  In this work, we developed a network inference method from incomplete data
("PathInf") , as massive and non-uniformly distributed missing values is a
common challenge in practical problems. PathInf is a two-stages inference
model. In the first stage, it applies a data summarization model based on
maximum likelihood to deal with the massive distributed missing values by
transforming the observation-wise items in the data into state matrix. In the
second stage, transition pattern (i.e. pathway) among variables is inferred as
a graph inference problem solved by greedy algorithm with constraints. The
proposed method was validated and compared with the state-of-art Bayesian
network method on the simulation data, and shown consistently superior
performance. By applying the PathInf on the lymph vascular metastasis data, we
obtained the holistic pathways of the lymph node metastasis with novel
discoveries on the jumping metastasis among nodes that are physically apart.
The discovery indicates the possible presence of sentinel node groups in the
lung lymph nodes which have been previously speculated yet never found. The
pathway map can also improve the current dissection examination protocol for
better individualized treatment planning, for higher diagnostic accuracy and
reducing the patients trauma.
