  Given a sequence of random (directed and weighted) graphs, we address the
problem of online monitoring and detection of changes in the underlying data
distribution. Our idea is to endow sequential change-point detection (CPD)
techniques with a graph representation learning substrate based on the
versatile Random Dot Product Graph (RDPG) model. We consider efficient, online
updates of a judicious monitoring function, which quantifies the discrepancy
between the streaming graph observations and the nominal RDPG. This reference
distribution is inferred via spectral embeddings of the first few graphs in the
sequence. We characterize the distribution of this running statistic to select
thresholds that guarantee error-rate control, and under simplifying
approximations we offer insights on the algorithm's detection resolution and
delay. The end result is a lightweight online CPD algorithm, that is also
explainable by virtue of the well-appreciated interpretability of RDPG
embeddings. This is in stark contrast with most existing graph CPD approaches,
which either rely on extensive computation, or they store and process the
entire observed time series. An apparent limitation of the RDPG model is its
suitability for undirected and unweighted graphs only, a gap we aim to close
here to broaden the scope of the CPD framework. Unlike previous proposals, our
non-parametric RDPG model for weighted graphs does not require a priori
specification of the weights' distribution to perform inference and estimation.
This network modeling contribution is of independent interest beyond CPD. We
offer an open-source implementation of the novel online CPD algorithm for
weighted and direct graphs, whose effectiveness and efficiency are demonstrated
via (reproducible) synthetic and real network data experiments.
