# Sparse Principal Component Analysis with Missing Observations

@article{Lounici2013SparsePC, title={Sparse Principal Component Analysis with Missing Observations}, author={Karim Lounici}, journal={arXiv: Statistics Theory}, year={2013}, pages={327-356} }

In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial observations. Existing estimation techniques are usually derived for fully observed data sets and require a prior knowledge of the sparsity of the first principal component in order to achieve good statistical guarantees. Our contributions is essentially theoretical in…

## 36 Citations

Sparse PCA with Oracle Property

- Computer Science, MathematicsNIPS
- 2014

It is proved that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated.

High-dimensional principal component analysis with heterogeneous missingness

- Computer Science
- 2019

An incoherence condition on the principal components is introduced and it is proved that in the noiseless case, the error of primePCA converges to zero at a geometric rate when the signal strength is not too small.

MINIMAX SPARSE PRINCIPAL SUBSPACE ESTIMATION IN HIGH DIMENSIONS

- Computer Science
- 2013

We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the…

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- Computer ScienceStat
- 2019

A convex method for sparse subspace estimation is extended to the case of missing and corrupted measurements by correcting the bias instead of imputing the missing values to improve the overall statistical performance.

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- Mathematics, Computer Science
- 2013

Under mild technical conditions, this paper establishes the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty of the estimation problem in term of the convergence rate.

Online sparse and orthogonal subspace estimation from partial information

- Computer Science2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2016

This work considers an online version of the sparse PCA problem with missing data in which they seek a set of sparse orthogonal basis vectors and proposes two different algorithms for solving this problem, where the main idea is to find a rotation matrix such that the subspace basis is sparse after rotation.

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- Computer ScienceIEEE Transactions on Information Theory
- 2016

This paper examines a general class of noisy matrix completion tasks, where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random…

Sparsistency and agnostic inference in sparse PCA

- Computer Science
- 2015

The properties of the recently proposed Fantope projection and selection (FPS) method in the high-dimensional setting are investigated and it is shown that FPS provides a sparse, linear dimension-reducing transformation that is close to the best possible in terms of maximizing the predictive covariance.

Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data

- Computer Science, MathematicsJ. Multivar. Anal.
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A Literature Survey on High-Dimensional Sparse Principal Component Analysis

- Computer Science
- 2015

A comprehensive literatures review to recent progress in highdimensional sparse PCA from algorithm and statistical theory is given and the future trends as well as challenges are given.

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