What is a Gaussian Process 🌱

Here is a very detailed explanation

  • A Gaussian Process (GP) is a collection of random variables of any finite number which have a joint Gaussian distribution
  • Using a Gaussian Process we can generate data from the prior distribution as well as the posterior
  • In the case below, \(f\) is a Gaussian process with mean function \(m(x)\) and covariance kernel \(k(x_i,x_j)\)
\[f(x) \sim GP(m,k) \\ \implies \text{we generate } \begin{bmatrix} f(x_1) \\ \vdots \\ f(x_n) \end{bmatrix} \sim N(\boldsymbol{\mu}, \mathbf{K}) \\ \text{where } \boldsymbol{\mu}_i = m(x_i) \text{ and } \mathbf{K}_{ij} = k(x_i,x_j)\]

10-708 Lecture

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