2025/05/29 by Yanqiu Ruan, Ruan, Yanqiu, Karthyek Murthy +3
Business, Management and Accounting · #Business Strategy and Innovation #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2505.23546
openalex publication_date 2025/05/29 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
We study decision-making problems where data comprises points from a collection of binary polytopes, capturing aggregate information stemming from various combinatorial selection environments. We propose a nonparametric approach for counterfactual inference in this setting based on a representative agent model, where the available data is viewed as arising from maximizing separable concave utility functions over the respective binary polytopes. Our first contribution is to precisely characterize the selection probabilities representable under this model and show that verifying the consistency of any given aggregated selection dataset reduces to solving a polynomial-sized linear program. Building on this characterization, we develop a nonparametric method for counterfactual prediction. When data is inconsistent with the model, finding a best-fitting approximation for prediction reduces to solving a compact mixed-integer convex program. Numerical experiments based on synthetic data demonstrate the method's flexibility, predictive accuracy, and strong representational power even under model misspecification.