  Graphs are widely adopted for modeling complex systems, including financial,
biological, and social networks. Nodes in networks usually entail attributes,
such as the age or gender of users in a social network. However, real-world
networks can have very large size, and nodal attributes can be unavailable to a
number of nodes, e.g., due to privacy concerns. Moreover, new nodes can emerge
over time, which can necessitate real-time evaluation of their nodal
attributes. In this context, the present paper deals with scalable learning of
nodal attributes by estimating a nodal function based on noisy observations at
a subset of nodes. A multikernel-based approach is developed which is scalable
to large-size networks. Unlike most existing methods that re-solve the function
estimation problem over all existing nodes whenever a new node joins the
network, the novel method is capable of providing real-time evaluation of the
function values on newly-joining nodes without resorting to a batch solver.
Interestingly, the novel scheme only relies on an encrypted version of each
node's connectivity in order to learn the nodal attributes, which promotes
privacy. Experiments on both synthetic and real datasets corroborate the
effectiveness of the proposed methods.
