Related papers: Improvements on "Fast space-variant elliptical fil…
We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…
Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors. By deriving improved variance bounds related to binary Gaussian…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
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…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
The bilateral and nonlocal means filters are instances of kernel-based filters that are popularly used in image processing. It was recently shown that fast and accurate bilateral filtering of grayscale images can be performed using a…
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…
While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice…
Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…
Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…