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.

Existing multimodal tasks mostly target at the complete input modality setting, i.e., each modality is either complete or completely missing in both training and test sets. However, the randomly missing situations have still been underexplored. In this paper, we present a novel approach named MM-Align to address the missing-modality inference problem. Concretely, we propose 1) an alignment dynamics learning module based on the theory of optimal transport (OT) for indirect missing data imputation; 2) a denoising training algorithm to simultaneously enhance the imputation results and backbone network performance. Compared with previous methods which devote to reconstructing the missing inputs, MM-Align learns to capture and imitate the alignment dynamics between modality sequences. Results of comprehensive experiments on three datasets covering two multimodal tasks empirically demonstrate that our method can perform more accurate and faster inference and relieve overfitting under various missing conditions.

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.