Approximate Message Passing with Spectral Initialization for Generalized Linear Models

Understand

We consider the problem of estimating a signal from measurements obtained via a generalized linear model.

• We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the performance of AMP in the high-dimensional limit can be succinctly characterized under suitable model assumptions; AMP can also be tailored to the empirical distribution of the signal entries, and for a wide class of estimation problems, AMP is conjectured to be optimal among all polynomial-time algorithms.
• However, a major issue of AMP is that in many models (such as phase retrieval), it requires an initialization correlated with the ground-truth signal and independent from the measurement matrix.
• Assuming that such an initialization is available is typically not realistic.