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Learning Preference from Observed Rankings

Yu-Chang Chen, Chen Chian Fuh, Shang En Tsai

TL;DR

The paper tackles learning individual preferences from incomplete ranking data subject to exposure bias. It develops a flexible logistic framework that decomposes utility into interpretable attributes, item fixed effects, and a low-rank latent factor term, while correcting observability bias with inverse-probability weighting and ridge regularization. Estimation is scalable via SGD with inverse-probability resampling, and the method is demonstrated on online wine transaction data, delivering improved out-of-sample recommendations, especially for previously unconsumed products, and enabling market-level targeting through composition-based lifts. The results highlight substantial heterogeneity in origin and price preferences, the value of combining attribute information with latent structure, and practical managerial gains in both personalized recommendations and segment-focused marketing decisions.

Abstract

Estimating consumer preferences is central to many problems in economics and marketing. This paper develops a flexible framework for learning individual preferences from partial ranking information by interpreting observed rankings as collections of pairwise comparisons with logistic choice probabilities. We model latent utility as the sum of interpretable product attributes, item fixed effects, and a low-rank user-item factor structure, enabling both interpretability and information sharing across consumers and items. We further correct for selection in which comparisons are observed: a comparison is recorded only if both items enter the consumer's consideration set, inducing exposure bias toward frequently encountered items. We model pair observability as the product of item-level observability propensities and estimate these propensities with a logistic model for the marginal probability that an item is observable. Preference parameters are then estimated by maximizing an inverse-probability-weighted (IPW), ridge-regularized log-likelihood that reweights observed comparisons toward a target comparison population. To scale computation, we propose a stochastic gradient descent (SGD) algorithm based on inverse-probability resampling, which draws comparisons in proportion to their IPW weights. In an application to transaction data from an online wine retailer, the method improves out-of-sample recommendation performance relative to a popularity-based benchmark, with particularly strong gains in predicting purchases of previously unconsumed products.

Learning Preference from Observed Rankings

TL;DR

The paper tackles learning individual preferences from incomplete ranking data subject to exposure bias. It develops a flexible logistic framework that decomposes utility into interpretable attributes, item fixed effects, and a low-rank latent factor term, while correcting observability bias with inverse-probability weighting and ridge regularization. Estimation is scalable via SGD with inverse-probability resampling, and the method is demonstrated on online wine transaction data, delivering improved out-of-sample recommendations, especially for previously unconsumed products, and enabling market-level targeting through composition-based lifts. The results highlight substantial heterogeneity in origin and price preferences, the value of combining attribute information with latent structure, and practical managerial gains in both personalized recommendations and segment-focused marketing decisions.

Abstract

Estimating consumer preferences is central to many problems in economics and marketing. This paper develops a flexible framework for learning individual preferences from partial ranking information by interpreting observed rankings as collections of pairwise comparisons with logistic choice probabilities. We model latent utility as the sum of interpretable product attributes, item fixed effects, and a low-rank user-item factor structure, enabling both interpretability and information sharing across consumers and items. We further correct for selection in which comparisons are observed: a comparison is recorded only if both items enter the consumer's consideration set, inducing exposure bias toward frequently encountered items. We model pair observability as the product of item-level observability propensities and estimate these propensities with a logistic model for the marginal probability that an item is observable. Preference parameters are then estimated by maximizing an inverse-probability-weighted (IPW), ridge-regularized log-likelihood that reweights observed comparisons toward a target comparison population. To scale computation, we propose a stochastic gradient descent (SGD) algorithm based on inverse-probability resampling, which draws comparisons in proportion to their IPW weights. In an application to transaction data from an online wine retailer, the method improves out-of-sample recommendation performance relative to a popularity-based benchmark, with particularly strong gains in predicting purchases of previously unconsumed products.
Paper Structure (25 sections, 26 equations, 6 figures, 4 tables)

This paper contains 25 sections, 26 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Method
  4. Observed Rankings
  5. Modeling Utility Function
  6. Correcting for Selection in Observability
  7. Estimation and Computation
  8. Empirical Illustration
  9. Data and Background
  10. Construction of Ranking Data
  11. Model Specificaiton
  12. Estimation Results
  13. Application I: Recommender System
  14. Recommender System
  15. Evaluation Methods
  16. ...and 10 more sections

Figures (6)

  • Figure 1: Distributions of individual-specific region effect coefficients $\delta_r$ for the six regions.
  • Figure 2: Correlation matrix of customer-specific region preference effects. Each entry reports the pairwise correlation between two regions' preference effects.
  • Figure 3: Distributions of user-specific price-tier coefficients. Each panel shows the estimated coefficient distribution for one price tier in the ranking model. Using an exchange rate of 1 USD = 32 NTD, these cutoffs correspond to approximately USD 16, 31, 63, 94, 125, 156, 313, 625, and above 625.
  • Figure 4: Correlation matrix of price preference effects. Each entry reports the pairwise correlation across customers between two price-tier preference effects. Prices shown in the figure are in NTD. Using an exchange rate of 1 USD = 32 NTD, these cutoffs correspond to approximately USD 16, 31, 63, 94, 125, 156, 313, 625, and above 625.
  • Figure 5: Lift curve analysis across three key wine regions: Bordeaux (Left column), Burgundy (Middle column), and Marlborough (Right column), segmented by (a) Gender, (b) Age Group, and (c) Average Price per Bottle (APB). The x-axis represents the threshold $q$, defining the set of product fans as the top $q\%$ of customers who rank the region highest within their personal preferences. The y-axis displays the composition lift for each segment at that threshold, quantifying the segment's over-representation among fans relative to its share in the general population. The red dashed line ($y=1$) indicates the baseline where a segment's representation among fans equals its population share.
  • ...and 1 more figures