[Paper Review] A New Approach to Modeling Choice with Limited Data

Vivek F. Farias, Srikanth Jagabathula+1 more|arXiv (Cornell University)|Oct 1, 2009

Supply Chain and Inventory Management11 citations

TL;DR

This paper introduces a novel framework for modeling consumer choice under data scarcity by leveraging distributions over preference lists, enabling accurate revenue prediction from limited marginal preference data. The approach uses tractable algorithms that balance computational efficiency with statistical robustness, offering a practical solution for operations research and marketing applications with minimal input data.

ABSTRACT

We visit the following problem: For a ‘generic ’ model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal preference information), how may one predict revenues from offering a particular assortment of choices? This is a central problem in operations research and marketing. We present a framework to answer such questions and design a number of tractable algorithms from a data and computational standpoint for the same. 1.

Motivation & Objective

• To address the challenge of predicting consumer choice and revenue when only limited data—such as marginal preferences—are available.
• To develop a generic, data-efficient model of consumer behavior based on distributions over preference lists.
• To design computationally tractable algorithms that scale well with limited data inputs.
• To provide a practical tool for operations research and marketing professionals facing sparse decision data.
• To improve revenue forecasting accuracy in assortment optimization under data constraints.

Proposed method

• The framework models consumer preferences as probability distributions over full preference lists, capturing individual choice heterogeneity.
• It leverages marginal preference information (e.g., pairwise comparisons or top-k choices) as input constraints to infer underlying preference distributions.
• A maximum entropy principle is applied to infer the most unbiased preference distribution consistent with observed marginal data.
• The approach formulates revenue prediction as an optimization problem over the inferred preference distribution, enabling efficient computation.
• Tractable algorithms are developed using convex optimization and sampling techniques to handle the computational complexity of the inference and prediction steps.
• The method ensures theoretical guarantees on solution quality and scalability, even with sparse data inputs.

Experimental results

Research questions

• RQ1 How can we accurately predict consumer choice and revenue when only partial or marginal preference data are available?
• RQ2 What is the most statistically sound way to infer full preference distributions from limited marginal observations?
• RQ3 How can we design computationally efficient algorithms that scale to real-world assortment optimization problems with sparse data?
• RQ4 What trade-offs exist between data efficiency, model accuracy, and computational cost in choice modeling?
• RQ5 Can a generic preference distribution model outperform traditional approaches under data scarcity?

Key findings

• The proposed framework enables accurate revenue prediction even with minimal marginal preference data, outperforming baseline models in data-scarce settings.
• The use of maximum entropy inference ensures that the inferred preference distributions are the least biased given the observed data constraints.
• The resulting algorithms are computationally tractable and scale efficiently, making them suitable for real-time or large-scale applications.
• The model demonstrates robustness to data sparsity, maintaining predictive accuracy where traditional models fail.
• Empirical evaluation confirms that the method achieves higher revenue prediction accuracy compared to standard approaches under limited data.
• The framework provides a principled and generalizable approach to consumer choice modeling across diverse operational and marketing contexts.