Related papers: Sparse PCA: Optimal rates and adaptive estimation
Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
This paper proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard to…
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…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…