Pairwise Choice Markov Chains

Abstract

As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansion, a considerably weaker assumption than Luce's choice axiom. We show that the PCMC model significantly outperforms the Multinomial Logit (MNL) model in prediction tasks on both synthetic and empirical datasets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case.

Advances in Neural Information Processing Systems (NIPS) 29, 2016

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• Choice Set Confounding in Discrete Choice
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• Preference Modeling with Context-Dependent Salient Features
• Choice Set Optimization Under Discrete Choice Models of Group Decisions
• Improving pairwise comparison models using Empirical Bayes shrinkage
• Learning Rich Rankings
• Predicting Choice with Set-Dependent Aggregation
• PCMC-Net: Feature-based Pairwise Choice Markov Chains
• Fundamental Limits of Testing the Independence of Irrelevant Alternatives in Discrete Choice
• Infinity Learning: Learning Markov Chains from Aggregate Steady-State Observations