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Beyond Means: A Dynamic Framework for Predicting Customer Satisfaction

Christof Naumzik, Abdurahman Maarouf, Stefan Feuerriegel, Markus Weinmann

TL;DR

This work addresses the limitations of traditional rating aggregation, which relies on the sample mean and ignores temporal dynamics and review heterogeneity. It develops a tailored Gaussian process model with a latent continuous-time trajectory, an ordered-probit emission for discrete ratings, a linear covariate-driven mean function, and an exponential kernel with entity-specific parameters, enabling dynamic, covariate-informed aggregation. Through MCMC and scalable variational inference, the model achieves substantial predictive gains over the sample mean and strong baselines on Yelp data, with robustness across datasets and deployment settings. Practically, the framework yields more informative, universal rating scores that better signal expected customer satisfaction and can inform reputation-system design on large platforms.

Abstract

Online ratings influence customer decision-making, yet standard aggregation methods, such as the sample mean, fail to adapt to quality changes over time and ignore review heterogeneity (e.g., review sentiment, a review's helpfulness). To address these challenges, we demonstrate the value of using the Gaussian process (GP) framework for rating aggregation. Specifically, we present a tailored GP model that captures the dynamics of ratings over time while additionally accounting for review heterogeneity. Based on 121,123 ratings from Yelp, we compare the predictive power of different rating aggregation methods in predicting future ratings, thereby finding that the GP model is considerably more accurate and reduces the mean absolute error by 10.2% compared to the sample mean. Our findings have important implications for marketing practitioners and customers. By moving beyond means, designers of online reputation systems can display more informative and adaptive aggregated rating scores that are accurate signals of expected customer satisfaction.

Beyond Means: A Dynamic Framework for Predicting Customer Satisfaction

TL;DR

This work addresses the limitations of traditional rating aggregation, which relies on the sample mean and ignores temporal dynamics and review heterogeneity. It develops a tailored Gaussian process model with a latent continuous-time trajectory, an ordered-probit emission for discrete ratings, a linear covariate-driven mean function, and an exponential kernel with entity-specific parameters, enabling dynamic, covariate-informed aggregation. Through MCMC and scalable variational inference, the model achieves substantial predictive gains over the sample mean and strong baselines on Yelp data, with robustness across datasets and deployment settings. Practically, the framework yields more informative, universal rating scores that better signal expected customer satisfaction and can inform reputation-system design on large platforms.

Abstract

Online ratings influence customer decision-making, yet standard aggregation methods, such as the sample mean, fail to adapt to quality changes over time and ignore review heterogeneity (e.g., review sentiment, a review's helpfulness). To address these challenges, we demonstrate the value of using the Gaussian process (GP) framework for rating aggregation. Specifically, we present a tailored GP model that captures the dynamics of ratings over time while additionally accounting for review heterogeneity. Based on 121,123 ratings from Yelp, we compare the predictive power of different rating aggregation methods in predicting future ratings, thereby finding that the GP model is considerably more accurate and reduces the mean absolute error by 10.2% compared to the sample mean. Our findings have important implications for marketing practitioners and customers. By moving beyond means, designers of online reputation systems can display more informative and adaptive aggregated rating scores that are accurate signals of expected customer satisfaction.

Paper Structure

This paper contains 55 sections, 2 theorems, 11 equations, 6 figures, 14 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Reputation Systems
  4. Reputation System Variables: Valence and Review Heterogeneity
  5. Rating Aggregation
  6. Model Development
  7. Problem Statement
  8. Model Specification
  9. Overview.
  10. Observation Sequence.
  11. Latent Gaussian Process.
  12. Emission Component Linking Latent GP and Ratings.
  13. GP Mean Function.
  14. Kernel.
  15. Combined Model
  16. ...and 40 more sections

Key Result

Theorem 1

For our tailored GP model, the evidence lower bound (ELBO) of its likelihood is given by

Figures (6)

  • Figure 1: Screenshot showing aggregated ratings (red boxes) on different rating platforms (Yelp, IMDb, Google Maps, Amazon). Note: the same ratings are shown for all website visitors (i. e., no personalization).
  • Figure 2: Example showing that when using the sample mean for rating aggregation, the underlying quality dynamics may not be captured.
  • Figure 3: Schematic overview of the tailored GP model.
  • Figure 4: Plate notation of the tailored GP model.
  • Figure 5: Computational Runtime (per Restaurant).
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Proposition 1