PhD Thesis Defense
Graphical models provide useful tools for the analysis of data defined over networks, and they present interesting theoretical challenges and insights due to their rich structure. In this talk, we will consider a setting in which nodes (of a graph) communicate with each other randomly and asynchronously. We model such systems with a randomized asynchronous variant of the discrete time-invariant state-space models, in which only a random subset of the state variables is updated in every iteration. We present the necessary and sufficient condition that ensures the stability of a randomized asynchronous system, which does not necessarily require the stability of the underlying state transition matrix. So, some unstable systems (in the synchronous world) may get stable with randomized asynchronicity. As an application, we utilize the randomized updates to obtain a spectral clustering of a network of autonomous agents. In addition, we consider asynchronous computation of principal components of distributed data. Throughout the talk, we highlight the open problems and future directions.