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A Rank Minimization Heuristic with Application to Minimum Order System Approximation
Rank Minimization Heuristic Minimum Order System Approximation
2015/7/10
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
Log-Det Heuristic for Matrix Rank Minimization with Applications to Hankel and Euclidean Distance Matrices
Log-Det Heuristic Matrix Rank Minimization Applications Hankel Euclidean Distance Matrices
2015/7/10
We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize thi...
Rank Minimization and Applications in System Theory
Rank Minimization Applications System Theory
2015/7/10
In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification...
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...
Rank 2 Integrable Systems of Prym Varieties.
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical...
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 ...
Optimal Estimation and Rank Detection for Sparse Spiked Covariance Matrices
Covariance matrix group sparsity low-rank matrix minimax rate of convergence sparse principal component analysis principal subspace,rank detection
2013/6/14
This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minima...
Optimal Estimation and Rank Detection for Sparse Spiked Covariance Matrices
Covariance matrix group sparsity low-rank matrix minimax rate of convergence sparse principal component analysis principal subspace,rank detection
2013/6/14
This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minima...
We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary the result extends to samples with ties, and the vector...
Tensors of Nonnegative Rank Two
nonnegative tensor rank latent class model binary tree model
2013/6/14
A nonnegative tensor has nonnegative rank at most 2 if and only if it is supermodular and has flattening rank at most 2. We prove this result, then explore the semialgebraic geometry of the general Ma...
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...
For the evaluation of information flow in bivariate time series, information measures have been employed, such as the transfer entropy (TE), the symbolic transfer entropy (STE), defined similarly to T...
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...