Principal components analysis (PCA) is a standard tool for identifying good lowdimensional approximations to data sets in high dimension. Many current data sets of interest contain private or sensitive information about individuals. Algorithms which operate on such data should be sensitive

The principal components analysis (PCA) algorithm is a standard tool for identifying good low-dimensional approximations to high-dimensional data. Many data sets of interest contain private or sensitive information about individuals. Algorithms which operate on such data should be sensitive

Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a p-variate Wishart

different mechanisms. It is useful, therefore, to define a core set of independent features for the expression states that allow them to be compared directly. Principal components analysis (PCA) is a statistical technique for determining the key variables in a multidimensional data set that explain

Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation. We discuss an approach to studying population structure (principal components analysis) that was first applied to genetic data by Cavalli

Theoretically, measures of household wealth can be reflected by income, consumption or expenditure information. However, the collection of accurate income and consumption data requires extensive resources for household surveys. Given the increasingly routine application of principal components

, are tractable; however, finding the most likely configuration (MAP), which is often required in practice for decoding, is NP-hard, so we must resort to approximate inference. This optimization problem, which also arises in experimental design and sensor placement, involves finding the largest principal minor

Identification and quantification of cyanobacteria in water resources is the principal component of cyanotoxin monitoring programmes and can provide an effective early warning system for the development of potentially toxic blooms. Data on concentrations of total phosphate, nitrate and ammonia

you quite quickly what to choose. However, you cannot use the same simple emotional judgment when you are in the shoes of an economist trying to optimize the access to the locks on the Mississippi River. The task is to find a pricing structure that assures the most efficient and uninterrupted use

an algorithm for computing convolutions which satisfies (ε, δ)-differentially privacy and is nearly optimal for every public h, i.e. is instance optimal with respect to the public input. We prove optimality via spectral lower bounds on the hereditary discrepancy of convolution matrices. Our algorithm is very