Related papers: Mixed precision HODLR matrices
Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and…
Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…
Recently, a number of competitive methods have tackled unsupervised representation learning by maximising the mutual information between the representations produced from augmentations. The resulting representations are then invariant to…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…
In the iterative solution of dense linear systems from boundary integral equations or systems involving kernel matrices, the main challenges are the expensive matrix-vector multiplication and the storage cost which are usually tackled by…
The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level…
We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We describe a second-order accurate approach to sparsifying the off-diagonal blocks in the hierarchical approximate factorizations of sparse symmetric positive definite matrices. The norm of the error made by the new approach depends…
${\cal H}^2$-matrix constitutes a general mathematical framework for efficient computation of both partial-differential-equation and integral-equation-based operators. Existing linear-complexity ${\cal H}^2$ matrix-matrix product (MMP)…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…