Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of… (More)

Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting,… (More)

We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted… (More)

Suppose n points are scattered uniformly at random in the unit square [0, 1]. Question: How many of these points can possibly lie on some curve of length λ? Answer, proved here: OP (λ · √ n). We… (More)

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph… (More)

We construct detectors for "geometric" objects in noisy data. Examples include a detector for presence of a line segment of unknown length, position, and orientation in two-dimensional image data… (More)

The literature on compressed sensing has focused almost entirely on settings where the signal is noiseless and the measurements are contaminated by noise. In practice, however, the signal itself is… (More)

We consider the problem of detecting whether or not in a given sensor network, there is a cluster of sensors which exhibit an “unusual behavior.” Formally, suppose we are given a set of nodes and… (More)

We are given a set of n points that appears uniformly distributed in the unit square [0, 1]. We wish to test whether the set actually is generated from a non-uniform distribution having a small… (More)

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are… (More)