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Solving interpolation problems via generalized eigenvalue minimization
Solving interpolation problems generalized eigenvalue minimization
2015/7/13
A number of problems in the analysis and design of control systems may be reformulated as the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affi...
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...
Enhancing Sparsity by Reweighted l1 Minimization
Iterative reweighting Underdetermined systems of linear equations Compressive sensing Dantzig selector Sparsity
2015/7/9
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
A Comparison of Cross-Entropy and Variance Minimization Strategies
variance minimization cross-entropy importance sampling rareevent simulation likelihood ratio degeneracy
2015/7/6
The variance minimization (VM) and cross-entropy (CE) methods are two versatile adaptive importance sampling procedures that have been successfully applied to a wide variety of difficult rare-event es...
Stochastic Dual Coordinate Ascent Methods for Regularized Loss Minimization
Stochastic Dual Coordinate Ascent Methods Regularized Loss Minimization
2012/11/22
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closel...
Stochastic Dual Coordinate Ascent Methods for Regularized Loss Minimization
Stochastic Dual Coordinate Ascent Methods Regularized Loss Minimization
2012/11/22
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closel...
Fast and Accurate Algorithms for Re-Weighted L1-Norm Minimization
Fast and Accurate Algorithms Re-Weighted L1-Norm Minimization
2012/9/17
To recover a sparse signal from an underdetermined system, we often solve a constrained`1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further impr...
Non-Convex Rank Minimization via an Empirical Bayesian Approach
Non-Convex Rank Minimization via Empirical Bayesian Approach
2012/9/19
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem.Consequently, the convex nuclear ...
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 ...
Robust approachability and regret minimization in games with partial monitoring
Robust approachability regret games partial monitoring
2011/6/20
Approachability has become a standard tool in analyzing learning algorithms in the adversarial
online learning setup. We develop a variant of approachability for games where there is ambiguity
in th...
Complexity of Unconstrained L_2-L_p Minimization
Nonsmooth optimization nonconvex optimization variable selection sparse solution reconstruction bridge estimator
2011/6/21
We consider the unconstrained L2-Lp minimization: find a minimizer of kAx−bk2
2+λkxkp
p
for given A ∈ Rm×n, b ∈ Rm and parameters λ > 0, p ∈ [0, 1). This problem has been
studied extensively...
Sharper lower bounds on the performance of the empirical risk minimization algorithm
empirical risk minimization learning theory lower bound multidimensional central limit theorem uniform central limit theorem
2011/3/24
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$...
A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation
constrained ℓ 1 minimization covariance matrix Frobenius norm Gaus-sian graphical model rate of convergence precision matrix spectral norm
2011/3/21
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy ...