The Unreasonable Effectiveness of Nonconvex Methods for High-Dimensional Statistical Data Analysis
Abstract
Nonconvex statistical information processing plays a central role in modern defense-related applications that involve extracting critical information and actionable insights from highdimensional data. The interplay between nonconvexity and high dimensionality creates a ubiquitous challenge. This calls for novel statistical data analysis methods that allow significant reduction of sample and computational complexities, while at the same time preserving useful information with statistical guarantees. In this proposal, we plan to develop provably effective, low-complexity, robust, and model-agnostic nonconvex statistical estimation methods, which are of critical importance to the Navy. The main goal is towards demystifying the ``unreasonable effectiveness of simple nonconvex methods and releasing their power in reduced-dimensionalinformation extraction. This will be achieved by integrated consideration of statistics and optimization, which will result in new foundational theory that improves upon the state-of-the-art results.The proposed research consists of four major thrusts.Thrust 1: Optimality of Spectral Initialization for Discrete Statistical Problems.Thrust 2: Self-Regularization in Nonconvex Statistical Estimation.Thrust 3: Implicit Saddle-Point Avoidance under Random Initialization.Thrust 4: Over-parametrization for Multi-Modal Data.The proposed research will offer important practical insights for a broad range of Navy applications where it is desirable to extract critical information from large-scale and multi-modal data samples, especially when the sensing mechanisms are highly imperfect and when the environment is dynamically changing. The proposed topics are of fundamental importance in enabling real-time decision making and enhancing automatic situation awareness.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 23, 2019
- Source ID
- N000141912120
Entities
People
- Yuxin Chen
Organizations
- Office of Naval Research
- Trustees of Princeton University
- United States Navy