相关论文: Gauss' Separation Algorithm for the Magnetic Field…

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier…

Common workflows in machine learning and statistics rely on the ability to partition the information in a data set into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Data compression is a critical technology for large-scale plasma simulations. Storing complete particle information requires Terabyte-scale data storage, and analysis requires ad-hoc scalable post-processing tools. We propose a…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of…

The Energy Conserving Semi-Implicit Method (ECSIM) introduced by Lapenta (2017) has many advantageous properties compared to the classical semi-implicit and explicit PIC methods. Most importantly, energy conservation eliminates the growth…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…

Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based…

An important challenge in robotics is understanding the interactions between robots and deformable terrains that consist of granular material. Granular flows and their interactions with rigid bodies still pose several open questions. A…

Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet…

3D Gaussian Splatting (3DGS) has emerged as a transformative method in the field of real-time novel synthesis. Based on 3DGS, recent advancements cope with large-scale scenes via spatial-based partition strategy to reduce video memory and…

This paper presents novel Gaussian process decentralized data fusion algorithms exploiting the notion of agent-centric support sets for distributed cooperative perception of large-scale environmental phenomena. To overcome the limitations…

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…