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Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of…
Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix…
The notion of signal sparsity has been gaining increasing interest in information theory and signal processing communities. As a consequence, a plethora of sparsity metrics has been presented in the literature. The appropriateness of these…
This letter investigates the joint recovery of a frequency-sparse signal ensemble sharing a common frequency-sparse component from the collection of their compressed measurements. Unlike conventional arts in compressed sensing, the…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…
The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive…
Spectral data reduction pipelines deal with a wide variety of challenges including masking cosmic rays, calibrating wavelength solutions, and estimating background noise while trying to remain model-agnostic. Traditional methods rely on…
Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
The application that motivates this paper is molecular imaging at the atomic level. When discretized at sub-atomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
In genomics, differential abundance and expression analyses are complicated by the compositional nature of sequence count data, which reflect only relative-not absolute-abundances or expression levels. Many existing methods attempt to…
Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…
Stochastic computing (SC) has emerged as an efficient low-power alternative for deploying neural networks (NNs) in resource-limited scenarios, such as the Internet of Things (IoT). By encoding values as serial bitstreams, SC significantly…
This paper is concerned with estimating unknown multi-dimensional frequencies from linear compressive measurements. This is accomplished by employing the recently proposed atomic norm minimization framework to recover these frequencies…
This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the…
A method is described for the detection and estimation of transient chirp signals that are characterized by smoothly evolving, but otherwise unmodeled, amplitude envelopes and instantaneous frequencies. Such signals are particularly…