Anastasios Kyrillidis

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Many natural and man-made signals can be described as having a few degrees of freedom relative to their size due to natural parameterizations or constraints; examples include bandlimited signals, collections of signals observed from multiple viewpoints in ...

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-ti ...

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 ...

Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a ...

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 ...

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for different configura ...

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 ...

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 ...

Certain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent M-ary phase-shift keying (MPSK) sequence detection, result in the maximization of a fixed-rank positive semidefinite quadratic for ...

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 ...

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a well-known memory ...

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 ...

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying o ...

We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity as well as faster convergence speed. Moreover, many of ...

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 ...

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 ...

Compressive sensing (CS) is a data acquisition and recovery technique for finding sparse solutions to linear inverse problems from sub-Nyquist measurements. CS features a wide range of computationally efficient and robust signal recovery methods, based on ...

Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of ``interpretable" signals along with ...

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 ...

We propose a new proximal, path-following framework for a class of---possibly non-smooth---constrained convex problems. We consider settings where the non-smooth part is endowed with a proximity operator, and the constraint set is equipped with a self-conc ...

Anastasios Kyrillidis

Chat with Graph Search

Rigorous optimization recipes for sparse and low rank inverse problems with applications in data sciences

Convex block-sparse linear regression with expanders - provably

Multi-Way Compressed Sensing for Sparse Low-Rank Tensors

An inexact proximal path-following algorithm for constrained convex minimization

Approximate Matrix Multiplication with Application to Linear Embeddings

Matrix Recipes for Hard Thresholding Methods

Scalable sparse covariance estimation via self-concordance

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

Fixed-Rank Rayleigh Quotient Maximization by an MPSK Sequence

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

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

Composite Self-Concordant Minimization

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

Hard Thresholding with Norm Constraints

Sparse projections onto the simplex

Recipes on Hard Thresholding Methods

Group-Sparse Model Selection: Hardness and Relaxations

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

A single-phase, proximal path-following framework