The general theme of my research in recent years is spatio-temporal modeling and sparse recovery with high dimensional data under measurement error. In this talk, I will discuss several computational and statistical convergence results on graph and sparse vector recovery problems. Our methods are applicable to many application domains such as neuroscience, geoscience and spatio-temporal modeling, genomics, and network data analysis. I will present theory, simulation and data examples. Part of this talk is based on joint work with Mark Rudelson.