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We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis techn ...
We introduce a model-based excessive gap technique to analyze first-order primal- dual methods for constrained convex minimization. As a result, we construct new primal-dual methods with optimal convergence rates on the objective residual and the primal fe ...
This paper proposes a tradeoff between sample complexity and computation time that applies to statistical estimators based on convex optimization. As the amount of data increases, we can smooth optimization problems more and more aggressively to achieve ac ...
In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its applica ...
Institute of Electrical and Electronics Engineers2014
This paper proposes a smoothing technique for nonsmooth convex minimization using self-concordant barriers. To illustrate the main ideas, we compare our technique and the proximity smoothing approach (Nesterov2005) via the classical gradient method on both ...
We propose a Bayesian approach where the signal structure can be represented by a mixture model with a submodular prior. We consider an observation model that leads to Lipschitz functions. Due to its combinatorial nature, computing the maximum a posteriori ...
In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case. In Part I of this two-par ...
We consider the problem of learning multi-ridge functions of the form f (x) = g(Ax) from point evaluations of f. We assume that the function f is defined on an l(2)-ball in R-d, g is twice continuously differentiable almost everywhere, and A is an element ...
We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acou ...
In this paper, the problem of multiple speaker localization via speech separation based on model-based sparse recovery is studies. We compare and contrast computational sparse optimization methods incorporating harmonicity and block structures as well as a ...