KJM has received honoraria from Janssen, LEO Pharma, Lilly and Novartis. ADB consults lectures for Abbvie, Amgen, Boehringer Ingelheim, Celgene, Lilly, Novartis Pfizer. JNWN advisory boards at sponsored symposia together with grants research in the past 5 years AbbVie, Novartis, CEK and/or funding Galderma, GSK-Stiefel, Johnson & Johnson, Pfizer UCB Pharma. KM CEMG Actelion, Almirall, MSD, Pfiz...

We study several matrix diffusion processes constructed from a unitary Brownian motion. In particular, we use the Stiefel fibration to lift motion of complex Grassmannian manifold and deduce skew-product decomposition As an application, prove asymptotic laws for determinants block entries

We introduce a learning technique for regression between highdimensional spaces. Standard methods typically reduce this task to many onedimensional problems, with each output dimension considered independently. By contrast, in our approach the feature construction and the regression estimation are performed jointly, directly minimizing a loss function that we specify, subject to a rank constrai...