Multivariate Regression and Machine Learning with Sums of Separable Functions

We present an algorithm for learning (or estimating) 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. We present numerical evidence for the utility of these representations. In particular, we show that our method outperforms other methods on several benchmark data sets.