Gaussian Process (GP) is a random process in probability theory and mathematical statistics, which is a combination of a series of random variables with normal distribution on an index set.
The linear combination of any random variables in Gaussian process obeys normal distribution, and each finite-dimensional distribution is a joint normal distribution. Its probability density function on the continuous exponential set is the Gaussian measure of all random variables, so it is regarded as an infinite-dimensional generalized generalization of the joint normal distribution. Gaussian process is completely determined by its mathematical expectation and covariance function, and inherits many properties of normal distribution.
Examples of Gaussian processes include Wiener process, ornstein-Uhlenbeck process and so on. The modeling and prediction of Gaussian process is an important content in the field of machine learning and signal processing, among which the commonly used models are Gaussian process regression (GPR) and Gaussian process classification (GPC). The name of Gaussian process comes from German mathematician C.F. Gaussian to commemorate his concept of normal distribution.