Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

In many real-world applications, collected data are contaminated by noise with heavy-tailed
distribution and might contain outliers of large magnitude. In this situation, it is necessary to …

Let X, X₁,..., Xn,... be iid centered Gaussian random variables in a separable Banach space
E with covariance operator∑:∑: E*↦ E,∑ u= E (X, u) X, u ϵ E*. The sample covariance …

We study a completion problem of broad practical interest: the reconstruction of a low-rank
symmetric tensor from highly incomplete and randomly corrupted observations of its entries …

This paper considers a sparse spiked covariance matrix model in the high-dimensional
setting and studies the minimax estimation of the covariance matrix and the principal …

Many theoretical results for lasso require the samples to be iid Recent work has provided
guarantees for lasso assuming that the time series is generated by a sparse Vector …

Heteroskedastic PCA: Algorithm, optimality, and applications Page 1 The Annals of Statistics
2022, Vol. 50, No. 1, 53–80 https://doi.org/10.1214/21-AOS2074 © Institute of Mathematical …

Subspace estimation from unbalanced and incomplete data matrices: l2,infty statistical
guarantees Page 1 The Annals of Statistics 2021, Vol. 49, No. 2, 944–967 https://doi.org/10.1214/20-AOS1986 …

Many real world datasets exhibit an embedding of low-dimensional structure in a high-
dimensional manifold. Examples include images, videos and internet traffic data. It is of great …

This paper presents a new method for estimating high dimensional covariance matrices. The
method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product …