Publications de Anastasios Kyrillidis

Scalable sparse covariance estimation via self-concordance

Volkan Cevher, Quoc Tran Dinh, Anastasios Kyrillidis, Rabeeh Karimi Mahabadi

We consider the class of convex minimization problems, composed of a self-concordant function, such as the logdet metric, a convex data fidelity term h and, a regularizing -- possibly non-smooth -- function g. This type of problems have recently attracted ...

2014

Approximate Matrix Multiplication with Application to Linear Embeddings

Michail Vlachos, Anastasios Kyrillidis

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of th ...

Ieee2014

A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

Volkan Cevher, Quoc Tran Dinh, Anastasios Kyrillidis

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. Our method is a new proximal Newton algorithm that features a local quadra ...

2013

Sparse projections onto the simplex

Volkan Cevher, Christoph Koch, Anastasios Kyrillidis

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the`1-norm. However, several important learning applications cannot benet from this approach as they feature these convex no ...

JMLR W&CP2013

Randomized Low-Memory Singular Value Projection

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 steps are expensive, heuristics are often used for approximations that reduce co ...

2013

Fast Proximal algorithms for Self-concordant function minimization with application to sparse graph selection

Volkan Cevher, Anastasios Kyrillidis

The convex

\ell_1

-regularized

\log\det

divergence criterion has been shown to produce theoretically consistent graph learning. However, this objective function is challenging since the

\ell_1

-regularization is nonsmooth, the

\log\det

objective is n ...

2013

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

Volkan Cevher, Anastasios Kyrillidis

The convex l(1)-regularized log det divergence criterion has been shown to produce theoretically consistent graph learning. However, this objective function is challenging since the l(1)-regularization is nonsmooth, the log det objective is not globally Li ...

IEEE2013

Multi-Way Compressed Sensing for Sparse Low-Rank Tensors

Anastasios Kyrillidis

For linear models, compressed sensing theory and methods enable recovery of sparse signals of interest from few measurements-in the order of the number of nonzero entries as opposed to the length of the signal of interest. Results of similar flavor have mo ...

Institute of Electrical and Electronics Engineers2012

Hard Thresholding with Norm Constraints

Volkan Cevher, Gilles Puy, Anastasios Kyrillidis

We introduce a new sparse recovery paradigm, called Normed Pursuits, where efficient algorithms from combinatorial and convex optimization interface for interpretable and model-based solutions. Synthetic and real data experiments illustrate that Normed Pur ...

Ieee2012

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

Volkan Cevher, Anastasios Kyrillidis

The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the

\ell_2

-data error objective and the

\ell_1

-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection ...

IEEE2012

Anastasios Kyrillidis

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Scalable sparse covariance estimation via self-concordance

Approximate Matrix Multiplication with Application to Linear Embeddings

A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

Sparse projections onto the simplex

Randomized Low-Memory Singular Value Projection

Fast Proximal algorithms for Self-concordant function minimization with application to sparse graph selection

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

Multi-Way Compressed Sensing for Sparse Low-Rank Tensors

Hard Thresholding with Norm Constraints

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

Scalable sparse covariance estimation via self-concordance

Sparse projections onto the simplex

Randomized Low-Memory Singular Value Projection

Approximate Matrix Multiplication with Application to Linear Embeddings

Fast Proximal algorithms for Self-concordant function minimization with application to sparse graph selection

Multi-Way Compressed Sensing for Sparse Low-Rank Tensors

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

Hard Thresholding with Norm Constraints

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm