Distribution Regression and its Applications.

The most common machine learning algorithms operate on finite-dimensional vectorial feature representations. In many applications, however, the natural representation of the data consists of distributions, sets, and other complex objects rather than finite-dimensional vectors. In this talk we will review machine learning algorithms that can operate directly on these complex objects. We will discuss applications in various scientific problems including estimating the cosmological parameters of our Universe, dynamical mass measurements of galaxy clusters, finding anomalous events in fluid dynamics, and estimating phenotypes in agriculturally important plants.