The ability to detect weak distributed activation patterns in networks is critical to several applications, 
such as identifying the onset of anomalous activity or incipient congestion in the Internet, or faint traces 
of a biochemical spread by a sensor network. This is a challenging problem since weak distributed patterns 
can be invisible in per node statistics as well as a global network-wide aggregate. Most prior work considers 
situations in which the activation/non-activation of each node is statistically independent, but this is 
unrealistic in many problems. In this talk, I will describe a method that can exploit the (possibly non-local) 
statistical dependencies in the activation process to enable detection of much weaker patterns than could be 
detected with current techniques.

The proposed method constructs a sparsifying wavelet transform that succinctly represents structured activation 
patterns that conform to a hierarchical dependency graph. Transforming the network data effectively achieves 
adaptive fusion of the network measurements. Thus, weak network activity gets amplified and can be detected in 
the transform domain. I will present theoretical guarantees of the method as well as some practical results for 
detecting incipient congestion in Internet-like topologies.