相关论文: Low-Precision Streaming PCA

In this paper, we propose an acceleration scheme for online memory-limited PCA methods. Our scheme converges to the first $k>1$ eigenvectors in a single data pass. We provide empirical convergence results of our scheme based on the spiked…

The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

In a streaming constraint satisfaction problem (streaming CSP), a $p$-pass algorithm receives the constraints of an instance sequentially, making $p$ passes over the input in a fixed order, with the goal of approximating the maximum…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

Many online learning algorithms, including classical online PCA methods, enforce explicit normalization steps that discard the evolving norm of the parameter vector. We show that this norm can in fact encode meaningful information about the…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

The performance of the standard Online Robust Principal Component Analysis (OR-PCA) technique depends on the optimum tuning of the explicit regularizers and this tuning is dataset sensitive. We aim to remove the dependency on these tuning…

We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

We present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations. We show that, with proper time scaling, the…

Principal component analysis (PCA) is a simple and popular tool for processing high-dimensional data. We investigate its effectiveness for matrix denoising. We consider the clean data are generated from a low-dimensional subspace, but…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

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,…

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…

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…