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Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, or kriging; extending Gaussian process regression to multiple target variables is known as cokriging. [26] Gaussian processes are thus useful as a powerful non-linear multivariate interpolation tool. Kriging is also used to extend Gaussian ...
A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit , in the sense of distribution .
In computational chemistry, a solvent model is a computational method that accounts for the behavior of solvated condensed phases. [1] [2] [3] Solvent models enable simulations and thermodynamic calculations applicable to reactions and processes which take place in solution. These include biological, chemical and environmental processes. [1]
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary Gauss–Markov process is unique [citation needed] up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process.
Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [8]Bayesian optimization is typically used on problems of the form (), where is a set of points, , which rely upon less (or equal to) than 20 dimensions (,), and whose membership can easily be evaluated.
A one-dimensional GRF is also called a Gaussian process. An important special case of a GRF is the Gaussian free field . With regard to applications of GRFs, the initial conditions of physical cosmology generated by quantum mechanical fluctuations during cosmic inflation are thought to be a GRF with a nearly scale invariant spectrum.
In mathematics, Brownian motion is described by the Wiener process, a continuous-time stochastic process named in honor of Norbert Wiener. It is one of the best known Lévy processes ( càdlàg stochastic processes with stationary independent increments ) and occurs frequently in pure and applied mathematics, economics and physics .
A diffusion model consists of three major components: the forward process, the reverse process, and the sampling procedure. [1] The goal of diffusion models is to learn a diffusion process for a given dataset, such that the process can generate new elements that are distributed similarly as the original dataset.