gpLib.NonStationaryGeneralizedOU

class gpLib.NonStationaryGeneralizedOU(H_constraint: Interval | None = None, alpha_constraint: Positive | None = None, **kwargs)

Time-varying generalised OU kernel

Let \(x = t + \tau/2,\; y = t - \tau/2\). With parameters \(H,\alpha>0\)

\[k(x,y) = \cosh\!\bigl[(H+\alpha t)\,|\tau|\bigr] \;-\; \bigl[2\sinh(|\tau|/2)\bigr]^{\,H+\alpha t}.\]

The process is non-stationary in mean square; variance grows with t.

Parameters:

• H_constraint – Interval \((0,1)\).

• alpha_constraint – Positive.

Variables:

alpha (torch.Tensor H,) – Shape (*batch,1).