Related papers: Parsimonious Volterra System Identification
The methodology discussed in this paper aims to enhance choice models' comprehensiveness and explanatory power for forecasting choice outcomes. To achieve these, we have developed a data-driven method that leverages machine learning…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's…
This note addresses identification of the $A$-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
Scoring systems are classification models that only require users to add, subtract and multiply a few meaningful numbers to make a prediction. These models are often used because they are practical and interpretable. In this paper, we…
In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
This note presents a more efficient formulation of the robust online subspace estimation and tracking algorithm (ROSETA) that is capable of identifying and tracking a time-varying low dimensional subspace from incomplete measurements and in…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
In general, one often encounters the systems that have sparse impulse response, with time varying system sparsity. Conventional adaptive filters which perform well for identification of non-sparse systems fail to exploit the system sparsity…
We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the "sparsest rule", which is equivalent to the plurality rule but becomes operational in…
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…
In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…
Time-series prediction has drawn considerable attention during the past decades fueled by the emerging advances of deep learning methods. However, most neural network based methods lack interpretability and fail in extracting the hidden…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…