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Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…
The ensemble Gaussian mixture filter (EnGMF) is a non-linear filter suited to data assimilation of highly non-Gaussian and non-linear models that has practical utility in the case of a small number of samples, and theoretical convergence to…
We introduce a novel method for weak-lensing measurements, which is based on a mathematically exact deconvolution of the moments of the apparent brightness distribution of galaxies from the telescope's PSF. No assumptions on the shape of…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
A simple Gaussian size deconvolution method is routinely used to remove the blur of observed images caused by insufficient angular resolutions of existing telescopes, thereby to estimate the physical sizes of extracted sources and…
We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually…
Gaussian random matrix (GRM) has been widely used to generate linear measurements in compressed sensing (CS) of natural images. However, there actually exist two disadvantages with GRM in practice. One is that GRM has large memory…
In the rapidly evolving field of 3D reconstruction, 3D Gaussian Splatting (3DGS) and 2D Gaussian Splatting (2DGS) represent significant advancements. Although 2DGS compresses 3D Gaussian primitives into 2D Gaussian surfels to effectively…
In this work, we propose low-complexity adaptive biased estimation algorithms, called group-based shrinkage estimators (GSEs), for parameter estimation and interference suppression scenarios with mechanisms to automatically adjust the…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue…
In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels…
Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key result in this area shows that with accurate score estimates, SGMs can efficiently generate samples…
Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample…