Related papers: A fast Gauss transform in one dimension using sum-…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large…
We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…
Given a combinatorial decomposition for a counting problem, we resort to the simple scheme of approximating large numbers by floating-point representations in order to obtain efficient Fully Polynomial Time Approximation Schemes (FPTASes)…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are…
We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin…
This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…