Bayesian method improves ordinal regression with better preference queries
Bayesian Deck-of-cards-based Ordinal Regression with Sequential Preference Elicitation
Machine Learning
Summary
Choosing items or ranking options can be hard when people have to say how much they like things compared to others. The authors present a new Bayesian method that learns these preferences better by listening not just to order but also to how strongly differences are felt, using 'blank cards' as a metaphor. Their approach works gradually over multiple short sessions, making it easier for people to express their preferences. They tested two algorithms that can handle inconsistent answers and found their methods make better predictions about preferences than older ones.
What this means in practice
- •For healthcare policy analysts: Create composite performance indicators for regional healthcare systems using improved preference modeling.
- •For user experience researchers: Design preference elicitation tasks that reduce cognitive load by spreading queries over multiple sessions while improving data quality.
Authors
Marco Grillo, Silvano Zappalà
Abstract
The Deck-of-cards-based Ordinal Regression (DOR) infers a value function from a ranking of reference alternatives in which the Decision Maker (DM) inserts blank cards between consecutive levels to express preference intensity. DOR, and its stochastic extension (SMAA-DOR), treat these answers as hard constraints defining a set of compatible value functions. We propose B-DOR, a probabilistic reformulation of DOR in which each pair of adjacent levels yields an ordinal observation, the declared direction and the number of cards, modelled through a cumulative-link likelihood that relates the number of blank cards to the latent value difference between alternatives. Two Bayesian inference algorithms are proposed: BAYES-DOR samples the whole posterior distribution by Hamiltonian Monte Carlo; FTRL-DOR tracks the maximum a posteriori estimate by constrained convex optimization. Moreover, through a multi-step elicitation process, elicitation can be spread over several short sessions reducing the cognitive burden on the DM. Both algorithms enjoy logarithmic regret bounds for prediction that hold for any sequence of DM responses and that guide the choice of the prior hyperparameters. A Monte Carlo study over 768 configurations shows that accuracy grows with the number of sessions, that blank cards add significant information over preference directions alone, that both algorithms maintain good performance under inconsistent answers, and that both outperform DOR and SMAA-DOR. An illustrative application to Italian regional healthcare performance demonstrates the practical applicability of the approach for building composite indicators.