Related papers: N2SID: Nuclear Norm Subspace Identification
In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our…
Atomic norm minimization is of great interest in various applications of sparse signal processing including super-resolution line-spectral estimation and signal denoising. In practice, atomic norm minimization (ANM) is formulated as…
Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex…
Traffic-density matrices from different days exhibit both low rank and stable correlations in their singular-vector subspaces. Leveraging this, we introduce SATORIS-N, a framework for imputing partially observed traffic-density by informed…
This paper introduces a novel approach to solving multi-block nonconvex composite optimization problems through a proximal linearized Alternating Direction Method of Multipliers (ADMM). This method incorporates an Increasing Penalization…
This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this trade-off is…
This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
In many practical applications including remote sensing, multi-task learning, and multi-spectrum imaging, data are described as a set of matrices sharing a common column space. We consider the joint estimation of such matrices from their…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
We present an algorithmic framework for the identification of candidate invariant subspaces for switched linear systems. Namely, the framework allows to compute an orthonormal basis in which the matrices of the system are close to…
Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…
Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…
Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…