RESUMEN
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.
RESUMEN
BACKGROUND: Translating in vitro results to clinical tests is a major challenge in systems biology. Here we present a new Multi-Task learning framework which integrates thousands of cell line expression experiments to reconstruct drug specific response networks in cancer. RESULTS: The reconstructed networks correctly identify several shared key proteins and pathways while simultaneously highlighting many cell type specific proteins. We used top proteins from each drug network to predict survival for patients prescribed the drug. CONCLUSIONS: Predictions based on proteins from the in-vitro derived networks significantly outperformed predictions based on known cancer genes indicating that Multi-Task learning can indeed identify accurate drug response networks.