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[2602.11505] Calibrating an Imperfect Auxiliary Predictor for Unobserved No-Purchase Choice
Summary
This paper presents methods for calibrating biased auxiliary predictors to improve estimates of unobserved no-purchase choices in market analysis, enhancing decision-making in assortment optimization.
Why It Matters
Understanding consumer behavior is crucial for firms, especially when key actions like no-purchase choices are unobserved. This research addresses a significant gap in market analysis by providing calibration techniques that improve the accuracy of predictions, ultimately aiding in better decision-making and revenue optimization.
Key Takeaways
- Calibration methods can convert biased auxiliary predictions into valid no-purchase estimates.
- A regression approach can identify outside-option utility parameters without new data collection.
- Rank-based calibration methods provide finite-sample error bounds, clarifying the impact of predictor quality.
- The study quantifies how calibration accuracy affects downstream decision quality in assortment optimization.
- Numerical experiments demonstrate significant improvements in no-purchase estimation.
Computer Science > Machine Learning arXiv:2602.11505 (cs) [Submitted on 12 Feb 2026 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Calibrating an Imperfect Auxiliary Predictor for Unobserved No-Purchase Choice Authors:Jiangkai Xiong, Kalyan Talluri, Hanzhao Wang View a PDF of the paper titled Calibrating an Imperfect Auxiliary Predictor for Unobserved No-Purchase Choice, by Jiangkai Xiong and 1 other authors View PDF HTML (experimental) Abstract:Firms typically cannot observe key consumer actions: whether customers buy from a competitor, choose not to buy, or even fully consider the firm's offer. This missing outside-option information makes market-size and preference estimation difficult even in simple multinomial logit (MNL) models, and it is a central obstacle in practice when only transaction data are recorded. Existing approaches often rely on auxiliary market-share, aggregated, or cross-market data. We study a complementary setting in which a black-box auxiliary predictor provides outside-option probabilities, but is potentially biased or miscalibrated because it was trained in a different channel, period, or population, or produced by an external machine-learning system. We develop calibration methods that turn such imperfect predictions into statistically valid no-purchase estimates using purchase-only data from the focal environment. First, under affine miscalibration in logit space, we show that a simple regression identifies outside-option utility para...
