Learn More
In problem of sparse principal components analysis (SPCA), the goal is to use n i.i.d. samples to estimate the leading eigenvector(s) of a p times p covariance matrix, which are known a priori to be sparse, say with at most k non-zero entries. This paper studies SPCA in the high-dimensional regime, where the model dimension p, sparsity index k, and sample(More)
We consider the problem of community detection in a network, that is, partitioning the nodes into groups that, in some sense, reveal the structure of the network. Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. We present a fast(More)
We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and prove their asymptotic optimality in terms of expected detection delay. Drawing from graphical model formalism, the(More)
We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for functionals of change points, and prove their asymptotic optimality properties in terms of expected detection delay time. Drawing from graphical model formalism, the sequential(More)
Principal component analysis (PCA) is a classical method for dimension-ality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the " large p, small n " setting, in which the problem dimension p is comparable to or larger than the sample size n. This paper studies PCA in(More)
We consider the problem of estimating a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with p ≫ n. Our main results establish nonasymptotic deviation bounds on the estimation error, sparsity bounds, and model selection consistency for a penalized least squares estimator under concave regularization. The proofs(More)
We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map from H to R m , where the functional components to lie in some Hilbert subspace H of L 2 , such as a reproducing kernel(More)