Related papers: Sequential Low-Rank Change Detection
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense…
We introduce a new methodology 'charcoal' for estimating the location of sparse changes in high-dimensional linear regression coefficients, without assuming that those coefficients are individually sparse. The procedure works by…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in…
Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to…
Keypoint detection, integral to modern machine perception, faces challenges in few-shot learning, particularly when source data from the same distribution as the query is unavailable. This gap is addressed by leveraging sketches, a popular…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al.…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…