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Fast and Stable Maximum Likelihood Estimation for Incomplete Multinomial Models
Chenyang ZHANG · Guosheng Yin

Thu Jun 13 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #230

We propose a fixed-point iteration approach to the maximum likelihood estimation for the incomplete multinomial model, which provides a unified framework for ranking data analysis. Incomplete observations typically fall in a subset of categories, and thus cannot be distinguished as belonging to a unique category. We develop a minorization--maximization (MM) type of algorithm, which requires relatively fewer iterations and shorter time to achieve convergence. Under such a general framework, incomplete multinomial models can be reformulated to include several well-known ranking models as special cases, such as the Bradley--Terry, Plackett--Luce models and their variants. The simple form of iteratively updating equations in our algorithm involves only basic matrix operations, which makes it efficient and easy to implement with large data. Experimental results show that our algorithm runs faster than existing methods on synthetic data and real data.

Author Information

Chenyang ZHANG (University of Hong Kong)
Guosheng Yin (University of Hong Kong)

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