Related papers: A general error analysis for randomized low-rank a…
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 reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
We consider the problem of low rank matrix recovery in a stochastically noisy high dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, and that is computationally…
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
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…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension…
In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm…