The Order-Dependent Luce Model

I develop a simple axiomatic model that incorporates the order effect: the ordering of alternatives (e.g., ranking of universities, the location of products in a grocery store, the order of candidates on a ballot) affects choice frequencies. In my model, the probability of choosing an alternative is proportional to the utility of the alternative, similar to the Luce model. However, the utility of the alternative depends on the relative ordering of the alternative in the menu. I characterize this model by two weakenings of Luce’s axiom of independence of irrelevant alternatives. I discuss how to identify the ordering of alternatives from choice data when it is not observed. Finally, I apply my model to an optimal ordering problem and to experimental data on intertemporal choice. This paper was accepted by Manel Baucells, decision analysis.

Learning Plackett-Luce Mixtures from Partial Preferences

We propose an EM-based framework for learning Plackett-Luce model and its mixtures from partial orders. The core of our framework is the efficient sampling of linear extensions of partial orders under Plackett-Luce model. We propose two Markov Chain Monte Carlo (MCMC) samplers: Gibbs sampler and the generalized repeated insertion method tuned by MCMC (GRIM-MCMC), and prove the efficiency of GRIM-MCMC for a large class of preferences.Experiments on synthetic data show that the algorithm with Gibbs sampler outperforms that with GRIM-MCMC. Experiments on real-world data show that the likelihood of test dataset increases when (i) partial orders provide more information; or (ii) the number of components in mixtures of PlackettLuce model increases.

Near-Neighbor Methods in Random Preference Completion

This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with n agents (users) {xi}i∈[n] and m alternatives (items) {yl}l∈[m], each of which is associated with a latent feature vector. Agents rank items nondeterministically according to the Plackett-Luce model, where the higher the utility of an item to the agent, the more likely this item will be ranked high by the agent. Our goal is to identify near neighbors of an arbitrary agent in the latent space for prediction.We first show that the Kendall-tau distance based kNN produces incorrect results in our model. Next, we propose a new anchor-based algorithm to find neighbors of an agent. A salient feature of our algorithm is that it leverages the rankings of many other agents (the so-called “anchors”) to determine the closeness/similarities of two agents. We provide a rigorous analysis for one-dimensional latent space, and complement the theoretical results with experiments on synthetic and real datasets. The experiments confirm that the new algorithm is robust and practical.