Related papers: Asymptotically Scale-invariant Multi-resolution Qu…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Quantile regression (QR) is a powerful tool for estimating one or more conditional quantiles of a target variable $\mathrm{Y}$ given explanatory features $\boldsymbol{\mathrm{X}}$. A limitation of QR is that it is only defined for scalar…
The problem of quantizing a circularly-symmetric complex Gaussian random variable is considered. For this purpose, we design two non-uniform quantizers, a high-rate-, and a Lloyd-Max-, quantizer that are both based on the (golden angle)…
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled, and noisy observations. We focus on the low SNR regime, and show that a signal in $\mathbb{R}^M$ is uniquely…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we…
Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important…
The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to…
With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…
Analog-to-digital (quantization) and digital-to-analog (de-quantization) conversion are fundamental operations of many information processing systems. In practice, the precision of these operations is always bounded, first by the random…
Quantum computing has shown considerable promise for compute-intensive tasks in recent years. For instance, classification tasks based on quantum neural networks (QNN) have garnered significant interest from researchers and have been…
We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…