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High Dimensional Robust M-Estimation: Asymptotic Variance via Approximate Message Passing
David Donoho, Andrea Montanari
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of par…
Sparse PCA via Covariance Thresholding
Yash Deshpande, Andrea Montanari
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension and seek to reconstruct it under additional sparsity assumption…
Learning Mixtures of Linear Classifiers
Yuekai Sun, Stratis Ioannidis, Andrea Montanari
We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM…
Nearly Optimal Sample Size in Hypothesis Testing for High-Dimensional Regression
Adel Javanmard, Andrea Montanari
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters is comparable to or exceeds the sa…
Conditional Random Fields, Planted Constraint Satisfaction, and Entropy Concentration
Emmanuel Abbe, Andrea Montanari
This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted…
Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
Adel Javanmard, Andrea Montanari
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact ch…
Model Selection for High-Dimensional Regression under the Generalized Irrepresentability Condition
Adel Javanmard, Andrea Montanari
In the high-dimensional regression model a response variable is linearly related to covariates, but the sample size is smaller than . We assume that only a small subset…
Finding Hidden Cliques of Size \sqrt{N/e} in Nearly Linear Time
Yash Deshpande, Andrea Montanari
Consider an Erdös-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset $\sC_N$ of the vertices that form a clique (a completely…
The Phase Transition of Matrix Recovery from Gaussian Measurements Matches the Minimax MSE of Matrix Denoising
David L. Donoho, Matan Gavish, Andrea Montanari
Let be an unknown by matrix. In matrix recovery, one takes linear measurements of , where $y_i = \Tr(a_i^T X_0)$ and each is a …
Linear Bandits in High Dimension and Recommendation Systems
Yash Deshpande, Andrea Montanari
A large number of online services provide automated recommendations to help users to navigate through a large collection of items. New items (products, videos, songs, advertisement…
Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory
Adel Javanmard, Andrea Montanari
We consider linear regression in the high-dimensional regime where the number of observations is smaller than the number of parameters . A very successful approach in this s…