  Information transfer which reveals the state variation of variables usually
plays a vital role in big data analytics and processing. In fact, the measures
for information transfer could reflect the system change by use of the variable
distributions, similar to KL divergence and Renyi divergence. Furthermore, in
terms of the information transfer in big data, small probability events usually
dominate the importance of the total message to some degree. Therefore, it is
significant to design an information transfer measure based on the message
importance which emphasizes the small probability events. In this paper, we
propose a message importance transfer measure (MITM) and investigate its
characteristics and applications on three aspects. First, the message
importance transfer capacity based on MITM is presented to offer an upper bound
for the information transfer process with disturbance. Then, we extend the MITM
to the continuous case and discuss the robustness by using it to measuring
information distance. Finally, we utilize the MITM to guide the queue length
selection in the caching operation of mobile edge computing.
