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Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets c...
Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations
Parallel Gaussian Process Regression Low-Rank Covariance Matrix Approximations
2013/6/14
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due ...
A least-squares method for sparse low rank approximation of multivariate functions
least-squares method sparse low rank approximation multivariate functions
2013/6/14
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regul...
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of specia...
Sharp analysis of low-rank kernel matrix approximations
Sharp analysis low-rank kernel matrix approximations
2012/9/18
We consider supervised learning problems within the positive-definite kernel framework,such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading t...
Let (V,A) be a weighted graph with a finite vertex set V,with a symmetric matrix of nonnegative weightsAand with Laplacian ∆. LetS∗: V ×V 7→ R be a symmetric kernel defined on the vertex s...
Large-Scale Convex Minimization with a Low-Rank Constraint
Large-Scale Convex Minimization Low-Rank Constraint
2011/7/6
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and ...
Sparse Bayesian Methods for Low-Rank Matrix Estimation
Low-Rank Matrix Estimation Sparse Bayesian Methods
2011/3/24
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesti...
Concentration-Based Guarantees for Low-Rank Matrix Reconstruction
Low-Rank Matrix Reconstruction
2011/3/25
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate...
On Low Rank Matrix Approximations with Applications to Synthesis Problem in Compressed Sensing
Low Rank Matrix Approximations Applications Synthesis Problem Compressed Sensing
2010/3/9
We consider the synthesis problem of Compressed Sensing –given s and an M×n
matrix A, extract from it an m × n submatrix Am, certified to be s-good, with m
as small as possible. Starting from the ve...