Related papers: Finite-Length and Asymptotic Analysis of Correlogr…
This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator (comprising interconnected local estimators) is first described for estimating the…
The functional linear regression model has been widely studied and utilized for dealing with functional predictors. In this paper, we study the Nystr\"om subsampling method, a strategy used to tackle the computational complexities inherent…
In the field of signal processing, the sampling theorem plays a fundamental role for signal reconstruction as it bridges the gap between analog and digital signals. Following the celebrated Nyquist-Shannon sampling theorem, generalizing the…
The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern…
The problem tackled in this paper is the determination of sample size for a given level and power in the context of a simple linear regression model. At a technical level, the simple linear regression model is a five-parameter model. It is…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
Matching a target spectrum with known spectra in a spectral library is a common method for material identification in hyperspectral imaging research. Hyperspectral spectra exhibit precise absorption features across different wavelength…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
Understanding representational similarity between neural recordings and computational models is essential for neuroscience, yet remains challenging to measure reliably due to the constraints on the number of neurons that can be recorded…
We present a statistical analysis of a variant of the periodogram method that forms power spectral density estimates by cross-correlating the discrete Fourier transforms of adjacent time windows. The proposed estimator is closely related to…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…
It is shown that the two-part Minimum Description Length Principle can be used to discriminate among different models that can explain a given observed dataset. The description length is chosen to be the sum of the lengths of the message…
This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…