148 citations · 1.2k across the 75 of their papers we have counts for
6 papers · 1 filter
The generalized orthogonal Procrustes problem in the high noise regime
Thomas Pumir, Amit Singer, Nicolas Boumal
We consider the problem of estimating a cloud of points from numerous noisy observations of that cloud after unknown rotations, and possibly reflections. This is an instance of the…
Optimal prediction in the linearly transformed spiked model
Edgar Dobriban, William Leeb, Amit Singer
We consider the linearly transformed spiked model, where observations are noisy linear transforms of unobserved signals of interest : \begin{align*} Y_i = A_i X_i + \var…
Factor Analysis for Spectral Estimation
Joakim Andén, Amit Singer
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short s…
PCA from noisy, linearly reduced data: the diagonal case
Edgar Dobriban, William Leeb, Amit Singer
Suppose we observe data of the form or , , where $D_i \in \mathbb{R…
Marchenko-Pastur Law for Tyler's M-estimator
Teng Zhang, Xiuyuan Cheng, Amit Singer
This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples and their dimension both go to infinity, an…
Vector Diffusion Maps and the Connection Laplacian
Amit Singer, Hau-tieng Wu
We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes. VDM is a mathematic…