Gaussian process
Undergraduate (probability)
A Gaussian process is a stochastic process $(X_t)_{t \in T}$ such that, for every finite list of times $t_1, \dots, t_n$ in $T$, the random vector
\[(X_{t_1}, \dots, X_{t_n})\]has a multivariate normal distribution.
Properties
- A Gaussian process is determined by the mean function $m(t) = \mathbb{E}[X_t]$ and the covariance function $k(s, t) = \operatorname{Cov}(X_s, X_t)$.
- Every value $X_t$ of a Gaussian process has a normal distribution.
Notes
In machine learning, Gaussian processes are used as prior distributions over unknown functions, and “Gaussian process regression” computes the posterior distribution of the function after observing some of the function’s values.