Related papers: Improved Gaussian Approximation

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…

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…

Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

For spin rotational symmetric models with a positive-definite high-temperature expansion of the partition function, a stochastic sampling of the series expansion upon partial resummation becomes logically equivalent to sampling an…

A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…

We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…

Two recent landmark experiments have performed Gaussian boson sampling (GBS) with a non-programmable linear interferometer and threshold detectors on up to 144 output modes (see Refs.~\onlinecite{zhong_quantum_2020,zhong2021phase}). Here we…

We describe a post-Minkowskii approximation of general relativity as a power series expansion in G, Newton's gravitational constant. Material sources are hidden behind boundaries, and only the vacuum Einstein equations are considered. An…

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

This paper deals with the Gaussian process based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of co-kriging, allows us to improve a surrogate model of a complex computer…

Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…

The well-established effective action and effective potential framework from the quantum field theory domain is adapted and successfully applied to classical field theories of the Doi and Peliti type for diffusion controlled reactions.…

We consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. The approximation is of rational type and comes from the use of the Gauss-Legendre rule applied to a special integral formulation…

Using a path integral formulation for correlation functions of stochastic partial differential equations based on the Onsager-Machlup approach, we show how, by introducing a composite auxiliary field one can generate an auxiliary field loop…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…