Announcements

(11/08/18) New paper: Optimal spectral method for high-dimensional signal estimation

November 8, 2018

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...

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(09/26/18) New paper: Nonconvex optimization meets low-rank matrix factorization

September 26, 2018
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. In our recent paper, we (Yuejie Chi, Yuxin Chen, and I) present a technical overview to highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored... Read more about (09/26/18) New paper: Nonconvex optimization meets low-rank matrix factorization

(05/27/18) Phase retrieval via polytope optimization: Geometry, phase transitions, and new algorithms

May 27, 2018
In our recent paper, we study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal by solving a simple linear program over a polytope constructed from the measurements. We present a sharp characterization of the high-dimensional geometry of the aforementioned polytope under Gaussian measurements. This... Read more about (05/27/18) Phase retrieval via polytope optimization: Geometry, phase transitions, and new algorithms

(05/08/18) Subspace estimation from incomplete observations: a high dimensional analysis

May 7, 2018
In our recent paper, we present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations.  We show that, with proper time scaling, the time-varying principal angles between the true subspace and its estimates... Read more about (05/08/18) Subspace estimation from incomplete observations: a high dimensional analysis

(04/16/18) ICASSP tutorial on nonconvex methods for high-dimensional statistical estimation (slides available online)

April 16, 2018

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...

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(12/11/17) Best Student Paper Award (First Prize) at IEEE CAMSAP

December 11, 2017

Best Student Paper Award (first prize) at the 2017 IEEE CAMSAP Workshop:

O. Dhifallah and Y. M. Lu, Fundamental Limits of PhaseMax for Phase Retrieval: A Replica Analysis, 2017.

Congratulations to Oussama!

Note: The replica predictions derived in this paper has been rigorously proved in our more recent work, based on a convex version...

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(12/06/17) Understanding the Dynamics of Online Learning Algorithms via Scaling and Mean-Field Limits

December 6, 2017
In our recent paper, we present a tractable and asymptotically exact framework for analyzing the dynamics of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal component analysis. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical measures of the target feature vector and its estimates provided by the... Read more about (12/06/17) Understanding the Dynamics of Online Learning Algorithms via Scaling and Mean-Field Limits