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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 ...
Probabilistic Recovery of Multiple Subspaces in Point Clouds by Geometric lp Minimization
Detection and clustering of subspaces in point clouds hybrid linear modeling lp minimizationas relaxation for l0 minimization
2010/3/10
We assume data independently sampled froma mixture distribution on the unit ball of RD withK+1
components: the first component is a uniform distribution on that ball representing outliers and the oth...
Empirical risk minimization in inverse problems
Deconvolution empirical risk minimization multivariate density estimation nonparametric function estimation Radon transform tomography
2010/3/9
We study estimation of a multivariate function f :Rd
!R when
the observations are available from the function Af, where A is a
known linear operator. Both the Gaussian white noise model and
densit...
Extension of Lipschitz integrands and minimization of nonconvex integral functionals. Applications to the optimal recourse problem in discrete time
Extension of Lipschitz integrands minimization of nonconvex integral functionals
2009/9/24
Extension of Lipschitz integrands and minimization of nonconvex integral functionals. Applications to the optimal recourse problem in discrete time。
Penalized empirical risk minimization over Besov spaces
Penalized empirical risk Besov spaces
2009/9/16
Kernel methods are closely related to the notion of reproducing kernel Hilbert space (RKHS). A kernel machine is based on the minimization of an empirical cost and a stabilizer (usually the norm in th...
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
rank convex optimization matrix norms random matrices compressed sensing semidefinite program-ming
2010/4/29
The ane rank minimization problem consists of finding a matrix of minimum rank that
satisfies a given system of linear equality constraints. Such problems have appeared in the literature
of a divers...
Suboptimality of Penalized Empirical Risk Minimization in Classification
Suboptimality Penalized Empirical Risk Minimization Classification
2010/4/27
Let F be a set of M classification procedures with values in
[−1, 1]. Given a loss function, we want to construct a procedure which
mimics at the best possible rate the best procedure in F. Th...