Related papers: Scaling positive random matrices: concentration an…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency…
We study random matrices with independent subgaussian columns. Assuming each column has a fixed Euclidean norm, we establish conditions under which such matrices act as near-isometries when restricted to a given subset of their domain. We…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
In this note we answer a question of G. Lecu\'{e}, by showing that column normalization of a random matrix with iid entries need not lead to good sparse recovery properties, even if the generating random variable has a reasonable moment…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
Biclustering algorithms play a central role in the biotechnological and biomedical domains. The knowledge extracted supports the extraction of putative regulatory modules, essential to understanding diseases, aiding therapy research, and…
Generative models typically sample outputs independently, and recent inference-time guidance and scaling algorithms focus on improving the quality of individual samples. However, in real-world applications, users are often presented with a…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
Recent research has generated hope that inference scaling, such as resampling solutions until they pass verifiers like unit tests, could allow weaker models to match stronger ones. Beyond inference, this approach also enables training…