runlmc.mean.mean_function module

class runlmc.mean.mean_function.MeanFunction(input_dim, output_dim, name='mapping')

Bases: runlmc.parameterization.parameterized.Parameterized

Base class for mean functions in multi-output regressions.

f(Xs)

Evaluation of the mean function \(f\).

Returns:

mean_gradient(Xs)

Let this mean be parameterized by some parameters \(\boldsymbol\theta\in\mathbb{R}^p\). For every \(\theta_j\in\boldsymbol\theta\), at each input point \(\textbf{x}^{(i)}\) (for a certain output index \(i\)), we can compute the derivative \(\partial_{\theta_j}f(\textbf{x}^{(i)})\). For the evaluation of this partial derivative at multiple places, \(\textbf{X}\), we call the list of vectors of partial derivatives \(\partial_{\theta_j}f(\textbf{X})\) (a list with one vector per output index).

Parameters:Xs – inputs to evaluate at Returns:A list of parameter gradients; the \(j\)-th entry of this list is \(\partial_{\theta_j}f(\textbf{X})\). Each \(\partial_{\theta_j}f(\textbf{X})\) in turn is another list with one entry per output \(i\); the \(i\)-th entry is a one-dimensional numpy array with \(k\)-th entry the derivative of the \(j\)-th mean parameter at the \(k\)-th input for the \(i\)-th output, \(\partial_{\theta_j}f(\textbf{x}^{(i)}_k)\).

update_gradient(grad)

Parameters:grad – a one-dimensional array, representing the gradient vector \(\nabla_{\boldsymbol\theta}L\) for the likelihood with respect to this mean’s parameters, in the same order of parameters as the row order returned by mean_gradient().