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High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
Measurement samples are often taken in various monitoring applications. To reduce the sensing cost, it is desirable to achieve better sensing quality while using fewer samples. Compressive Sensing (CS) technique finds its role when the…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N…
We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…
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…
We present a new method to obtain spatio-temporal information from aggregated data of stationary traffic detectors, the ``adaptive smoothing method''. In essential, a nonlinear spatio-temporal lowpass filter is applied to the input detector…
A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper. We show that its recoverability for sparse signals depends on the…
Mining spatio-temporal correlation patterns for traffic prediction is a well-studied field. However, most approaches are based on the assumption of the availability of and accessibility to a sufficiently dense data source, which is rather…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…
Sparse coding networks, which utilize unsupervised learning to maximize coding efficiency, have successfully reproduced response properties found in primary visual cortex \cite{AN:OlshausenField96}. However, conventional sparse coding…