be exponential in the number of products, but at most equal to the number of products for random utility models.We show that the ratio is at most 2 for the α-shaken multinomial logit (α-MNL) which includes the MNL and the general attraction model (GAM) as special cases. We also provide sufficient conditions for the ratio of at most 2 to hold for the latent class MNL, and in fact show that in the limit as the coefficient of variation of the utilities goes to infinity the bound is at most 1.5. For all of these cases the revenue-ordered heuristic yields the stated guarantees relevant to the clairvoyant firm.

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“…For example, choice set effects abundant in online data has led to richer data models [6,19,28,41,44,45], new methods for testing the presence of choice set effects [4,45,46], and new learning algorithms [9,23]. More broadly, there are efforts on learning algorithms for multinomial logits mixtures [2,21,36,57], Placket-Luce models [30,56], and other random utility models [5,8,37].…”

Section: Related Workmentioning

confidence: 99%

Choice Set Optimization Under Discrete Choice Models of Group Decisions

Tomlinson¹,

Benson²

2020

Preprint

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The way that people make choices or exhibit preferences can be strongly affected by the set of available alternatives, often called the choice set. Furthermore, there are usually heterogeneous preferences, either at an individual level within small groups or within sub-populations of large groups. Given the availability of choice data, there are now many models that capture this behavior in order to make effective predictions. However, there is little work in understanding how directly changing the choice set can be used to influence a group's preferences or decisions. Here, we use discrete choice modeling to develop an optimization framework of such interventions for several problems of group influence, including maximizing agreement or disagreement and promoting a particular choice. We show that these problems are NP-hard in general but imposing restrictions reveals a fundamental boundary: promoting an item is easier than maximizing agreement or disagreement. After, we design approximation algorithms for the hard problems and show that they work extremely well for real-world choice data.

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Discrete Choice, Permutations, and Reconstruction

Cited by 6 publications

References 11 publications

Representing Random Utility Choice Models with Neural Networks

Representing Random Utility Choice Models with Neural Networks

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

Choice Set Optimization Under Discrete Choice Models of Group Decisions

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