# botorch.models¶

## Model APIs¶

### Abstract Model API¶

Abstract base module for all BoTorch models.

class botorch.models.model.Model[source]

Bases: torch.nn.modules.module.Module, abc.ABC

Abstract base class for BoTorch models.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

abstract posterior(X, output_indices=None, observation_noise=False, **kwargs)[source]

Computes the posterior over model outputs at the provided points.

Parameters
• X (Tensor) – A b x q x d-dim Tensor, where d is the dimension of the feature space, q is the number of points considered jointly, and b is the batch dimension.

• output_indices (Optional[List[int]]) – A list of indices, corresponding to the outputs over which to compute the posterior (if the model is multi-output). Can be used to speed up computation if only a subset of the model’s outputs are required for optimization. If omitted, computes the posterior over all model outputs.

• observation_noise (bool) – If True, add observation noise to the posterior.

Return type

Posterior

Returns

A Posterior object, representing a batch of b joint distributions over q points and m outputs each.

property num_outputs

The number of outputs of the model.

Return type

int

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

Model

Returns

A Model object of the same type and with the same parameters as the current model, subset to the specified output indices.

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, n’ is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• Y (Tensor) – A batch_shape’ x n’ x m-dim Tensor, where m is the number of model outputs, n’ is the number of points per batch, and batch_shape’ is the batch shape of the observations. batch_shape’ must be broadcastable to batch_shape using standard broadcasting semantics. If Y has fewer batch dimensions than X, it is assumed that the missing batch dimensions are the same for all Y.

Return type

Model

Returns

A Model object of the same type, representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs).

fantasize(X, sampler, observation_noise=True, **kwargs)[source]

Construct a fantasy model.

Constructs a fantasy model in the following fashion: (1) compute the model posterior at X (including observation noise if observation_noise=True). (2) sample from this posterior (using sampler) to generate “fake” observations. (3) condition the model on the new fake observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, n’ is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• sampler (MCSampler) – The sampler used for sampling from the posterior at X.

• observation_noise (bool) – If True, include observation noise.

Return type

Model

Returns

The constructed fantasy model.

### GPyTorch Model API¶

Abstract model class for all GPyTorch-based botorch models.

To implement your own, simply inherit from both the provided classes and a GPyTorch Model class such as an ExactGP.

class botorch.models.gpytorch.GPyTorchModel[source]

Bases: botorch.models.model.Model, abc.ABC

Abstract base class for models based on GPyTorch models.

The easiest way to use this is to subclass a model from a GPyTorch model class (e.g. an ExactGP) and this GPyTorchModel. See e.g. SingleTaskGP.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

property num_outputs

The number of outputs of the model.

Return type

int

posterior(X, observation_noise=False, **kwargs)[source]

Computes the posterior over model outputs at the provided points.

Parameters
• X (Tensor) – A (batch_shape) x q x d-dim Tensor, where d is the dimension of the feature space and q is the number of points considered jointly.

• observation_noise (Union[bool, Tensor]) – If True, add the observation noise from the likelihood to the posterior. If a Tensor, use it directly as the observation noise (must be of shape (batch_shape) x q).

Return type

GPyTorchPosterior

Returns

A GPyTorchPosterior object, representing a batch of b joint distributions over q points. Includes observation noise if specified.

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, n’ is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• Y (Tensor) – A batch_shape’ x n x m-dim Tensor, where m is the number of model outputs, n’ is the number of points per batch, and batch_shape’ is the batch shape of the observations. batch_shape’ must be broadcastable to batch_shape using standard broadcasting semantics. If Y has fewer batch dimensions than X, its is assumed that the missing batch dimensions are the same for all Y.

Return type

Model

Returns

A Model object of the same type, representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X[:, 0]) + torch.cos(train_X[:, 1])
>>> new_X = torch.rand(5, 2)
>>> new_Y = torch.sin(new_X[:, 0]) + torch.cos(new_X[:, 1])
>>> model = model.condition_on_observations(X=new_X, Y=new_Y)

class botorch.models.gpytorch.BatchedMultiOutputGPyTorchModel[source]

Base class for batched multi-output GPyTorch models with independent outputs.

This model should be used when the same training data is used for all outputs. Outputs are modeled independently by using a different batch for each output.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

static get_batch_dimensions(train_X, train_Y)[source]

Get the raw batch shape and output-augmented batch shape of the inputs.

Parameters
• train_X (Tensor) – A n x d or batch_shape x n x d (batch mode) tensor of training features.

• train_Y (Tensor) – A n x m or batch_shape x n x m (batch mode) tensor of training observations.

Return type

Tuple[Size, Size]

Returns

2-element tuple containing

• The input_batch_shape

• The output-augmented batch shape: input_batch_shape x (m)

posterior(X, output_indices=None, observation_noise=False, **kwargs)[source]

Computes the posterior over model outputs at the provided points.

Parameters
• X (Tensor) – A (batch_shape) x q x d-dim Tensor, where d is the dimension of the feature space and q is the number of points considered jointly.

• output_indices (Optional[List[int]]) – A list of indices, corresponding to the outputs over which to compute the posterior (if the model is multi-output). Can be used to speed up computation if only a subset of the model’s outputs are required for optimization. If omitted, computes the posterior over all model outputs.

• observation_noise (Union[bool, Tensor]) – If True, add the observation noise from the likelihood to the posterior. If a Tensor, use it directly as the observation noise (must be of shape (batch_shape) x q x m).

Return type

GPyTorchPosterior

Returns

A GPyTorchPosterior object, representing batch_shape joint distributions over q points and the outputs selected by output_indices each. Includes observation noise if specified.

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, m is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• Y (Tensor) – A batch_shape’ x n’ x m-dim Tensor, where m is the number of model outputs, n’ is the number of points per batch, and batch_shape’ is the batch shape of the observations. batch_shape’ must be broadcastable to batch_shape using standard broadcasting semantics. If Y has fewer batch dimensions than X, its is assumed that the missing batch dimensions are the same for all Y.

Return type

BatchedMultiOutputGPyTorchModel

Returns

A BatchedMultiOutputGPyTorchModel object of the same type with n + n’ training examples, representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.cat(
>>>     [torch.sin(train_X[:, 0]), torch.cos(train_X[:, 1])], -1
>>> )
>>> new_X = torch.rand(5, 2)
>>> new_Y = torch.cat([torch.sin(new_X[:, 0]), torch.cos(new_X[:, 1])], -1)
>>> model = model.condition_on_observations(X=new_X, Y=new_Y)

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

BatchedMultiOutputGPyTorchModel

Returns

The current model, subset to the specified output indices.

class botorch.models.gpytorch.ModelListGPyTorchModel[source]

Bases: botorch.models.gpytorch.GPyTorchModel, abc.ABC

Abstract base class for models based on multi-output GPyTorch models.

This is meant to be used with a gpytorch ModelList wrapper for independent evaluation of submodels.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

posterior(X, output_indices=None, observation_noise=False, **kwargs)[source]

Computes the posterior over model outputs at the provided points.

Parameters
• X (Tensor) – A b x q x d-dim Tensor, where d is the dimension of the feature space, q is the number of points considered jointly, and b is the batch dimension.

• output_indices (Optional[List[int]]) – A list of indices, corresponding to the outputs over which to compute the posterior (if the model is multi-output). Can be used to speed up computation if only a subset of the model’s outputs are required for optimization. If omitted, computes the posterior over all model outputs.

• observation_noise (Union[bool, Tensor]) – If True, add the observation noise from the respective likelihoods to the posterior. If a Tensor of shape (batch_shape) x q x m, use it directly as the observation noise (with observation_noise[…,i] added to the posterior of the i-th model).

Return type

GPyTorchPosterior

Returns

A GPyTorchPosterior object, representing batch_shape joint distributions over q points and the outputs selected by output_indices each. Includes measurement noise if observation_noise is specified.

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, n’ is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• Y (Tensor) – A batch_shape’ x n x m-dim Tensor, where m is the number of model outputs, n’ is the number of points per batch, and batch_shape’ is the batch shape of the observations. batch_shape’ must be broadcastable to batch_shape using standard broadcasting semantics. If Y has fewer batch dimensions than X, its is assumed that the missing batch dimensions are the same for all Y.

Return type

ModelListGPyTorchModel

Returns

A Model object of the same type, representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X[:, 0]) + torch.cos(train_X[:, 1])
>>> new_X = torch.rand(5, 2)
>>> new_Y = torch.sin(new_X[:, 0]) + torch.cos(new_X[:, 1])
>>> model = model.condition_on_observations(X=new_X, Y=new_Y)

class botorch.models.gpytorch.MultiTaskGPyTorchModel[source]

Bases: botorch.models.gpytorch.GPyTorchModel, abc.ABC

Abstract base class for multi-task models baed on GPyTorch models.

This class provides the posterior method to models that implement a “long-format” multi-task GP in the style of MultiTaskGP.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

posterior(X, output_indices=None, observation_noise=False, **kwargs)[source]

Computes the posterior over model outputs at the provided points.

Parameters
• X (Tensor) – A q x d or batch_shape x q x d (batch mode) tensor, where d is the dimension of the feature space (not including task indices) and q is the number of points considered jointly.

• output_indices (Optional[List[int]]) – A list of indices, corresponding to the outputs over which to compute the posterior (if the model is multi-output). Can be used to speed up computation if only a subset of the model’s outputs are required for optimization. If omitted, computes the posterior over all model outputs.

• observation_noise (Union[bool, Tensor]) – If True, add observation noise from the respective likelihoods. If a Tensor, specifies the observation noise levels to add.

Return type

GPyTorchPosterior

Returns

A GPyTorchPosterior object, representing batch_shape joint distributions over q points and the outputs selected by output_indices. Includes measurement noise if observation_noise is specified.

### Deterministic Model API¶

Deterministic Models. Simple wrappers that allow the usage of deterministic mappings via the BoTorch Model and Posterior APIs. Useful e.g. for defining known cost functions for cost-aware acquisition utilities.

class botorch.models.deterministic.DeterministicModel[source]

Bases: botorch.models.model.Model, abc.ABC

Abstract base class for deterministic models.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

abstract forward(X)[source]

Compute the (deterministic) model output at X.

Parameters

X (Tensor) – A batch_shape x n x d-dim input tensor X.

Return type

Tensor

Returns

A batch_shape x n x m-dimensional output tensor (the outcome dimension m must be explicit if m=1).

property num_outputs

The number of outputs of the model.

Return type

int

posterior(X, output_indices=None, **kwargs)[source]

Compute the (deterministic) posterior at X.

Return type

DeterministicPosterior

class botorch.models.deterministic.GenericDeterministicModel(f, num_outputs=1)[source]

A generic deterministic model constructed from a callable.

A generic deterministic model constructed from a callable.

Parameters
• f (Callable[[Tensor], Tensor]) – A callable mapping a batch_shape x n x d-dim input tensor X to a batch_shape x n x m-dimensional output tensor (the outcome dimension m must be explicit, even if m=1).

• num_outputs (int) – The number of outputs m.

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

GenericDeterministicModel

Returns

The current model, subset to the specified output indices.

forward(X)[source]

Compute the (deterministic) model output at X.

Parameters

X (Tensor) – A batch_shape x n x d-dim input tensor X.

Return type

Tensor

Returns

A batch_shape x n x m-dimensional output tensor.

class botorch.models.deterministic.AffineDeterministicModel(a, b=0.01)[source]

An affine deterministic model.

Affine deterministic model from weights and offset terms.

A simple model of the form

y[…, m] = b[m] + sum_{i=1}^d a[i, m] * X[…, i]

Parameters
• a (Tensor) – A d x m-dim tensor of linear weights, where m is the number of outputs (must be explicit if m=1)

• b (Union[Tensor, float]) – The affine (offset) term. Either a float (for single-output models or if the offset is shared), or a m-dim tensor (with different offset values for for the m different outputs).

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

AffineDeterministicModel

Returns

The current model, subset to the specified output indices.

forward(X)[source]

Compute the (deterministic) model output at X.

Parameters

X (Tensor) – A batch_shape x n x d-dim input tensor X.

Return type

Tensor

Returns

A batch_shape x n x m-dimensional output tensor (the outcome dimension m must be explicit if m=1).

## Models¶

### Cost Models (for cost-aware optimization)¶

Cost models to be used with multi-fidelity optimization.

class botorch.models.cost.AffineFidelityCostModel(fidelity_weights=None, fixed_cost=0.01)[source]

Affine cost model operating on fidelity parameters.

For each (q-batch) element of a candidate set X, this module computes a cost of the form

cost = fixed_cost + sum_j weights[j] * X[fidelity_dims[j]]

Affine cost model operating on fidelity parameters.

Parameters
• fidelity_weights (Optional[Dict[int, float]]) – A dictionary mapping a subset of columns of X (the fidelity parameters) to it’s associated weight in the affine cost expression. If omitted, assumes that the last column of X is the fidelity parameter with a weight of 1.0.

• fixed_cost (float) – The fixed cost of running a single candidate point (i.e. an element of a q-batch).

forward(X)[source]

Evaluate the cost on a candidate set X.

Computes a cost of the form

cost = fixed_cost + sum_j weights[j] * X[fidelity_dims[j]]

for each element of the q-batch

Parameters

X (Tensor) – A batch_shape x q x d’-dim tensor of candidate points.

Return type

Tensor

Returns

A batch_shape x q x 1-dim tensor of costs.

### GP Regression Models¶

Gaussian Process Regression models based on GPyTorch models.

class botorch.models.gp_regression.SingleTaskGP(train_X, train_Y, likelihood=None, covar_module=None, outcome_transform=None)[source]

Bases: botorch.models.gpytorch.BatchedMultiOutputGPyTorchModel, gpytorch.models.exact_gp.ExactGP

A single-task exact GP using relatively strong priors on the Kernel hyperparameters, which work best when covariates are normalized to the unit cube and outcomes are standardized (zero mean, unit variance).

This model works in batch mode (each batch having its own hyperparameters). When the training observations include multiple outputs, this model will use batching to model outputs independently.

Use this model when you have independent output(s) and all outputs use the same training data. If outputs are independent and outputs have different training data, use the ModelListGP. When modeling correlations between outputs, use the MultiTaskGP.

Parameters
• train_X (Tensor) – A batch_shape x n x d tensor of training features.

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• likelihood (Optional[Likelihood]) – A likelihood. If omitted, use a standard GaussianLikelihood with inferred noise level.

• covar_module (Optional[Module]) – The module computing the covariance (Kernel) matrix. If omitted, use a MaternKernel.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)

forward(x)[source]

Defines the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

Return type

MultivariateNormal

class botorch.models.gp_regression.FixedNoiseGP(train_X, train_Y, train_Yvar, covar_module=None, outcome_transform=None)[source]

Bases: botorch.models.gpytorch.BatchedMultiOutputGPyTorchModel, gpytorch.models.exact_gp.ExactGP

A single-task exact GP model using fixed noise levels.

A single-task exact GP that uses fixed observation noise levels. This model also uses relatively strong priors on the Kernel hyperparameters, which work best when covariates are normalized to the unit cube and outcomes are standardized (zero mean, unit variance).

This model works in batch mode (each batch having its own hyperparameters).

A single-task exact GP model using fixed noise levels.

Parameters
• train_X (Tensor) – A batch_shape x n x d tensor of training features.

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• train_Yvar (Tensor) – A batch_shape x n x m tensor of observed measurement noise.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)
>>> train_Yvar = torch.full_like(train_Y, 0.2)
>>> model = FixedNoiseGP(train_X, train_Y, train_Yvar)

fantasize(X, sampler, observation_noise=True, **kwargs)[source]

Construct a fantasy model.

Constructs a fantasy model in the following fashion: (1) compute the model posterior at X (if observation_noise=True, this includes observation noise taken as the mean across the observation noise in the training data. If observation_noise is a Tensor, use it directly as the observation noise to add). (2) sample from this posterior (using sampler) to generate “fake” observations. (3) condition the model on the new fake observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, n’ is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• sampler (MCSampler) – The sampler used for sampling from the posterior at X.

• observation_noise (Union[bool, Tensor]) – If True, include the mean across the observation noise in the training data as observation noise in the posterior from which the samples are drawn. If a Tensor, use it directly as the specified measurement noise.

Return type

FixedNoiseGP

Returns

The constructed fantasy model.

forward(x)[source]

Defines the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

Return type

MultivariateNormal

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

BatchedMultiOutputGPyTorchModel

Returns

The current model, subset to the specified output indices.

class botorch.models.gp_regression.HeteroskedasticSingleTaskGP(train_X, train_Y, train_Yvar, outcome_transform=None)[source]

A single-task exact GP model using a heteroskeastic noise model.

This model internally wraps another GP (a SingleTaskGP) to model the observation noise. This allows the likelihood to make out-of-sample predictions for the observation noise levels.

A single-task exact GP model using a heteroskedastic noise model.

Parameters
• train_X (Tensor) – A batch_shape x n x d tensor of training features.

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• train_Yvar (Tensor) – A batch_shape x n x m tensor of observed measurement noise.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale). Note that the noise model internally log-transforms the variances, which will happen after this transform is applied.

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)
>>> se = torch.norm(train_X, dim=1, keepdim=True)
>>> train_Yvar = 0.1 + se * torch.rand_like(train_Y)
>>> model = HeteroskedasticSingleTaskGP(train_X, train_Y, train_Yvar)

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, m is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• Y (Tensor) – A batch_shape’ x n’ x m-dim Tensor, where m is the number of model outputs, n’ is the number of points per batch, and batch_shape’ is the batch shape of the observations. batch_shape’ must be broadcastable to batch_shape using standard broadcasting semantics. If Y has fewer batch dimensions than X, its is assumed that the missing batch dimensions are the same for all Y.

Return type

HeteroskedasticSingleTaskGP

Returns

A BatchedMultiOutputGPyTorchModel object of the same type with n + n’ training examples, representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.cat(
>>>     [torch.sin(train_X[:, 0]), torch.cos(train_X[:, 1])], -1
>>> )
>>> new_X = torch.rand(5, 2)
>>> new_Y = torch.cat([torch.sin(new_X[:, 0]), torch.cos(new_X[:, 1])], -1)
>>> model = model.condition_on_observations(X=new_X, Y=new_Y)

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

HeteroskedasticSingleTaskGP

Returns

The current model, subset to the specified output indices.

### Multi-Fidelity GP Regression Models¶

Gaussian Process Regression models based on GPyTorch models.

Wu2019mf(1,2)

J. Wu, S. Toscano-Palmerin, P. I. Frazier, and A. G. Wilson. Practical multi-fidelity bayesian optimization for hyperparameter tuning. ArXiv 2019.

class botorch.models.gp_regression_fidelity.SingleTaskMultiFidelityGP(train_X, train_Y, iteration_fidelity=None, data_fidelity=None, linear_truncated=True, nu=2.5, likelihood=None, outcome_transform=None)[source]

A single task multi-fidelity GP model.

A SingleTaskGP model using a DownsamplingKernel for the data fidelity parameter (if present) and an ExponentialDecayKernel for the iteration fidelity parameter (if present).

This kernel is described in [Wu2019mf].

Parameters
• train_X (Tensor) – A batch_shape x n x (d + s) tensor of training features, where s is the dimension of the fidelity parameters (either one or two).

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• iteration_fidelity (Optional[int]) – The column index for the training iteration fidelity parameter (optional).

• data_fidelity (Optional[int]) – The column index for the downsampling fidelity parameter (optional).

• linear_truncated (bool) – If True, use a LinearTruncatedFidelityKernel instead of the default kernel.

• nu (float) – The smoothness parameter for the Matern kernel: either 1/2, 3/2, or 5/2. Only used when linear_truncated=True.

• likelihood (Optional[Likelihood]) – A likelihood. If omitted, use a standard GaussianLikelihood with inferred noise level.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale).

Example

>>> train_X = torch.rand(20, 4)
>>> train_Y = train_X.pow(2).sum(dim=-1, keepdim=True)
>>> model = SingleTaskMultiFidelityGP(train_X, train_Y, data_fidelity=3)


Parameters
• train_X (Tensor) – A batch_shape x n x d tensor of training features.

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• likelihood (Optional[Likelihood]) – A likelihood. If omitted, use a standard GaussianLikelihood with inferred noise level.

• covar_module – The module computing the covariance (Kernel) matrix. If omitted, use a MaternKernel.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)

class botorch.models.gp_regression_fidelity.FixedNoiseMultiFidelityGP(train_X, train_Y, train_Yvar, iteration_fidelity=None, data_fidelity=None, linear_truncated=True, nu=2.5, outcome_transform=None)[source]

A single task multi-fidelity GP model using fixed noise levels.

A FixedNoiseGP model analogue to SingleTaskMultiFidelityGP, using a DownsamplingKernel for the data fidelity parameter (if present) and an ExponentialDecayKernel for the iteration fidelity parameter (if present).

This kernel is described in [Wu2019mf].

Parameters
• train_X (Tensor) – A batch_shape x n x (d + s) tensor of training features, where s is the dimension of the fidelity parameters (either one or two).

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• train_Yvar (Tensor) – A batch_shape x n x m tensor of observed measurement noise.

• iteration_fidelity (Optional[int]) – The column index for the training iteration fidelity parameter (optional).

• data_fidelity (Optional[int]) – The column index for the downsampling fidelity parameter (optional).

• linear_truncated (bool) – If True, use a LinearTruncatedFidelityKernel instead of the default kernel.

• nu (float) – The smoothness parameter for the Matern kernel: either 1/2, 3/2, or 5/2. Only used when linear_truncated=True.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale).

Example

>>> train_X = torch.rand(20, 4)
>>> train_Y = train_X.pow(2).sum(dim=-1, keepdim=True)
>>> train_Yvar = torch.full_like(train_Y) * 0.01
>>> model = FixedNoiseMultiFidelityGP(
>>>     train_X,
>>>     train_Y,
>>>     train_Yvar,
>>>     data_fidelity=3,
>>> )


A single-task exact GP model using fixed noise levels.

Parameters
• train_X (Tensor) – A batch_shape x n x d tensor of training features.

• train_Y (Tensor) – A batch_shape x n x m tensor of training observations.

• train_Yvar (Tensor) – A batch_shape x n x m tensor of observed measurement noise.

• outcome_transform (Optional[OutcomeTransform]) – An outcome transform that is applied to the training data during instantiation and to the posterior during inference (that is, the Posterior obtained by calling .posterior on the model will be on the original scale).

Example

>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)
>>> train_Yvar = torch.full_like(train_Y, 0.2)
>>> model = FixedNoiseGP(train_X, train_Y, train_Yvar)


### Model List GP Regression Models¶

Model List GP Regression models.

class botorch.models.model_list_gp_regression.ModelListGP(*gp_models)[source]

Bases: gpytorch.models.model_list.IndependentModelList, botorch.models.gpytorch.ModelListGPyTorchModel

A multi-output GP model with independent GPs for the outputs.

This model supports different-shaped training inputs for each of its sub-models. It can be used with any BoTorch models.

Internally, this model is just a list of individual models, but it implements the same input/output interface as all other BoTorch models. This makes it very flexible and convenient to work with. The sequential evaluation comes at a performance cost though - if you are using a block design (i.e. the same number of training example for each output, and a similar model structure, you should consider using a batched GP model instead).

A multi-output GP model with independent GPs for the outputs.

Parameters

*gp_models – An variable number of single-output BoTorch models. If models have input/output transforms, these are honored individually for each model.

Example

>>> model1 = SingleTaskGP(train_X1, train_Y1)
>>> model = ModelListGP(model1, model2)

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Parameters
• X (Tensor) – A batch_shape x n’ x d-dim Tensor, where d is the dimension of the feature space, n’ is the number of points per batch, and batch_shape is the batch shape (must be compatible with the batch shape of the model).

• Y (Tensor) – A batch_shape’ x n’ x m-dim Tensor, where m is the number of model outputs, n’ is the number of points per batch, and batch_shape’ is the batch shape of the observations. batch_shape’ must be broadcastable to batch_shape using standard broadcasting semantics. If Y has fewer batch dimensions than X, its is assumed that the missing batch dimensions are the same for all Y.

Return type

ModelListGP

Returns

A ModelListGPyTorchModel representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs). Here the i-th model has n_i + n’ training examples, where the n’ training examples have been added and all test-time caches have been updated.

subset_output(idcs)[source]

Subset the model along the output dimension.

Parameters

idcs (List[int]) – The output indices to subset the model to.

Return type

ModelListGP

Returns

The current model, subset to the specified output indices.

class botorch.models.multitask.MultiTaskGP(train_X, train_Y, task_feature, output_tasks=None, rank=None)[source]

Bases: gpytorch.models.exact_gp.ExactGP, botorch.models.gpytorch.MultiTaskGPyTorchModel

Multi-Task GP model using an ICM kernel, inferring observation noise.

Multi-task exact GP that uses a simple ICM kernel. Can be single-output or multi-output. This model uses relatively strong priors on the base Kernel hyperparameters, which work best when covariates are normalized to the unit cube and outcomes are standardized (zero mean, unit variance).

This model infers the noise level. WARNING: It currently does not support different noise levels for the different tasks. If you have known observation noise, please use FixedNoiseMultiTaskGP instead.

Multi-Task GP model using an ICM kernel, inferring observation noise.

Parameters
• train_X (Tensor) – A n x (d + 1) or b x n x (d + 1) (batch mode) tensor of training data. One of the columns should contain the task features (see task_feature argument).

• train_Y (Tensor) – A n or b x n (batch mode) tensor of training observations.

• task_feature (int) – The index of the task feature (-d <= task_feature <= d).

• output_tasks (Optional[List[int]]) – A list of task indices for which to compute model outputs for. If omitted, return outputs for all task indices.

• rank (Optional[int]) – The rank to be used for the index kernel. If omitted, use a full rank (i.e. number of tasks) kernel.

Example

>>> X1, X2 = torch.rand(10, 2), torch.rand(20, 2)
>>> i1, i2 = torch.zeros(10, 1), torch.ones(20, 1)
>>> train_X = torch.cat([
>>>     torch.cat([X1, i1], -1), torch.cat([X2, i2], -1),
>>> ])
>>> train_Y = torch.cat(f1(X1), f2(X2)).unsqueeze(-1)

forward(x)[source]

Defines the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

Return type

MultivariateNormal

class botorch.models.multitask.FixedNoiseMultiTaskGP(train_X, train_Y, train_Yvar, task_feature, output_tasks=None, rank=None)[source]

Multi-Task GP model using an ICM kernel, with known observation noise.

Multi-task exact GP that uses a simple ICM kernel. Can be single-output or multi-output. This model uses relatively strong priors on the base Kernel hyperparameters, which work best when covariates are normalized to the unit cube and outcomes are standardized (zero mean, unit variance).

This model requires observation noise data (specified in train_Yvar).

Multi-Task GP model using an ICM kernel and known observatioon noise.

Parameters
• train_X (Tensor) – A n x (d + 1) or b x n x (d + 1) (batch mode) tensor of training data. One of the columns should contain the task features (see task_feature argument).

• train_Y (Tensor) – A n or b x n (batch mode) tensor of training observations.

• train_Yvar (Tensor) – A n or b x n (batch mode) tensor of observation noise standard errors.

• task_feature (int) – The index of the task feature (-d <= task_feature <= d).

• output_tasks (Optional[List[int]]) – A list of task indices for which to compute model outputs for. If omitted, return outputs for all task indices.

• rank (Optional[int]) – The rank to be used for the index kernel. If omitted, use a full rank (i.e. number of tasks) kernel.

Example

>>> X1, X2 = torch.rand(10, 2), torch.rand(20, 2)
>>> i1, i2 = torch.zeros(10, 1), torch.ones(20, 1)
>>> train_X = torch.cat([
>>>     torch.cat([X1, i1], -1), torch.cat([X2, i2], -1),
>>> ], dim=0)
>>> train_Y = torch.cat(f1(X1), f2(X2))
>>> train_Yvar = 0.1 + 0.1 * torch.rand_like(train_Y)
>>> model = FixedNoiseMultiTaskGP(train_X, train_Y, train_Yvar, -1)


### Pairwise GP Models¶

Preference Learning with Gaussian Process

Chu2005preference(1,2)

Wei Chu, and Zoubin Ghahramani. Preference learning with Gaussian processes. Proceedings of the 22nd international conference on Machine learning. 2005.

Brochu2010tutorial

Eric Brochu, Vlad M. Cora, and Nando De Freitas. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:1012.2599 (2010).

class botorch.models.pairwise_gp.PairwiseGP(datapoints, comparisons, covar_module=None, **kwargs)[source]

Bases: botorch.models.model.Model, gpytorch.models.gp.GP

Probit GP for preference learning with Laplace approximation

Implementation is based on [Chu2005preference]. Also see [Brochu2010tutorial] for additional reference.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

property std_noise
Return type

Tensor

property num_outputs

The number of outputs of the model.

Return type

int

set_train_data(datapoints, comparisons, update_model=True)[source]

Set datapoints and comparisons and update model properties if needed

Parameters
• datapoints (Tensor) – A batch_shape x n x d dimension tensor X

• comparisons (Tensor) – A tensor of size batch_shape x m x 2. (i, j) means f_i is preferred over f_j

• update_model (bool) – True if we want to refit the model (see _update) after re-setting the data

Return type

None

forward(datapoints)[source]

Calculate a posterior or prior prediction.

During training mode, forward implemented solely for gradient-based hyperparam opt. Essentially what it does is to re-calculate the utility f using its analytical form at f_map so that we are able to obtain gradients of the hyperparameters. We only take in one parameter datapoints without the comparisons for the compatibility with other gpytorch/botorch APIs. It assumes datapoints is the same as self.datapoints. That’s what “Must train on training data” means.

Parameters

datapoints (Tensor) – A batch_shape x n x d Tensor, should be the same as self.datapoints

Returns

1. Posterior centered at MAP points for training data (training mode)

2. Prior predictions (prior mode)

3. Predictive posterior (eval mode)

Return type

A MultivariateNormal object, being one of the followings

posterior(X, output_indices=None, observation_noise=False, **kwargs)[source]

Computes the posterior over model outputs at the provided points.

Parameters
• X (Tensor) – A batch_shape x q x d-dim Tensor, where d is the dimension of the feature space and q is the number of points considered jointly.

• output_indices (Optional[List[int]]) – As defined in parent Model class, not used for this model.

• observation_noise (bool) – If True, add observation noise to the posterior.

Return type

Posterior

Returns

A Posterior object, representing joint

distributions over q points. Includes observation noise if specified.

condition_on_observations(X, Y, **kwargs)[source]

Condition the model on new observations.

Note that unlike other BoTorch models, PairwiseGP requires Y to be pairwise comparisons

Parameters
• X (Tensor) – A batch_shape x n x d dimension tensor X

• Y (Tensor) – A tensor of size batch_shape x m x 2. (i, j) means f_i is preferred over f_j

Return type

Model

Returns

A (deepcopied) Model object of the same type, representing the original model conditioned on the new observations (X, Y) (and possibly noise observations passed in via kwargs).

class botorch.models.pairwise_gp.PairwiseLaplaceMarginalLogLikelihood(model)[source]

Bases: gpytorch.mlls.marginal_log_likelihood.MarginalLogLikelihood

Laplace-approximated marginal log likelihood/evidence for PairwiseGP

See (12) from [Chu2005preference].

Parameters

model (PairwiseGP) – A model using laplace approximation (currently only supports PairwiseGP)

forward(post, comp)[source]

Calculate approximated log evidence, i.e., log(P(D|theta))

Parameters
• post (Posterior) – training posterior distribution from self.model

• comp (Tensor) – Comparisons pairs, see PairwiseGP.__init__ for more details

Return type

Tensor

Returns

The approximated evidence, i.e., the marginal log likelihood

## Model Components¶

### Kernels¶

class botorch.models.kernels.downsampling.DownsamplingKernel(power_prior=None, offset_prior=None, power_constraint=None, offset_constraint=None, **kwargs)[source]

Bases: gpytorch.kernels.kernel.Kernel

GPyTorch Downsampling Kernel.

Computes a covariance matrix based on the down sampling kernel between inputs x_1 and x_2 (we expect d = 1):

K(mathbf{x_1}, mathbf{x_2}) = c + (1 - x_1)^(1 + delta) *

(1 - x_2)^(1 + delta).

where c is an offset parameter, and delta is a power parameter.

Parameters
• power_constraint (Optional[Interval]) – Constraint to place on power parameter. Default is Positive.

• power_prior (Optional[Prior]) – Prior over the power parameter.

• offset_constraint (Optional[Interval]) – Constraint to place on offset parameter. Default is Positive.

• active_dims – List of data dimensions to operate on. len(active_dims) should equal num_dimensions.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

class botorch.models.kernels.exponential_decay.ExponentialDecayKernel(power_prior=None, offset_prior=None, power_constraint=None, offset_constraint=None, **kwargs)[source]

Bases: gpytorch.kernels.kernel.Kernel

GPyTorch Exponential Decay Kernel.

Computes a covariance matrix based on the exponential decay kernel between inputs x_1 and x_2 (we expect d = 1):

K(x_1, x_2) = w + beta^alpha / (x_1 + x_2 + beta)^alpha.

where w is an offset parameter, beta is a lenthscale parameter, and alpha is a power parameter.

Parameters
• lengthscale_constraint – Constraint to place on lengthscale parameter. Default is Positive.

• lengthscale_prior – Prior over the lengthscale parameter.

• power_constraint (Optional[Interval]) – Constraint to place on power parameter. Default is Positive.

• power_prior (Optional[Prior]) – Prior over the power parameter.

• offset_constraint (Optional[Interval]) – Constraint to place on offset parameter. Default is Positive.

• active_dims – List of data dimensions to operate on. len(active_dims) should equal num_dimensions.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

class botorch.models.kernels.linear_truncated_fidelity.LinearTruncatedFidelityKernel(fidelity_dims, dimension=None, power_prior=None, power_constraint=None, nu=2.5, lengthscale_prior_unbiased=None, lengthscale_prior_biased=None, lengthscale_constraint_unbiased=None, lengthscale_constraint_biased=None, covar_module_unbiased=None, covar_module_biased=None, **kwargs)[source]

Bases: gpytorch.kernels.kernel.Kernel

GPyTorch Linear Truncated Fidelity Kernel.

Computes a covariance matrix based on the Linear truncated kernel between inputs x_1 and x_2 for up to two fidelity parmeters:

K(x_1, x_2) = k_0 + c_1(x_1, x_2)k_1 + c_2(x_1,x_2)k_2 + c_3(x_1,x_2)k_3

where

• k_i(i=0,1,2,3) are Matern kernels calculated between non-fidelity

parameters of x_1 and x_2 with different priors.

• c_1=(1 - x_1[f_1])(1 - x_2[f_1]))(1 + x_1[f_1] x_2[f_1])^p is the kernel

of the the bias term, which can be decomposed into a determistic part and a polynomial kernel. Here f_1 is the first fidelity dimension and p is the order of the polynomial kernel.

• c_3 is the same as c_1 but is calculated for the second fidelity

dimension f_2.

• c_2 is the interaction term with four deterministic terms and the

polynomial kernel between x_1[…, [f_1, f_2]] and x_2[…, [f_1, f_2]].

Parameters
• fidelity_dims (List[int]) – A list containing either one or two indices specifying the fidelity parameters of the input.

• dimension (Optional[int]) – The dimension of x. Unused if active_dims is specified.

• power_prior (Optional[Prior]) – Prior for the power parameter of the polynomial kernel. Default is None.

• power_constraint (Optional[Interval]) – Constraint on the power parameter of the polynomial kernel. Default is Positive.

• nu (float) – The smoothness parameter for the Matern kernel: either 1/2, 3/2, or 5/2. Unused if both covar_module_unbiased and covar_module_biased are specified.

• lengthscale_prior_unbiased (Optional[Prior]) – Prior on the lengthscale parameter of Matern kernel k_0. Default is Gamma(1.1, 1/20).

• lengthscale_constraint_unbiased (Optional[Interval]) – Constraint on the lengthscale parameter of the Matern kernel k_0. Default is Positive.

• lengthscale_prior_biased (Optional[Prior]) – Prior on the lengthscale parameter of Matern kernels k_i(i>0). Default is Gamma(5, 1/20).

• lengthscale_constraint_biased (Optional[Interval]) – Constraint on the lengthscale parameter of the Matern kernels k_i(i>0). Default is Positive.

• covar_module_unbiased (Optional[Kernel]) – Specify a custom kernel for k_0. If omitted, use a MaternKernel.

• covar_module_biased (Optional[Kernel]) – Specify a custom kernel for the biased parts k_i(i>0). If omitted, use a MaternKernel.

• batch_shape – If specified, use a separate lengthscale for each batch of input data. If x1 is a batch_shape x n x d tensor, this should be batch_shape.

• active_dims – Compute the covariance of a subset of input dimensions. The numbers correspond to the indices of the dimensions.

Example

>>> x = torch.randn(10, 5)
>>> # Non-batch: Simple option
>>> covar_module = LinearTruncatedFidelityKernel()
>>> covar = covar_module(x)  # Output: LazyVariable of size (10 x 10)
>>>
>>> batch_x = torch.randn(2, 10, 5)
>>> # Batch: Simple option
>>> covar_module = LinearTruncatedFidelityKernel(batch_shape = torch.Size([2]))
>>> covar = covar_module(x)  # Output: LazyVariable of size (2 x 10 x 10)


Initializes internal Module state, shared by both nn.Module and ScriptModule.

## Transforms¶

### Outcome Transforms¶

class botorch.models.transforms.outcome.OutcomeTransform[source]

Bases: torch.nn.modules.module.Module, abc.ABC

Abstract base class for outcome transforms.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

abstract forward(Y, Yvar=None)[source]

Transform the outcomes in a model’s training targets

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of training targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of observation noises associated with the training targets (if applicable).

Returns

• The transformed outcome observations.

• The transformed observation noise (if applicable).

Return type

A two-tuple with the transformed outcomes

untransform(Y, Yvar=None)[source]

Un-transform previously transformed outcomes

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of transfomred training targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of transformed observation noises associated with the training targets (if applicable).

Returns

• The un-transformed outcome observations.

• The un-transformed observation noise (if applicable).

Return type

A two-tuple with the un-transformed outcomes

untransform_posterior(posterior)[source]

Un-transform a posterior

Parameters

posterior (Posterior) – A posterior in the transformed space.

Return type

Posterior

Returns

The un-transformed posterior.

class botorch.models.transforms.outcome.ChainedOutcomeTransform(**transforms)[source]

Bases: botorch.models.transforms.outcome.OutcomeTransform, torch.nn.modules.container.ModuleDict

An outcome transform representing the chaining of individual transforms

Chaining of outcome transforms.

Parameters

transforms (OutcomeTransform) – The transforms to chain. Internally, the names of the kwargs are used as the keys for accessing the individual transforms on the module.

forward(Y, Yvar=None)[source]

Transform the outcomes in a model’s training targets

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of training targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of observation noises associated with the training targets (if applicable).

Returns

• The transformed outcome observations.

• The transformed observation noise (if applicable).

Return type

A two-tuple with the transformed outcomes

untransform(Y, Yvar=None)[source]

Un-transform previously transformed outcomes

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of transfomred training targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of transformed observation noises associated with the training targets (if applicable).

Returns

• The un-transformed outcome observations.

• The un-transformed observation noise (if applicable).

Return type

A two-tuple with the un-transformed outcomes

untransform_posterior(posterior)[source]

Un-transform a posterior

Parameters

posterior (Posterior) – A posterior in the transformed space.

Return type

Posterior

Returns

The un-transformed posterior.

class botorch.models.transforms.outcome.Standardize(m, outputs=None, batch_shape=torch.Size([]), min_stdv=1e-08)[source]

Standardize outcomes (zero mean, unit variance).

This module is stateful: If in train mode, calling forward updates the module state (i.e. the mean/std normalizing constants). If in eval mode, calling forward simply applies the standardization using the current module state.

Standardize outcomes (zero mean, unit variance).

Parameters
• m (int) – The output dimension.

• outputs (Optional[List[int]]) – Which of the outputs to standardize. If omitted, all outputs will be standardized.

• batch_shape (Size) – The batch_shape of the training targets.

• min_stddv – The minimum standard deviation for which to perform standardization (if lower, only de-mean the data).

forward(Y, Yvar=None)[source]

Standardize outcomes.

If the module is in train mode, this updates the module state (i.e. the mean/std normalizing constants). If the module is in eval mode, simply applies the normalization using the module state.

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of training targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of observation noises associated with the training targets (if applicable).

Returns

• The transformed outcome observations.

• The transformed observation noise (if applicable).

Return type

A two-tuple with the transformed outcomes

untransform(Y, Yvar=None)[source]

Un-standardize outcomes.

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of standardized targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of standardized observation noises associated with the targets (if applicable).

Returns

• The un-standardized outcome observations.

• The un-standardized observation noise (if applicable).

Return type

A two-tuple with the un-standardized outcomes

untransform_posterior(posterior)[source]

Un-standardize the posterior.

Parameters

posterior (Posterior) – A posterior in the standardized space.

Return type

Posterior

Returns

The un-standardized posterior. If the input posterior is a MVN, the transformed posterior is again an MVN.

class botorch.models.transforms.outcome.Log(outputs=None)[source]

Log-transform outcomes.

Useful if the targets are modeled using a (multivariate) log-Normal distribution. This means that we can use a standard GP model on the log-transformed outcomes and un-transform the model posterior of that GP.

Log-transform outcomes.

Parameters

outputs (Optional[List[int]]) – Which of the outputs to log-transform. If omitted, all outputs will be standardized.

forward(Y, Yvar=None)[source]

Log-transform outcomes.

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of training targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of observation noises associated with the training targets (if applicable).

Returns

• The transformed outcome observations.

• The transformed observation noise (if applicable).

Return type

A two-tuple with the transformed outcomes

untransform(Y, Yvar=None)[source]

Un-transform log-transformed outcomes

Parameters
• Y (Tensor) – A batch_shape x n x m-dim tensor of log-transfomred targets.

• Yvar (Optional[Tensor]) – A batch_shape x n x m-dim tensor of log- transformed observation noises associated with the training targets (if applicable).

Returns

• The exponentiated outcome observations.

• The exponentiated observation noise (if applicable).

Return type

A two-tuple with the un-transformed outcomes

untransform_posterior(posterior)[source]

Un-transform the log-transformed posterior.

Parameters

posterior (Posterior) – A posterior in the log-transformed space.

Return type

Posterior

Returns

The un-transformed posterior.

### Input Transforms¶

class botorch.models.transforms.input.InputTransform[source]

Bases: torch.nn.modules.module.Module, abc.ABC

Abstract base class for input transforms.

Initializes internal Module state, shared by both nn.Module and ScriptModule.

abstract forward(X)[source]

Transform the inputs to a model.

Parameters

X (Tensor) – A batch_shape x n x d-dim tensor of inputs.

Return type

Tensor

Returns

A batch_shape x n x d-dim tensor of transformed inputs.

untransform(X)[source]

Un-transform the inputs to a model.

Parameters

X (Tensor) – A batch_shape x n x d-dim tensor of transformed inputs.

Return type

Tensor

Returns

A batch_shape x n x d-dim tensor of un-transformed inputs.

class botorch.models.transforms.input.ChainedInputTransform(**transforms)[source]

Bases: botorch.models.transforms.input.InputTransform, torch.nn.modules.container.ModuleDict

An input transform representing the chaining of individual transforms

Chaining of input transforms.

Parameters

transforms (InputTransform) – The transforms to chain. Internally, the names of the kwargs are used as the keys for accessing the individual transforms on the module.

forward(X)[source]

Transform the inputs to a model.

Individual transforms are applied in sequence.

Parameters

X (Tensor) – A batch_shape x n x d-dim tensor of inputs.

Return type

Tensor

Returns

A batch_shape x n x d-dim tensor of transformed inputs.

untransform(X)[source]

Un-transform the inputs to a model.

Un-transforms of the individual transforms are applied in reverse sequence.

Parameters

X (Tensor) – A batch_shape x n x d-dim tensor of transformed inputs.

Return type

Tensor

Returns

A batch_shape x n x d-dim tensor of un-transformed inputs.

class botorch.models.transforms.input.Normalize(d, bounds=None, batch_shape=torch.Size([]))[source]

Normalize the inputs to the unit cube.

If no explicit bounds are provided this module is stateful: If in train mode, calling forward updates the module state (i.e. the normalizing bounds). If in eval mode, calling forward simply applies the normalization using the current module state.

Normalize the inputs to the unit cube.

Parameters
• d (int) – The dimension of the input space.

• bounds (Optional[Tensor]) – If provided, use these bounds to normalize the inputs. If omitted, learn the bounds in train mode.

• batch_shape (Size) – The batch shape of the inputs (asssuming input tensors of shape batch_shape x n x d). If provided, perform individual normalization per batch, otherwise uses a single normalization.

forward(X)[source]

Normalize the inputs.

If no explicit bounds are provided, this is stateful: In train mode, calling forward updates the module state (i.e. the normalizing bounds). In eval mode, calling forward simply applies the normalization using the current module state.

Parameters

X (Tensor) – A batch_shape x n x d-dim tensor of inputs.

Return type

Tensor

Returns

A batch_shape x n x d-dim tensor of inputs normalized to the module’s bounds.

untransform(X)[source]

Un-normalize the inputs.

Parameters

X (Tensor) – A batch_shape x n x d-dim tensor of normalized inputs.

Return type

Tensor

Returns

A batch_shape x n x d-dim tensor of un-normalized inputs.

property bounds

The bounds used for normalizing the inputs.

Return type

Tensor

### Transform Utilities¶

botorch.models.transforms.utils.lognorm_to_norm(mu, Cov)[source]

Compute mean and covariance of a MVN from those of the associated log-MVN

If Y is log-normal with mean mu_ln and covariance Cov_ln, then X ~ N(mu_n, Cov_n) with

Cov_n_{ij} = log(1 + Cov_ln_{ij} / (mu_ln_{i} * mu_n_{j})) mu_n_{i} = log(mu_ln_{i}) - 0.5 * log(1 + Cov_ln_{ii} / mu_ln_{i}**2)

Parameters
• mu (Tensor) – A batch_shape x n mean vector of the log-Normal distribution.

• Cov (Tensor) – A batch_shape x n x n covariance matrix of the log-Normal distribution.

Returns

• The batch_shape x n mean vector of the Normal distribution

• The batch_shape x n x n covariance matrix of the Normal distribution

Return type

A two-tuple containing

botorch.models.transforms.utils.norm_to_lognorm(mu, Cov)[source]

Compute mean and covariance of a log-MVN from its MVN sufficient statistics

If X ~ N(mu, Cov) and Y = exp(X), then Y is log-normal with

mu_ln_{i} = exp(mu_{i} + 0.5 * Cov_{ii}) Cov_ln_{ij} = exp(mu_{i} + mu_{j} + 0.5 * (Cov_{ii} + Cov_{jj})) * (exp(Cov_{ij}) - 1)

Parameters
• mu (Tensor) – A batch_shape x n mean vector of the Normal distribution.

• Cov (Tensor) – A batch_shape x n x n covariance matrix of the Normal distribution.

Returns

• The batch_shape x n mean vector of the log-Normal distribution.

• The batch_shape x n x n covariance matrix of the log-Normal

distribution.

Return type

A two-tuple containing

botorch.models.transforms.utils.norm_to_lognorm_mean(mu, var)[source]

Compute mean of a log-MVN from its MVN marginals

Parameters
• mu (Tensor) – A batch_shape x n mean vector of the Normal distribution.

• var (Tensor) – A batch_shape x n variance vectorof the Normal distribution.

Return type

Tensor

Returns

The batch_shape x n mean vector of the log-Normal distribution

botorch.models.transforms.utils.norm_to_lognorm_variance(mu, var)[source]

Compute variance of a log-MVN from its MVN marginals

Parameters
• mu (Tensor) – A batch_shape x n mean vector of the Normal distribution.

• var (Tensor) – A batch_shape x n variance vectorof the Normal distribution.

Return type

Tensor

Returns

The batch_shape x n variance vector of the log-Normal distribution.

## Utilities¶

### Model Conversion¶

Utilities for converting between different models.

botorch.models.converter.model_list_to_batched(model_list)[source]

Convert a ModelListGP to a BatchedMultiOutputGPyTorchModel.

Parameters

model_list (ModelListGP) – The ModelListGP to be converted to the appropriate BatchedMultiOutputGPyTorchModel. All sub-models must be of the same type and have the shape (batch shape and number of training inputs).

Return type

BatchedMultiOutputGPyTorchModel

Returns

The model converted into a BatchedMultiOutputGPyTorchModel.

Example

>>> list_gp = ModelListGP(gp1, gp2)
>>> batch_gp = model_list_to_batched(list_gp)

botorch.models.converter.batched_to_model_list(batch_model)[source]

Convert a BatchedMultiOutputGPyTorchModel to a ModelListGP.

Parameters

model_list – The BatchedMultiOutputGPyTorchModel to be converted to a ModelListGP.

Return type

ModelListGP

Returns

The model converted into a ModelListGP.

Example

>>> train_X = torch.rand(5, 2)
>>> train_Y = torch.rand(5, 2)
>>> list_gp = batched_to_model_list(batch_gp)


### Other Utilties¶

Utiltiy functions for models.

botorch.models.utils.multioutput_to_batch_mode_transform(train_X, train_Y, num_outputs, train_Yvar=None)[source]

Transforms training inputs for a multi-output model.

Used for multi-output models that internally are represented by a batched single output model, where each output is modeled as an independent batch.

Parameters
• train_X (Tensor) – A n x d or input_batch_shape x n x d (batch mode) tensor of training features.

• train_Y (Tensor) – A n x m or target_batch_shape x n x m (batch mode) tensor of training observations.

• num_outputs (int) – number of outputs

• train_Yvar (Optional[Tensor]) – A n x m or target_batch_shape x n x m tensor of observed measurement noise.

Return type

Tuple[Tensor, Tensor, Optional[Tensor]]

Returns

3-element tuple containing

• A input_batch_shape x m x n x d tensor of training features.

• A target_batch_shape x m x n tensor of training observations.

• A target_batch_shape x m x n tensor observed measurement noise.

botorch.models.utils.add_output_dim(X, original_batch_shape)[source]

Insert the output dimension at the correct location.

The trailing batch dimensions of X must match the original batch dimensions of the training inputs, but can also include extra batch dimensions.

Parameters
• X (Tensor) – A (new_batch_shape) x (original_batch_shape) x n x d tensor of features.

• original_batch_shape (Size) – the batch shape of the model’s training inputs.

Return type

Tuple[Tensor, int]

Returns

2-element tuple containing

• A (new_batch_shape) x (original_batch_shape) x m x n x d tensor of

features.

• The index corresponding to the output dimension.

botorch.models.utils.check_no_nans(Z)[source]

Check that tensor does not contain NaN values.

Raises an InputDataError if Z contains NaN values.

Parameters

Z (Tensor) – The input tensor.

Return type

None

botorch.models.utils.check_min_max_scaling(X, strict=False, atol=0.01, raise_on_fail=False)[source]

Check that tensor is normalized to the unit cube.

Parameters
• X (Tensor) – A batch_shape x n x d input tensor. Typically the training inputs of a model.

• strict (bool) – If True, require X to be scaled to the unit cube (rather than just to be contained within the unit cube).

• atol (float) – The tolerance for the boundary check. Only used if strict=True.

• raise_on_fail (bool) – If True, raise an exception instead of a warning.

Return type

None

botorch.models.utils.check_standardization(Y, atol_mean=0.01, atol_std=0.01, raise_on_fail=False)[source]

Check that tensor is standardized (zero mean, unit variance).

Parameters
• Y (Tensor) – The input tensor of shape batch_shape x n x m. Typically the train targets of a model. Standardization is checked across the n-dimension.

• atol_mean (float) – The tolerance for the mean check.

• atol_std (float) – The tolerance for the std check.

• raise_on_fail (bool) – If True, raise an exception instead of a warning.

Return type

None

botorch.models.utils.validate_input_scaling(train_X, train_Y, train_Yvar=None, raise_on_fail=False)[source]

Helper function to validate input data to models.

Parameters
• train_X (Tensor) – A n x d or batch_shape x n x d (batch mode) tensor of training features.

• train_Y (Tensor) – A n x m or batch_shape x n x m (batch mode) tensor of training observations.

• train_Yvar (Optional[Tensor]) – A batch_shape x n x m or batch_shape x n x m (batch mode) tensor of observed measurement noise.

• raise_on_fail (bool) – If True, raise an error instead of emitting a warning (only for normalization/standardization checks, an error is always raised if NaN values are present).

This function is typically called inside the constructor of standard BoTorch models. It validates the following: (i) none of the inputs contain NaN values (ii) the training data (train_X) is normalized to the unit cube (iii) the training targets (train_Y) are standardized (zero mean, unit var) No checks (other than the NaN check) are performed for observed variances (train_Yvar) at this point.

Return type

None

botorch.models.utils.mod_batch_shape(module, names, b)[source]

Recursive helper to modify gpytorch modules’ batch shape attribute.

Modifies the module in-place.

Parameters
• module (Module) – The module to be modified.

• names (List[str]) – The list of names to access the attribute. If the full name of the module is “module.sub_module.leaf_module”, this will be [“sub_module”, “leaf_module”].

• b (int) – The new size of the last element of the module’s batch_shape attribute.

Return type

None

botorch.models.utils.gpt_posterior_settings()[source]

Context manager for settings used for computing model posteriors.