Related papers: Adaptive Sparse-grid Gauss-Hermite Filter
This paper studies the convergence conditions and properties of the distributed adaptive signal fusion (DASF) algorithm, the framework itself having been introduced in a `Part I' companion paper. The DASF algorithm can be used to solve…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
We propose a simple modification to the iterative hard thresholding (IHT) algorithm, which recovers asymptotically sparser solutions as a function of the condition number. When aiming to minimize a convex function $f(x)$ with condition…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…
Recent work by Rauhut and Ward developed a notion of weighted sparsity and a corresponding notion of Restricted Isometry Property for the space of weighted sparse signals. Using these notions, we pose a best weighted sparse approximation…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
Federated learning faces critical challenges in balancing communication efficiency and model accuracy. One key issue lies in the approximation of update errors without incurring high computational costs. In this paper, we propose a…
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…
Geometric model fitting is a fundamental task in computer graphics and computer vision. However, most geometric model fitting methods are unable to fit an arbitrary geometric model (e.g. a surface with holes) to incomplete data, due to that…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
We introduce a hybrid Gaussian-hash-grid radiance representation for reconstructing 2D Gaussian scene models from multi-view images. Similar to NeST splatting, our approach reduces the entanglement between geometry and appearance common in…
We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Wireless sensor networks consist of sensor nodes that are physically distributed over different locations. Spatial filtering procedures exploit the spatial correlation across these sensor signals to fuse them into a filtered signal…
With the growing interest and applications in machine learning and data science, finding an efficient method to sparse analysis the high-dimensional data and optimizing a dimension reduction model to extract lower dimensional features has…
In this paper we present a novel geometric filter, a homogeneous moving least squares fitting-based filter (H-MLS filter), for anisotropic mesh filtering. Instead of fitting the noisy data by a moving parametric surface and projecting the…