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Bounding Duality Gap for Problems with Separable Objective
Bounding Duality Gap Problems Separable Objective
2015/7/9
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. We consider approximate solutions obtained by solving ...
A New Global Stochastic Search Approach for Inverse Problems: Application to Ultrasound Modulated Optical Tomography
inverse problems global stochastic search discretized Kushner-Stratonovich equation gain-based update ultrasound modulated optical tomography
2013/6/14
A global stochastic search method, which is strictly derivative-free yet directed through a gain-based additive update term, is proposed and applied to the inverse problem of ultrasound modulated opti...
Practical Tikhonov Regularized Estimators in Reproducing Kernel Hilbert Spaces for Statistical Inverse Problems
Tikhonov Regularized Estimators Reproducing Kernel Hilbert Spaces Statistical Inverse Problems
2013/6/13
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and comm...
Efficiently Using Second Order Information in Large l1 Regularization Problems
Efficiently Using Second Order Information Large l1 Regularization Problems
2013/4/28
We propose a novel general algorithm LHAC that efficiently uses second-order information to train a class of large-scale l1-regularized problems. Our method executes cheap iterations while achieving f...
A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems
A General Iterative Shrinkage Thresholding Algorithm Non-convex Regularized Optimization Problems
2013/5/2
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterp...
Large-Margin Metric Learning for Partitioning Problems
Large-Margin Metric Learning Partitioning Problems
2013/4/28
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems b...
A note on Bayesian credible sets in restricted parameter space problems and lower bounds for frequentist coverage
Bayesian methods Credible sets Frequentist coverage probability Lower bound Restricted Parameter Spending function
2012/9/17
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman(2006), we provide “through” a unified approach a class of Bayesian confidence intervals with credibility...
Efficient Estimators for Sequential and Resolution-Limited Inverse Problems
deconvolution ill-posed image processing sig-nal recovery
2012/9/18
A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In suchinverse problems, th...
Tchebycheff systems and extremal problems for generalized moments: a brief survey
Tchebycheff systems Markov systems extremal problems
2011/7/19
A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given.
Deterministic Sequencing of Exploration and Exploitation for Multi-Armed Bandit Problems
Deterministic Sequencing Exploration Exploitation Multi-Armed Bandit Problems
2011/7/7
In the Multi-Armed Bandit (MAB) problem, there are a given set of arms with unknown reward distributions. At each time, a player selects one arm to play, aiming to maximize the total expected reward o...
A Finite-Time Analysis of Multi-armed Bandits Problems with Kullback-Leibler Divergences
Finite-Time Multi-armed Bandits Problems Kullback-Leibler Divergences
2011/6/20
We consider a Kullback-Leibler-based algorithmfor the stochastic multi-armed bandit prob-
lem in the case of distributions with finite supports (not necessarily known beforehand),
whose asymptotic r...
Besov priors for Bayesian inverse problems
Bayesian inverse problems Fernique-like theorem
2011/6/16
We consider the inverse problem of estimating a function u from
noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the
problem and widen the existing theory, which is developed...
Exploiting Correlation in Sparse Signal Recovery Problems: Multiple Measurement Vectors, Block Sparsity, and Time-Varying Sparsity
Multiple Measurement Vectors Block Sparsity Time-Varying Sparsity
2011/6/16
A trend in compressed sensing (CS) is to exploit struc-
ture for improved reconstruction performance. In the
basic CS model (i.e. the single measurement vec-
tor model), exploiting the clustering s...
A Threshold Regularization Method for Inverse Problems
Inverse problems regularization oracle inequalities hard thresholding
2011/6/16
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally res...
The Convex Geometry of Linear Inverse Problems
Optimization and Control (math.OC) Statistics Theory (math.ST)
2010/12/17
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimensi...