Related papers: Communication-efficient Algorithms for Distributed…
This thesis is concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources such as photovoltaics (PV) and wind as well as load demands has recently gained attention. Normalizing flow density models…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least…
In this paper, we study distributed algorithms for large-scale AUC maximization with a deep neural network as a predictive model. Although distributed learning techniques have been investigated extensively in deep learning, they are not…
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…
Reverse engineering of undocumented protocols is a common task in security analyses of networked services. The communication itself, captured in traffic traces, contains much of the necessary information to perform such a protocol reverse…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
We study the following generalized matrix rank estimation problem: given an $n \times n$ matrix and a constant $c \geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…