Gaussian process

A probability distribution over functions in which every finite collection of function values has a joint multivariate normal distribution. Its mean function and covariance function determine the distribution.

Mean function: A function giving the expected value of a random quantity at each input. It specifies the expected function value at every input before observations are used.
Multivariate normal distribution: A probability distribution for a vector whose every linear combination of components is normally distributed. Every finite set of Gaussian-process values follows this distribution.
Bayesian optimization: A strategy for optimizing expensive black-box functions by combining a probabilistic model with sequential experiments. A Gaussian process models the objective and guides which input to evaluate next.
Bayesian linear regression: A regression model that places probability distributions over the coefficients of a linear predictor. It is a finite-parameter alternative to a prior over entire functions.
Norbert Wiener: An American mathematician who founded modern mathematical treatments of stochastic processes and cybernetics. His work on continuous stochastic processes helped establish the mathematical setting for Gaussian processes.
Covariance function: A function describing how pairs of random quantities vary together as their inputs change. It controls correlations between function values and determines the process's characteristic smoothness.
Random variable: A measurable quantity whose value is governed by chance. A Gaussian process assigns random variables to function values at individual inputs.
Kriging: A spatial prediction method that estimates values at unsampled locations from observed data and spatial covariance. Kriging is closely related to Gaussian process regression and originated in geostatistics.
Neural network: A machine-learning model composed of interconnected computational units with adjustable parameters. Neural networks can scale to large datasets where exact Gaussian process inference becomes costly.
Andrey Kolmogorov: A Russian mathematician whose axiomatic approach shaped modern probability theory. His foundations made rigorous treatment of stochastic processes possible.

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