Multivariate Regression and Machine Learning with Sums of Separable Functions

In order to touch your nose with your eyes closed, you need to be able to estimate the position of your finger from the angles of all the joints between your nose and finger. You could calculate this position each time, using geometry. Or you could watch how the position changes with these angles and try to learn this function; when you close your eyes you just evaluate this regression function, and use that as your estimate.

I will present an algorithm for learning a function of many variables from scattered data. The function is approximated by a sum of separable functions, following the paradigm of separated representations. The central fitting algorithm is linear in both the number of data points and the number of variables, and thus is suitable for large data sets in high dimensions.