The Use of Binary Choice Forests to Model and Estimate Discrete Choice Models

Chen, Ningyuan; Gallego, Guillermo; Tang, Zhuodong

doi:10.2139/ssrn.3430886

Cited by 7 publications

(8 citation statements)

References 28 publications

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“…The optimal price is solved for a family of possible distributions in the maximin sense. Chen et al (2019) adopt the estimate-then-model approach, which is model-free, to estimate choice models using random forests. They do not consider the optimization stage.…”

Section: Related Workmentioning

confidence: 99%

Model-Free Assortment Pricing with Transaction Data

Chen¹,

Ciré²,

Hu³

et al. 2021

Preprint

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We study a problem in which a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed.Our approach does not impose a model on the distribution of the customers' valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The individual valuation of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst-case revenue assuming that new customers' valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We show that the optimal prices in this setting can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. Moreover, we study special practical cases where the program can be solved efficiently, and design three approximation strategies that are of low computational complexity and interpretable. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification.

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Section: Related Workmentioning

confidence: 99%

Model-Free Assortment Pricing with Transaction Data

Chen¹,

Ciré²,

Hu³

et al. 2021

Preprint

Self Cite

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show abstract

“…However, this "model-free" logic means that the probabilistic structure of classical choice models (such as the rationality axiom or Independence of Irrelevant Alternatives property) can be lifted all-together. While training these predictive algorithms in theory may require large amounts of data, recent empirical studies have shown that this approach is successful on several real-world choice datasets (Wong and Farooq 2019, Chen et al 2019, Chen andMišić 2020).…”

Section: Introductionmentioning

confidence: 99%

“…In contrast with the above approach, a growing number of papers employ generic ML classifiers and relax the probabilistic structure of parametric choice models altogether. For example, Chen et al (2019) and Chen and Mišić (2020) train random forests to predict choices, while Jiang et al (2020) use a graphical Lasso method. The resulting probabilistic models have the ability to capture a variety of choice behaviors including complementarities between products (Jiang et al 2020), contextual effects (Rosenfeld et al 2020), and even irrational behaviors (Berbeglia 2018).…”

Section: Introductionmentioning

confidence: 99%

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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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“…There is a growing body of literature supporting the idea that using discrete choice models leads to better sales outcomes [Talluri and Van Ryzin, 2004, Vulcano et al, 2010, Farias et al, 2013. Parametric discrete choice models yield more accurate estimates than machine learning techniques Feldman et al [2018] unless data is abundant and the ground truth model cannot be easily captured by a parametric model [Chen et al, 2019b]. Parametric models have the additional advantage that they are amenable to optimization of the firm's objective such as expected sales or expected revenues.…”

Section: Introductionmentioning

confidence: 99%

The Refined Assortment Optimization Problem

Berbeglia,

Flores,

Gallego

2021

Preprint

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We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example, offer fares with severe restrictions rather than making them unavailable. This is a more subtle way of handling the trade-off between demand induction and demand cannibalization. For the latent class MNL model, a firm that engages in refined assortment optimization can make up to min(n, m) times more than one that insists on traditional assortment optimization, where n is the number of products and m the number of customer types. Surprisingly, the revenue-ordered assortment heuristic has the same performance guarantees relative to personalized refined assortment optimization as it does to traditional assortment optimization. Based on this finding, we construct refinements of the revenue-order heuristic and measure their improved performance relative to the revenue-ordered assortment and the optimal traditional assortment optimization problem. We also provide tight bounds on the ratio of the expected revenues for the refined versus the traditional assortment optimization for some well known discrete choice models.

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The Use of Binary Choice Forests to Model and Estimate Discrete Choice Models

Cited by 7 publications

References 28 publications

Model-Free Assortment Pricing with Transaction Data

Model-Free Assortment Pricing with Transaction Data

Representing Random Utility Choice Models with Neural Networks

The Refined Assortment Optimization Problem

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