  Learning the dynamics of complex systems features a large number of
applications in data science. Graph-based modeling and inference underpins the
most prominent family of approaches to learn complex dynamics due to their
ability to capture the intrinsic sparsity of direct interactions in such
systems. They also provide the user with interpretable graphs that unveil
behavioral patterns and changes. To cope with the time-varying nature of
interactions, this paper develops an estimation criterion and a solver to learn
the parameters of a time-varying vector autoregressive model supported on a
network of time series. The notion of local breakpoint is proposed to
accommodate changes at individual edges. It contrasts with existing works,
which assume that changes at all nodes are aligned in time. Numerical
experiments validate the proposed schemes.
