Related papers: BLISS: Global Blind Identification of Linear Syste…

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible…

This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of…

We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…

In this paper, we propose a unified framework for identifying interpretable nonlinear dynamical models that preserve physical properties. The proposed approach integrates physical principles with black-box basis functions to compensate for…

We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are…

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…

Classifiers are biased when trained on biased datasets. As a remedy, we propose Learning to Split (ls), an algorithm for automatic bias detection. Given a dataset with input-label pairs, ls learns to split this dataset so that predictors…

The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…

Dictionary learning and sparse representation (DLSR) is a recent and successful mathematical model for data representation that achieves state-of-the-art performance in various fields such as pattern recognition, machine learning, computer…

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation. The problem can also be seen as factorising a $\ddim \times \nsig$ matrix $Y=(y_1 >... y_\nsig),…

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…

This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be…

Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…

Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are…

Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a…

This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…