Statistical Estimation: From Denoising to Sparse Regression and Hidden Cliques

E. W. Tramel, S. Kumar, A. Giurgiu, & A. Montanari

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Astract

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.

BibTeX

    incollection{tvg2014,
    Author = {Eric W. Tramel and Santhosh Kumar and Andrei Giurgiu and Andrea Montanari},
    Booktitle = {Statistical Physics, Optimization, Inference, and Message-Passing Algorithms},
    Editor = {Florent Krzakala and Federico Ricci-Tersenghi and Lenka Zdeborov\`{a} and Riccardo Zecchina and Eric W. Tramel and Leticia F. Cugliandolo},
    Pages = {120--177},
    Publisher = {Oxford University Press},
    Title = {Statistical Estimation: From Denoising to Sparse Regression and Hidden Cliques},
    Year = {2015}}