Estimation in high dimensions: a geometric perspective

Abstract

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.

56 pages, 9 figures. Multiple minor changes

References in corpus (1)

• A new perspective on least squares under convex constraint

Cited by in corpus (8)

• Geometric Inference for General High-Dimensional Linear Inverse Problems
• The Gaussian min-max theorem in the Presence of Convexity
• Precise Error Analysis of Regularized M-estimators in High-dimensions
• Unified View of Matrix Completion under General Structural Constraints
• A Geometric View on Constrained M-Estimators
• Consistent Collective Matrix Completion under Joint Low Rank Structure
• Private Incremental Regression
• Sensing tensors with Gaussian filters