Professor Balzano and her students investigate problems in statistical signal processing, machine learning, and optimization, particularly dealing with large and messy data. Her applications typically have missing, corrupted, and uncalibrated data as well as heterogeneous data in terms of sensors, sensor quality, and scale in both time and space. Her theoretical interests involve classes of non-convex matrix factorization problems, such as PCA and many interesting variants such as sparse or structured principal components, orthogonality and non-negativity constraints, nonlinear variants such as low-dimensional algebraic variety models, heteroscedastic data, and even categorical data or human preference data. She concentrates on fast gradient methods and related optimization methods that are scalable to real-time operation and massive data. Her work provides algorithmic and statistical guarantees for these algorithms on the aforementioned non-convex problems, and she focuses carefully on assumptions that are realistic for the relevant application areas in sensor networks, power systems, control, and computer vision.