Related papers: Fast and Accurate Bilateral Filtering using Gauss-…
We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
A new image denoising algorithm to deal with the additive Gaussian white noise model is given. Like the non-local means method, the filter is based on the weighted average of the observations in a neighborhood, with weights depending on the…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient…
Median filtering is a cornerstone of computational image processing. It provides an effective means of image smoothing, with minimal blurring or softening of edges, invariance to monotonic transformations such as gamma adjustment, and…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…
We develop a new statistical model for photographic images, in which the local responses of a bank of linear filters are described as jointly Gaussian, with zero mean and a covariance that varies slowly over spatial position. We optimize…
We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approximations are obtained via best rational approximations of the…
The pencil-beam model is valid only when elementary Gaussian beams are small enough with respect to lateral heterogeneity of a medium, which is not always the case in heavy charged particle radiotherapy. This work addresses a solution for…
Computational complexity of the brute-force implementation of the bilateral filter (BF) depends on its filter kernel size. To achieve the constant-time BF whose complexity is irrelevant to the kernel size, many techniques have been…
This paper presents an analysis of properties of two hybrid discretization methods for Gaussian derivatives, based on convolutions with either the normalized sampled Gaussian kernel or the integrated Gaussian kernel followed by central…
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
Inferring the posterior distribution in SLAM is critical for evaluating the uncertainty in localization and mapping, as well as supporting subsequent planning tasks aiming to reduce uncertainty for safe navigation. However, real-time full…