Related papers: Structural shrinkage of nonparametric spectral est…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
The fuzzy linear regression (FLR) modeling was first proposed making use of linear programming and then followed by many improvements in a variety of ways. In almost all approaches changing the meters, objective function, and restrictions…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the…
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional…
Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical…
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…
Microstructures are critical to the physical properties of materials. Stochastic microstructures are commonly observed in many kinds of materials and traditional descriptor-based image analysis of them can be challenging. In this paper, we…
A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample…
The spectrogram is a classical DSP tool used to view signals in both time and frequency. Unfortunately, the Heisenberg Uncertainty Principal limits our ability to use them for detecting and measuring narrowband signal modulation in wideband…
Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…
Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
In ultrasound nondestructive testing, a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a…
The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative…
The endogeneity issue is fundamentally important as many empirical applications may suffer from the omission of explanatory variables, measurement error, or simultaneous causality. Recently, \cite{hllt17} propose a "Deep Instrumental…
The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…