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An Inexact Proximal Path-Following Algorithm for Constrained Convex Minimization
Quoc Tran Dinh, Anastasios Kyrillidis, Volkan Cevher
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class wh…
Convexity in source separation: Models, geometry, and algorithms
Michael B. McCoy, Volkan Cevher, Quoc Tran Dinh +2
Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separat…
Bilinear Generalized Approximate Message Passing
Jason T. Parker, Philip Schniter, Volkan Cevher
We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing…
Learning Non-Parametric Basis Independent Models from Point Queries via Low-Rank Methods
Hemant Tyagi, Volkan Cevher
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…
Composite Self-Concordant Minimization
Quoc Tran-Dinh, Anastasios Kyrillidis, Volkan Cevher
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal op…
Energy-aware adaptive bi-Lipschitz embeddings
Bubacarr Bah, Ali Sadeghian, Volkan Cevher
We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the…
Group-Sparse Model Selection: Hardness and Relaxations
Luca Baldassarre, Nirav Bhan, Volkan Cevher +2
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main pr…
Randomized Low-Memory Singular Value Projection
Stephen Becker, Volkan Cevher, Anastasios Kyrillidis
Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two step…
Fixed Points of Generalized Approximate Message Passing with Arbitrary Matrices
Sundeep Rangan, Philip Schniter, Erwin Riegler +2
The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of app…
A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions
Quoc Tran Dinh, Anastasios Kyrillidis, Volkan Cevher
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term…