Related papers: Sparse Time Frequency Representations and Dynamica…
Proportionate type algorithms were developed and excessively used in the echo cancellation problems due to sparse characteristics of the echo channels. In the past, most of the attention was paid to a particular type of proportionate…
Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…
We consider the problem of estimating mutual information between dependent data, an important problem in many science and engineering applications. We propose a data-driven, non-parametric estimator of mutual information in this paper. The…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the…
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
We propose a new statistical test to identify non-stationary frequency-modulated stochastic processes from time series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from…
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
Least-squares reverse time migration is well-known for its capability to generate artifact-free true-amplitude subsurface images through fitting observed data in the least-squares sense. However, when applied to realistic imaging problems,…
High-resolution time-frequency (TF) analysis plays crucial role in characterizing multicomponent signal (MCSs) and estimating oscillatory properties. Linear time-frequency representations (TFRs) such as classical short-time Fourier…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years,…
This paper deals with the modeling of non-stationary signals, from the point of view of signal synthesis. A class of random, non-stationary signals, generated by synthesis from a random timescale representation, is introduced and studied.…
In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions…
In this paper, we present a data-driven reduced order model of viscous Moore-Greitzer (MG) partial differential equation (PDE) by threading together ideas from principal component analysis (PCA) and autoencoder neural networks to sparse…
We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…