sigma_sq
Convenience functions for optimizing the sigma_sq parameter of
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_diffs, 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_diffs (
ndarray) – A tensor of shape(batch_count, nn_count, nn_count, feature_count)containing the(nn_count, nn_count, feature_count)-shaped pairwise nearest neighbor difference tensors 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_diffs, 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_diffs (
ndarray) – A tensor of shape(batch_count, nn_count, nn_count, feature_count)containing the(nn_count, nn_count, feature_count)-shaped pairwise nearest neighbor difference tensors 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_diffs, 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_diffs (
ndarray) – A tensor of shape(batch_count, nn_count, nn_count, feature_count)containing the(nn_count, nn_count, feature_count)-shaped pairwise nearest neighbor difference tensors 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_diffs, 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_diffs (
ndarray) – A tensor of shape(batch_count, nn_count, nn_count, feature_count)containing the(nn_count, nn_count, feature_count)-shaped pairwise nearest neighbor difference tensors 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.