Related papers: Revisiting the Nystrom Method for Improved Large-S…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Kernel methods provide an elegant framework for developing nonlinear learning algorithms from simple linear methods. Though these methods have superior empirical performance in several real data applications, their usefulness is inhibited…
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size,…
Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model,…
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…
Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
We present randomized algorithms for estimating the log-determinant of regularized symmetric positive semi-definite matrices. The algorithms access the matrix only through matrix vector products, and are based on the introduction of a…
We study Nystr\"om type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
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…
First, we extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Second, We develop a class of fast approximate generalized linear regression algorithms with respect to the spectral norm.…
Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…
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…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…