[Paper Review] Learning Preference from Observed Rankings

Yu‐Chang Chen, Chen Chian Fuh+1 more|arXiv (Cornell University)|Feb 18, 2026

Consumer Market Behavior and Pricing0 citations

TL;DR

The paper develops a scalable framework to learn individual consumer preferences from partial rankings by modeling latent utilities with attribute effects and low-rank factors, correcting for exposure bias via inverse-probability weighting, and applying SGD for large-scale incomplete ranking data.

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.

Motivation & Objective

• Estimate individual-level preferences from incomplete ranking data using a random-utility foundation.
• Incorporate interpretable product attributes and latent factors to capture heterogeneity.
• Address selection in observability (exposure bias) with inverse-probability weighting.
• Provide a scalable estimation method (IPW with SGD) for large, sparse ranking data.
• Demonstrate application to online wine purchases and evaluate predictive performance.

Proposed method

• Model latent utility as u_{ij}=x_j^{⊤}β_i+α_j+λ_i^{⊤}f_j+ε_{ij}, with ε_{ij} ~ Type-I EVT.
• Interpret observed rankings as pairwise comparisons with probability P(j ≽ j') = σ(u_{ij}-u_{ij'}) under logistic choice.
• Introduce IPW to correct for selection in observability with weights 1/π_{jj'}, where π_j = σ(x_j^{⊤}ψ) and π_{jj'}=π_j π_{j'}.
• Estimate ψ via maximum likelihood on observability indicators O_{ijj'}, and plug in igurπ_j.
• Use penalized (ridge) IPW objective: maximize ∑_{(i,j,j')∈D} (1/π_{jj'}) ln σ(u_{ij}-u_{ij'}) - κ||θ||_2^2.
• Employ inverse-probability resampling in SGD to draw comparisons with probability proportional to π_{jj'}^{-1}, updating θ with a standard log-likelihood gradient minus ridge term.
• Precompute π_{jj'} and use an alias table to efficiently sample comparisons for scalable optimization.

Experimental results

Research questions

• RQ1 How can we recover individual-specific preferences from incomplete ranking data?
• RQ2 Can a latent-factor structure alongside observed attributes capture heterogeneity and enable extrapolation to unobserved item pairs?
• RQ3 How does exposure/observability bias affect preference estimation, and can IPW correct for it in ranking data?
• RQ4 Is the proposed IPW-regularized, SGD-based estimation scalable to large, sparse ranking datasets?
• RQ5 Does the method improve out-of-sample recommendation accuracy, particularly for previously unconsumed items?

Key findings

• The model discovers substantial heterogeneity in region-specific preferences among wine consumers, with distributions that are right-skewed and often bimodal for prestigious regions like Bordeaux and Burgundy.
• Latent-factor structure enables sharing information across consumers and items, aiding inference for unobserved comparisons.
• Correcting for selection in observability via IPW reduces bias from exposure and improves predictive performance on held-out data.
• The SGD-based estimation with IPW weights scales to large, sparse ranking data and efficiently leverages pairwise comparisons implied by rankings.
• Application to online wine transactions demonstrates improvements in out-of-sample recommendations, especially for purchases of previously unconsumed products.