We show that the maximum-likelihood (ML) estimate of models derived from Luce's choice axiom (e.g., the Plackett-Luce model) can be expressed as the stationary distribution of a Markov chain. This conveys insight into several recently proposed spectral inference algorithms. We take advantage of this perspective and formulate a new spectral algorithm that is significantly more accurate than previous ones for the Plackett--Luce model. With a simple adaptation, this algorithm can be used iteratively, producing a sequence of estimates that converges to the ML estimate. The ML version runs faster than competing approaches on a benchmark of five datasets. Our algorithms are easy to implement, making them relevant for practitioners at large.
Lucas Maystre (EPFL)
Matt Grossglauser (EPFL)
More from the Same Authors
2019 Poster: Learning Hawkes Processes from a handful of events »
Farnood Salehi · William Trouleau · Matthias Grossglauser · Patrick Thiran