Title: Stochastic Block Models with Multiple Continuous Attributes,
Abstract: The stochastic block model (SBM) is a probabilistic model for community
structure in networks. Typically, only the adjacency matrix is used to perform
SBM parameter inference. In this paper, we consider circumstances in which
nodes have an associated vector of continuous attributes that are also used to
learn the node-to-community assignments and corresponding SBM parameters. While
this assumption is not realistic for every application, our model assumes that
the attributes associated with the nodes in a network's community can be
described by a common multivariate Gaussian model. In this augmented,
attributed SBM, the objective is to simultaneously learn the SBM connectivity
probabilities with the multivariate Gaussian parameters describing each
community. While there are recent examples in the literature that combine
connectivity and attribute information to inform community detection, our model
is the first augmented stochastic block model to handle multiple continuous
attributes. This provides the flexibility in biological data to, for example,
augment connectivity information with continuous measurements from multiple
experimental modalities. Because the lack of labeled network data often makes
community detection results difficult to validate, we highlight the usefulness
of our model for two network prediction tasks: link prediction and
collaborative filtering. As a result of fitting this attributed stochastic
block model, one can predict the attribute vector or connectivity patterns for
a new node in the event of the complementary source of information
(connectivity or attributes, respectively). We also highlight two biological
examples where the attributed stochastic block model provides satisfactory
performance in the link prediction and collaborative filtering tasks.