  Multinomial Logit (MNL) is one of the most popular discrete choice models and
has been widely used to model ranking data. However, there is a long-standing
technical challenge of learning MNL from many real-world ranking data: exact
calculation of the MNL likelihood of \emph{partial rankings} is generally
intractable. In this work, we develop a scalable method for approximating the
MNL likelihood of general partial rankings in polynomial time complexity. We
also extend the proposed method to learn mixture of MNL. We demonstrate that
the proposed methods are particularly helpful for applications to choice-based
network formation modeling, where the formation of new edges in a network is
viewed as individuals making choices of their friends over a candidate set. The
problem of learning mixture of MNL models from partial rankings naturally
arises in such applications. And the proposed methods can be used to learn MNL
models from network data without the strong assumption that temporal orders of
all the edge formation are available. We conduct experiments on both synthetic
and real-world network data to demonstrate that the proposed methods achieve
more accurate parameter estimation and better fitness of data compared to
conventional methods.
