Source code for pyro.contrib.gp.models.model

from __future__ import absolute_import, division, print_function

from pyro.contrib.gp.parameterized import Parameterized


def _zero_mean_function(x):
    return 0


[docs]class GPModel(Parameterized): r""" Base class for Gaussian Process models. The core of a Gaussian Process is a covariance function :math:`k` which governs the similarity between input points. Given :math:`k`, we can establish a distribution over functions :math:`f` by a multivarite normal distribution .. math:: p(f(X)) = \mathcal{N}(0, k(X, X)), where :math:`X` is any set of input points and :math:`k(X, X)` is a covariance matrix whose entries are outputs :math:`k(x, z)` of :math:`k` over input pairs :math:`(x, z)`. This distribution is usually denoted by .. math:: f \sim \mathcal{GP}(0, k). .. note:: Generally, beside a covariance matrix :math:`k`, a Gaussian Process can also be specified by a mean function :math:`m` (which is a zero-value function by default). In that case, its distribution will be .. math:: p(f(X)) = \mathcal{N}(m(X), k(X, X)). Gaussian Process models are :class:`~pyro.contrib.gp.util.Parameterized` subclasses. So its parameters can be learned, set priors, or fixed by using corresponding methods from :class:`~pyro.contrib.gp.util.Parameterized`. A typical way to define a Gaussian Process model is >>> X = torch.tensor([[1., 5, 3], [4, 3, 7]]) >>> y = torch.tensor([2., 1]) >>> kernel = gp.kernels.RBF(input_dim=3) >>> kernel.set_prior("variance", dist.Uniform(torch.tensor(0.5), torch.tensor(1.5))) >>> kernel.set_prior("lengthscale", dist.Uniform(torch.tensor(1.0), torch.tensor(3.0))) >>> gpr = gp.models.GPRegression(X, y, kernel) There are two ways to train a Gaussian Process model: + Using an MCMC algorithm (in module :mod:`pyro.infer.mcmc`) on :meth:`model` to get posterior samples for the Gaussian Process's parameters. For example: >>> hmc_kernel = HMC(gpr.model) >>> mcmc = MCMC(hmc_kernel, num_samples=10) >>> mcmc.run() >>> ls_name = "GPR/RBF/lengthscale" >>> posterior_ls = mcmc.get_samples()[ls_name] + Using a variational inference on the pair :meth:`model`, :meth:`guide`: >>> optimizer = torch.optim.Adam(gpr.parameters(), lr=0.01) >>> loss_fn = pyro.infer.TraceMeanField_ELBO().differentiable_loss >>> >>> for i in range(1000): ... svi.step() # doctest: +SKIP ... optimizer.zero_grad() ... loss = loss_fn(gpr.model, gpr.guide) # doctest: +SKIP ... loss.backward() # doctest: +SKIP ... optimizer.step() To give a prediction on new dataset, simply use :meth:`forward` like any PyTorch :class:`torch.nn.Module`: >>> Xnew = torch.tensor([[2., 3, 1]]) >>> f_loc, f_cov = gpr(Xnew, full_cov=True) Reference: [1] `Gaussian Processes for Machine Learning`, Carl E. Rasmussen, Christopher K. I. Williams :param torch.Tensor X: A input data for training. Its first dimension is the number of data points. :param torch.Tensor y: An output data for training. Its last dimension is the number of data points. :param ~pyro.contrib.gp.kernels.kernel.Kernel kernel: A Pyro kernel object, which is the covariance function :math:`k`. :param callable mean_function: An optional mean function :math:`m` of this Gaussian process. By default, we use zero mean. :param float jitter: A small positive term which is added into the diagonal part of a covariance matrix to help stablize its Cholesky decomposition. """ def __init__(self, X, y, kernel, mean_function=None, jitter=1e-6): super(GPModel, self).__init__() self.set_data(X, y) self.kernel = kernel self.mean_function = (mean_function if mean_function is not None else _zero_mean_function) self.jitter = jitter
[docs] def model(self): """ A "model" stochastic function. If ``self.y`` is ``None``, this method returns mean and variance of the Gaussian Process prior. """ raise NotImplementedError
[docs] def guide(self): """ A "guide" stochastic function to be used in variational inference methods. It also gives posterior information to the method :meth:`forward` for prediction. """ raise NotImplementedError
[docs] def forward(self, Xnew, full_cov=False): r""" Computes the mean and covariance matrix (or variance) of Gaussian Process posterior on a test input data :math:`X_{new}`: .. math:: p(f^* \mid X_{new}, X, y, k, \theta), where :math:`\theta` are parameters of this model. .. note:: Model's parameters :math:`\theta` together with kernel's parameters have been learned from a training procedure (MCMC or SVI). :param torch.Tensor Xnew: A input data for testing. Note that ``Xnew.shape[1:]`` must be the same as ``X.shape[1:]``. :param bool full_cov: A flag to decide if we want to predict full covariance matrix or just variance. :returns: loc and covariance matrix (or variance) of :math:`p(f^*(X_{new}))` :rtype: tuple(torch.Tensor, torch.Tensor) """ raise NotImplementedError
[docs] def set_data(self, X, y=None): """ Sets data for Gaussian Process models. Some examples to utilize this method are: .. doctest:: :hide: >>> X = torch.tensor([[1., 5, 3], [4, 3, 7]]) >>> y = torch.tensor([2., 1]) >>> kernel = gp.kernels.RBF(input_dim=3) >>> kernel.set_prior("variance", dist.Uniform(torch.tensor(0.5), torch.tensor(1.5))) >>> kernel.set_prior("lengthscale", dist.Uniform(torch.tensor(1.0), torch.tensor(3.0))) + Batch training on a sparse variational model: >>> Xu = torch.tensor([[1., 0, 2]]) # inducing input >>> likelihood = gp.likelihoods.Gaussian() >>> vsgp = gp.models.VariationalSparseGP(X, y, kernel, Xu, likelihood) >>> optimizer = torch.optim.Adam(vsgp.parameters(), lr=0.01) >>> loss_fn = pyro.infer.TraceMeanField_ELBO().differentiable_loss >>> batched_X, batched_y = X.split(split_size=10), y.split(split_size=10) >>> for Xi, yi in zip(batched_X, batched_y): ... optimizer.zero_grad() ... vsgp.set_data(Xi, yi) ... svi.step() # doctest: +SKIP ... loss = loss_fn(vsgp.model, vsgp.guide) # doctest: +SKIP ... loss.backward() # doctest: +SKIP ... optimizer.step() + Making a two-layer Gaussian Process stochastic function: >>> gpr1 = gp.models.GPRegression(X, None, kernel) >>> Z, _ = gpr1.model() >>> gpr2 = gp.models.GPRegression(Z, y, kernel) >>> def two_layer_model(): ... Z, _ = gpr1.model() ... gpr2.set_data(Z, y) ... return gpr2.model() References: [1] `Scalable Variational Gaussian Process Classification`, James Hensman, Alexander G. de G. Matthews, Zoubin Ghahramani [2] `Deep Gaussian Processes`, Andreas C. Damianou, Neil D. Lawrence :param torch.Tensor X: A input data for training. Its first dimension is the number of data points. :param torch.Tensor y: An output data for training. Its last dimension is the number of data points. """ if y is not None and X.size(0) != y.size(-1): raise ValueError("Expected the number of input data points equal to the " "number of output data points, but got {} and {}." .format(X.size(0), y.size(-1))) self.X = X self.y = y
def _check_Xnew_shape(self, Xnew): """ Checks the correction of the shape of new data. :param torch.Tensor Xnew: A input data for testing. Note that ``Xnew.shape[1:]`` must be the same as ``self.X.shape[1:]``. """ if Xnew.dim() != self.X.dim(): raise ValueError("Train data and test data should have the same " "number of dimensions, but got {} and {}." .format(self.X.dim(), Xnew.dim())) if self.X.shape[1:] != Xnew.shape[1:]: raise ValueError("Train data and test data should have the same " "shape of features, but got {} and {}." .format(self.X.shape[1:], Xnew.shape[1:]))