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We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…

Methodology · Statistics 2019-05-07 Milana Gataric , Tengyao Wang , Richard J. Samworth

We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set…

Optimization and Control · Mathematics 2017-04-13 Ankit Parekh , Ivan W. Selesnick

In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…

Numerical Analysis · Mathematics 2024-03-12 Hongyaoxing Gu

Accurate channel state information (CSI) is required for coherent detection in time-variant multiple-input multipleoutput (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) modulation. One of low-complexity…

Information Theory · Computer Science 2013-02-07 Guan Gui , Wei Peng , Fumiyuki Adachi

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an…

Statistics Theory · Mathematics 2014-05-27 Jacob Bien , Florentina Bunea , Luo Xiao

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Numerical Analysis · Mathematics 2014-07-01 Gil Shabat , Yaniv Shmueli , Amir Averbuch

In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…

Statistics Theory · Mathematics 2023-04-19 Taras Bodnar , Arjun K. Gupta , Nestor Parolya

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…

Optimization and Control · Mathematics 2021-11-18 Joseph E. Gaudio , Anuradha M. Annaswamy , Eugene Lavretsky , Michael A. Bolender

Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each…

Statistics Theory · Mathematics 2011-12-20 Garvesh Raskutti , Martin J. Wainwright , Bin Yu

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…

Machine Learning · Statistics 2015-01-28 Zhaoran Wang , Han Liu , Tong Zhang

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Machine Learning · Statistics 2011-06-28 Suvrit Sra , Dongmin Kim

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

Machine Learning · Statistics 2021-06-08 Antoine Dedieu , Hussein Hazimeh , Rahul Mazumder

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Machine Learning · Statistics 2017-03-01 Pan Xu , Jian Ma , Quanquan Gu

This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…

Optimization and Control · Mathematics 2019-07-15 Guoyong Gu , Junfeng Yang

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…

Statistics Theory · Mathematics 2017-07-10 Olga Klopp , Yu Lu , Alexandre B. Tsybakov , Harrison H. Zhou

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…

Computation · Statistics 2017-12-06 Per Sidén , Finn Lindgren , David Bolin , Mattias Villani

Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…

Methodology · Statistics 2025-11-11 Navonil Deb , Amy Kuceyeski , Sumanta Basu

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…

Methodology · Statistics 2019-01-01 Yiyuan She , Hoang Tran

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…

Multimedia · Computer Science 2016-02-22 Junhui Hou , Lap-Pui Chau , Nadia Magnenat-Thalmann , Ying He

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

Statistics Theory · Mathematics 2014-01-30 Quentin Berthet , Philippe Rigollet