botorch.posteriors

Posterior APIs

Abstract Posterior API

Abstract base module for all botorch posteriors.

class botorch.posteriors.posterior.Posterior[source]

Bases: abc.ABC

Abstract base class for botorch posteriors.

property base_sample_shape

The shape of a base sample used for constructing posterior samples.

This function may be overwritten by subclasses in case base_sample_shape and event_shape do not agree (e.g. if the posterior is a Multivariate Gaussian that is not full rank).

Return type

Size

abstract property device

The torch device of the posterior.

Return type

device

abstract property dtype

The torch dtype of the posterior.

Return type

dtype

abstract property event_shape

The event shape (i.e. the shape of a single sample).

Return type

Size

property mean

The mean of the posterior as a (b) x n x m-dim Tensor.

Return type

Tensor

property variance

The variance of the posterior as a (b) x n x m-dim Tensor.

Return type

Tensor

abstract rsample(sample_shape=None, base_samples=None)[source]

Sample from the posterior (with gradients).

Parameters

  • sample_shape (Optional[Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to torch.Size([b, n]).

  • base_samples (Optional[Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic optimization.

Return type

Tensor

Returns

A sample_shape x event-dim Tensor of samples from the posterior.

sample(sample_shape=None, base_samples=None)[source]

Sample from the posterior (without gradients).

This is a simple wrapper calling rsample using with torch.no_grad().

Parameters

  • sample_shape (Optional[Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to torch.Size([b, n]).

  • base_samples (Optional[Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler object. This is used for deterministic optimization.

Return type

Tensor

Returns

A sample_shape x event_shape-dim Tensor of samples from the posterior.

Posteriors

GPyTorch Posterior

Posterior Module to be used with GPyTorch models.

class botorch.posteriors.gpytorch.GPyTorchPosterior(mvn)[source]

Bases: botorch.posteriors.posterior.Posterior

A posterior based on GPyTorch’s multi-variate Normal distributions.

A posterior based on GPyTorch’s multi-variate Normal distributions.

Parameters

mvn (MultivariateNormal) – A GPyTorch MultivariateNormal (single-output case) or MultitaskMultivariateNormal (multi-output case).

property base_sample_shape

The shape of a base sample used for constructing posterior samples.

Return type

Size

property device

The torch device of the posterior.

Return type

device

property dtype

The torch dtype of the posterior.

Return type

dtype

property event_shape

The event shape (i.e. the shape of a single sample) of the posterior.

Return type

Size

rsample(sample_shape=None, base_samples=None)[source]

Sample from the posterior (with gradients).

Parameters

  • sample_shape (Optional[Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to torch.Size([b, n]).

  • base_samples (Optional[Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic optimization.

Return type

Tensor

Returns

A sample_shape x event_shape-dim Tensor of samples from the posterior.

property mean

The posterior mean.

Return type

Tensor

property variance

The posterior variance.

Return type

Tensor

botorch.posteriors.gpytorch.scalarize_posterior(posterior, weights, offset=0.0)[source]

Affine transformation of a multi-output posterior.

Parameters

  • posterior (GPyTorchPosterior) – The posterior over m outcomes to be scalarized. Supports t-batching.

  • weights (Tensor) – A tensor of weights of size m.

  • offset (float) – The offset of the affine transformation.

Return type

GPyTorchPosterior

Returns

The transformed (single-output) posterior. If the input posterior has

mean mu and covariance matrix Sigma, this posterior has mean weights^T * mu and variance weights^T Sigma w.

Example

Example for a model with two outcomes:

>>> X = torch.rand(1, 2)
>>> posterior = model.posterior(X)
>>> weights = torch.tensor([0.5, 0.25])
>>> new_posterior = scalarize_posterior(posterior, weights=weights)

Determinstic Posterior

Deterministic (degenerate) posteriors. Used in conjunction with deterministic models.

class botorch.posteriors.deterministic.DeterministicPosterior(values)[source]

Bases: botorch.posteriors.posterior.Posterior

Deterministic posterior.

property device

The torch device of the posterior.

Return type

device

property dtype

The torch dtype of the posterior.

Return type

dtype

property event_shape

The event shape (i.e. the shape of a single sample).

Return type

Size

property mean

The mean of the posterior as a (b) x n x m-dim Tensor.

Return type

Tensor

property variance

The variance of the posterior as a (b) x n x m-dim Tensor.

As this is a deterministic posterior, this is a tensor of zeros.

Return type

Tensor

rsample(sample_shape=None, base_samples=None)[source]

Sample from the posterior (with gradients).

For the deterministic posterior, this just returns the values expanded to the requested shape.

Parameters

  • sample_shape (Optional[Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to torch.Size([b, n]).

  • base_samples (Optional[Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. Ignored in construction of the samples (used only for shape validation).

Return type

Tensor

Returns

A sample_shape x event-dim Tensor of samples from the posterior.

Higher Order GP Posterior

class botorch.posteriors.higher_order.HigherOrderGPPosterior(mvn, joint_covariance_matrix, train_train_covar, test_train_covar, train_targets, output_shape, num_outputs)[source]

Bases: botorch.posteriors.gpytorch.GPyTorchPosterior

Posterior class for a Higher order Gaussian process model [Zhe2019hogp]. Extends the standard GPyTorch posterior class by overwriting the rsample method. The posterior variance is handled internally by the HigherOrderGP model. HOGP is a tensorized GP model so the posterior covariance grows to be extremely large, but is highly structured, which means that we can exploit Kronecker identities to sample from the posterior using Matheron’s rule as described in [Doucet2010sampl]. In general, this posterior should ONLY be used for HOGP models that have highly structured covariances. It should also only be used internally when called from the HigherOrderGP.posterior(…) method.

A Posterior for HigherOrderGP models.

Parameters

  • mvn (MultivariateNormal) – Posterior multivariate normal distribution

  • joint_covariance_matrix (LazyTensor) – Joint test train covariance matrix over the entire tensor

  • train_train_covar (LazyTensor) – covariance matrix of train points in the data space

  • test_train_covar (LazyTensor) – covariance matrix of test x train points in the data space

  • train_targets (Tensor) – training responses vectorized

  • output_shape (Size) – shape output training responses

  • num_outputs (int) – batch shaping of model

property base_sample_shape

The shape of a base sample used for constructing posterior samples.

property event_shape

The event shape (i.e. the shape of a single sample) of the posterior.

rsample(sample_shape=None, base_samples=None)[source]

Sample from the posterior (with gradients).

As the posterior covariance is difficult to draw from in this model, we implement Matheron’s rule as described in [Doucet2010sampl]-. This may not work entirely correctly for deterministic base samples unless base samples are provided that are of shape n + 2 * n_train because the sampling method draws 2 * n_train samples as well as the standard n. samples.

Parameters

  • sample_shape (Optional[Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to torch.Size([b, n]).

  • base_samples (Optional[Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic optimization.

Return type

Tensor

Returns

A sample_shape x event_shape-dim Tensor of samples from the posterior.

Transformed Posterior

class botorch.posteriors.transformed.TransformedPosterior(posterior, sample_transform, mean_transform=None, variance_transform=None)[source]

Bases: botorch.posteriors.posterior.Posterior

An generic transformation of a posterior (implicitly represented)

An implicitly represented transformed posterior

Parameters

  • posterior (Posterior) – The posterior object to be transformed.

  • sample_transform (Callable[[Tensor], Tensor]) – A callable applying a sample-level transform to a sample_shape x batch_shape x q x m-dim tensor of samples from the original posterior, returning a tensor of samples of the same shape.

  • mean_transform (Optional[Callable[[Tensor, Tensor], Tensor]]) – A callable transforming a 2-tuple of mean and variance (both of shape batch_shape x m x o) of the original posterior to the mean of the transformed posterior.

  • variance_transform (Optional[Callable[[Tensor, Tensor], Tensor]]) – A callable transforming a 2-tuple of mean and variance (both of shape batch_shape x m x o) of the original posterior to a variance of the transformed posterior.

property base_sample_shape

The shape of a base sample used for constructing posterior samples.

Return type

Size

property device

The torch device of the posterior.

Return type

device

property dtype

The torch dtype of the posterior.

Return type

dtype

property event_shape

The event shape (i.e. the shape of a single sample).

Return type

Size

property mean

The mean of the posterior as a batch_shape x n x m-dim Tensor.

Return type

Tensor

property variance

The variance of the posterior as a batch_shape x n x m-dim Tensor.

Return type

Tensor

rsample(sample_shape=None, base_samples=None)[source]

Sample from the posterior (with gradients).

Parameters

  • sample_shape (Optional[Size]) – A torch.Size object specifying the sample shape. To draw n samples, set to torch.Size([n]). To draw b batches of n samples each, set to torch.Size([b, n]).

  • base_samples (Optional[Tensor]) – An (optional) Tensor of N(0, I) base samples of appropriate dimension, typically obtained from a Sampler. This is used for deterministic optimization.

Return type

Tensor

Returns

A sample_shape x event-dim Tensor of samples from the posterior.