Statistical Estimation: From Denoising to Sparse Regression and Hidden Cliques

TL;DR

This paper reviews principles of statistical estimation in linear models and their applications to signal denoising, compressed sensing, low-rank matrix recovery, and hidden clique detection in networks.

Contribution

It synthesizes theoretical principles and practical algorithms across multiple problems in statistical estimation and signal processing.

Findings

Unified framework for minimax risk in linear models

Application of principles to diverse problems like denoising and clique detection

Insights into the effectiveness of various estimation techniques

Abstract

These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several practical problems in science and engineering. Specifically, these topics include denoising of error-laden signals, recovery of compressively sensed signals, reconstruction of low-rank matrices, and also the discovery of hidden cliques within large networks.