Efficient Learning of Generalized Linear and Single Index Models with Isotonic Regression

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, iterative local search heuristics are often used. Kalai and Sastry (2009) provided the first provably efficient method, the Isotron algorithm, for learning SIMs and GLMs, under the assumption that the data is in fact generated under a GLM and under certain monotonicity and Lipschitz (bounded slope) constraints.