Statistical Estimation: From Denoising to Sparse Regression and Hidden Cliques
This is an incremental review of existing methods for statistical estimation problems in science and engineering.
The notes review lectures on statistical estimation for linear models, covering principles of signal recovery from linear measurements and applying them to practical problems like denoising, compressive sensing, low-rank matrix reconstruction, and hidden clique discovery.
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.