Coresets: 6 Coresets for Gaussian processes (GPs)

We know that using feature space, we can generate coresets for linear (polynomial) regression. Gaussian processes are also linear (in parameters) models. If a kernel in a GP can be converted to Feature space, we can use the same algorithm to generate the coresets for GPs.

We know the following method for calculating “ridge leverage” scores if feature space is known as \(X\).

\[\begin{aligned} X_* &= \begin{bmatrix}X \\ \lambda I_d\end{bmatrix} \\ U \Sigma V^T &= X_* \\ \mathbf{p}(X) &= ||U(0:n, :)||_2^2 \end{aligned}\]

Now, Given any covariance matrix \(K\) in GPs, \(X\) (feature space) can be estimated like the following,

\[ XX^T = K \] Once, \(X\) is derived from \(K\), we can easily calculate the ridge leverage scores.