Appears in collection : Imaging and machine learning

Projecting data in low dimensions is often key to scale machine learning to large high-dimensional data-sets. In this talk we will take take a statistical learning tour of classic as well as recent projection methods: from classical principal component analysis, to sketching and random subsampling. We will show that, perhaps surprisingly, there are number of settings, where it is possible to substantially reduce data dimensions, hence computational costs, without losing statistical accuracy. As a byproduct we derive a massively scalable kernel/Gaussian process solver with optimal statistical guarantees, and excellent performance in a number of large scale problems.