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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…
3D Gaussian Splatting (3DGS) has shown convincing performance in rendering speed and fidelity, yet the generation of Gaussian Splatting remains a challenge due to its discreteness and unstructured nature. In this work, we propose DiffGS, a…
Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to…
A Gaussian distribution of cosmic microwave background temperature fluctuations is a generic prediction of inflation. Upcoming high-resolution maps of the microwave background will allow detailed tests of Gaussianity down to small angular…
Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in…
The Friedman's urn model is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we prove that both the urn composition…
Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…
The Gaussian-radial-basis function neural network (GRBFNN) has been a popular choice for interpolation and classification. However, it is computationally intensive when the dimension of the input vector is high. To address this issue, we…
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…
GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding…
We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a…
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Glitches represent a category of non-Gaussian and transient noise that frequently intersects with gravitational wave (GW) signals, exerting a notable impact on the processing of GW data. The inference of GW parameters, crucial for GW…
Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time…
Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…