# Batch GPs¶

GPyTorch makes it possible to train/perform inference with a batch of Gaussian processes in parallel. This can be useful for a number of applications:

• Modeling a function with multiple (independent) outputs
• Performing efficient cross-validation
• Parallel acquisition function sampling for Bayesian optimization
• And more!

Here we highlight a number of common batch GP scenarios and how to construct them in GPyTorch.

## A function with multiple (independent) outputs¶

(To model a multi-output function where the outputs are dependent, see the multitask GP examples.)

Consider the following simple GP:

>>> class ExactGPModel(gpytorch.models.ExactGP):
>>>     def __init__(self, train_x, train_y, likelihood, num_outputs):
>>>         super(ExactGPModel, self).__init__(train_x, train_y, likelihood)
>>>         self.mean_module = gpytorch.means.ConstantMean(batch_size=num_outputs)
>>>         self.covar_module = gpytorch.kernels.ScaleKernel(
>>>             gpytorch.kernels.RBFKernel(batch_size=num_outputs),
>>>             batch_size=num_outputs
>>>         )
>>>         self.num_outputs = num_outputs
>>>
>>>     def forward(self, x):
>>>         x = x.expand(self.num_outputs, x.shape)
>>>
>>>         mean_x = self.mean_module(x)
>>>         covar_x = self.covar_module(x)
>>>         return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)


This model, which can be used in non-batch mode, can also easily be used for a multi-output model. The model would expect:

• train_x - a n x 1 or n x d tensor (note that it should not be a 1D tensor!)
• train_y - a num_outputs x n tensor

In the forward pass, we expand x to be a num_outputs x n x d tensor. This makes the mean module and covariance modules return num_outputs x n and num_outputs x n x n outputs, respectively. Setting batch_size=num_outputs for all the modules ensures that the model will learn output-specific hyperparameters (rather than sharing the same lengthscale, etc. for all outputs). The corresponding MVN distribution is a batch of num_outputs n-dimensional Gaussians.

## Batches of testing data¶

For cross validation, or for some BayesOpt applications, it may make sense to evaluate the GP on different batches of test data. This can be accomplished by using a standard (non-batch) GP model. At test time, feeding a b x n x d tensor into the model will then return b batches of n test points.

NOTE: The test inputs MUST be a 3D tensor. For one dimensional inputs, the tensor should be b x n x 1.