sigma_sq¶
Convenience functions for optimizing the sigma_sq
parameter of
MuyGPyS.gp.muygps.MuyGPS
objects.
Currently only supports an analytic approximation, but will support other methods in the future.
- MuyGPyS.optimize.sigma_sq.mmuygps_analytic_sigma_sq_optim(mmuygps, pairwise_dists, nn_targets)[source]¶
Optimize the value of the \(\sigma^2\) scale parameter for each response dimension.
We approximate \(\sigma^2\) by way of averaging over the analytic solution from each local kernel.
\[\sigma^2 = \frac{1}{bk} * \sum_{i \in B} Y_{nn_i}^T K_{nn_i}^{-1} Y_{nn_i}\]Here \(Y_{nn_i}\) and \(K_{nn_i}\) are the target and kernel matrices with respect to the nearest neighbor set in scope, where \(k\) is the number of nearest neighbors and \(b = |B|\) is the number of batch elements considered.
- Parameters
muygps – The model to be optimized.
pairwise_dists (
ndarray
) – A tensor of shape(batch_count, nn_count, nn_count)
containing the(nn_count, nn_count)
-shaped pairwise nearest neighbor distance matrices corresponding to each of the batch elements.nn_targets (
ndarray
) – Tensor of floats of shape(batch_count, nn_count, response_count)
containing the expected response for each nearest neighbor of each batch element.
- Return type
- Returns
A new MuyGPs model whose sigma_sq parameter has been optimized.
- MuyGPyS.optimize.sigma_sq.mmuygps_sigma_sq_optim(mmuygps, pairwise_dists, nn_targets, sigma_method='analytic')[source]¶
Optimize the value of the \(\sigma^2\) scale parameter for each response dimension of a MultivariateMuyGPS object.
The optimization to be applied depends upon the value of
sigma_method
.- Parameters
mmuygps (
MultivariateMuyGPS
) – The model to be optimized.pairwise_dists (
ndarray
) – A tensor of shape(batch_count, nn_count, nn_count)
containing the(nn_count, nn_count)
-shaped pairwise nearest neighbor distance matrices corresponding to each of the batch elements.nn_targets (
ndarray
) – Tensor of floats of shape(batch_count, nn_count, response_count)
containing the expected response for each nearest neighbor of each batch element.sigma_method (
Optional
[str
]) – The optimization method to apply. Currently only supports"analytic"
andNone
.
- Return type
- Returns
A new MultivariateMuyGPs model whose sigma_sq parameter has been optimized.
- MuyGPyS.optimize.sigma_sq.muygps_analytic_sigma_sq_optim(muygps, pairwise_dists, nn_targets)[source]¶
Optimize the value of the \(\sigma^2\) scale parameter for each response dimension.
We approximate \(\sigma^2\) by way of averaging over the analytic solution from each local kernel.
\[\sigma^2 = \frac{1}{bk} * \sum_{i \in B} Y_{nn_i}^T K_{nn_i}^{-1} Y_{nn_i}\]Here \(Y_{nn_i}\) and \(K_{nn_i}\) are the target and kernel matrices with respect to the nearest neighbor set in scope, where \(k\) is the number of nearest neighbors and \(b = |B|\) is the number of batch elements considered.
- Parameters
muygps (
MuyGPS
) – The model to be optimized.pairwise_dists (
ndarray
) – A tensor of shape(batch_count, nn_count, nn_count)
containing the(nn_count, nn_count)
-shaped pairwise nearest neighbor distance matrices corresponding to each of the batch elements.nn_targets (
ndarray
) – Tensor of floats of shape(batch_count, nn_count, response_count)
containing the expected response for each nearest neighbor of each batch element.
- Return type
- Returns
A new MuyGPs model whose sigma_sq parameter has been optimized.
- MuyGPyS.optimize.sigma_sq.muygps_sigma_sq_optim(muygps, pairwise_dists, nn_targets, sigma_method='analytic')[source]¶
Optimize the value of the \(\sigma^2\) scale parameter for each response dimension.
The optimization to be applied depends upon the value of
sigma_method
.- Parameters
muygps (
MuyGPS
) – The model to be optimized.pairwise_dists (
ndarray
) – A tensor of shape(batch_count, nn_count, nn_count)
containing the(nn_count, nn_count)
-shaped pairwise nearest neighbor distance matrices corresponding to each of the batch elements.nn_targets (
ndarray
) – Tensor of floats of shape(batch_count, nn_count, response_count)
containing the expected response for each nearest neighbor of each batch element.sigma_method (
Optional
[str
]) – The optimization method to apply. Currently only supports"analytic"
andNone
.
- Return type
- Returns
A new MuyGPs model whose sigma_sq parameter has been optimized.