In our recent paper, we present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. Our work leverages recent results that provide an exact characterization of the performance of the spectral method in the high-dimensional limit. Interestingly, under a mild technical condition, our results show that there exists a fixed design that is uniformly optimal over all sampling...

Together with Yuxin Chen (Princeton) and Yuejie Chi (CMU), I gave a tutorial at this year's ICASSP on recent advances on nonconvex statistical estimation. We will be covering topics include the landscapes of nonconvex estimation, analyzing gradient descent and stochastic gradient descent methods, spectral methods for initialization, and example applications to phase retrieval, low-rank matrix recovery and blind deconvolution.

Here are...