#! /usr/bin/env python3
r"""
Multi-Task GP models.
"""
from typing import List, Optional, Tuple
import torch
from gpytorch.distributions.multivariate_normal import MultivariateNormal
from gpytorch.kernels.index_kernel import IndexKernel
from gpytorch.kernels.matern_kernel import MaternKernel
from gpytorch.kernels.scale_kernel import ScaleKernel
from gpytorch.likelihoods.gaussian_likelihood import (
FixedNoiseGaussianLikelihood,
GaussianLikelihood,
)
from gpytorch.means.constant_mean import ConstantMean
from gpytorch.models.exact_gp import ExactGP
from gpytorch.priors.torch_priors import GammaPrior
from torch import Tensor
from .gpytorch import MultiTaskGPyTorchModel
[docs]class MultiTaskGP(ExactGP, MultiTaskGPyTorchModel):
r"""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.
"""
def __init__(
self,
train_X: Tensor,
train_Y: Tensor,
task_feature: int,
output_tasks: Optional[List[int]] = None,
rank: Optional[int] = None,
) -> None:
r"""Multi-Task GP model using an ICM kernel, inferring observation noise.
Args:
train_X: 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: A `n` or `b x n` (batch mode) tensor of training
observations.
task_feature: The index of the task feature
(`-d <= task_feature <= d`).
output_tasks: A list of task indices for which to compute model
outputs for. If omitted, return outputs for all task indices.
rank: 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.stack([
>>> torch.cat([X1, i1], -1), torch.cat([X2, i2], -1),
>>> ])
>>> train_Y = torch.cat(f1(X1), f2(X2))
>>> model = MultiTaskGP(train_X, train_Y, task_feature=-1)
"""
if train_X.ndimension() != 2:
# Currently, batch mode MTGPs are blocked upstream in GPyTorch
raise ValueError(f"Unsupported shape {train_X.shape} for train_X.")
d = train_X.shape[-1] - 1
if not (-d <= task_feature <= d):
raise ValueError(f"Must have that -{d} <= task_feature <= {d}")
all_tasks = train_X[:, task_feature].unique().to(dtype=torch.long).tolist()
if output_tasks is None:
output_tasks = all_tasks
else:
if any(t not in all_tasks for t in output_tasks):
raise RuntimeError("All output tasks must be present in input data.")
self._output_tasks = output_tasks
# TODO (T41270962): Support task-specific noise levels in likelihood
likelihood = GaussianLikelihood(noise_prior=GammaPrior(1.1, 0.05))
# construct indexer to be used in forward
self._task_feature = task_feature
self._base_idxr = torch.arange(d)
self._base_idxr[task_feature:] += 1 # exclude task feature
super().__init__(
train_inputs=train_X, train_targets=train_Y, likelihood=likelihood
)
self.mean_module = ConstantMean()
self.covar_module = ScaleKernel(
base_kernel=MaternKernel(
nu=2.5, ard_num_dims=d, lengthscale_prior=GammaPrior(3.0, 6.0)
),
outputscale_prior=GammaPrior(2.0, 0.15),
)
num_tasks = len(all_tasks)
self._rank = rank if rank is not None else num_tasks
# TODO: Add LKJ prior for the index kernel
self.task_covar_module = IndexKernel(num_tasks=num_tasks, rank=self._rank)
self.to(train_X)
def _split_inputs(self, x: Tensor) -> Tuple[Tensor, Tensor]:
r"""Extracts base features and task indices from input data.
Args:
x: The full input tensor with trailing dimension of size `d + 1`.
Should be of float/double data type.
Returns:
2-element tuple containin
- A `q x d` or `b x q x d` (batch mode) tensor with trailing
dimension made up of the `d` non-task-index columns of `x`, arranged
in the order as specified by the indexer generated during model
instantiation.
- A `q` or `b x q` (batch mode) tensor of long data type containing
the task indices.
"""
batch_shape, d = x.shape[:-2], x.shape[-1]
x_basic = x[..., self._base_idxr].view(batch_shape + torch.Size([-1, d - 1]))
task_idcs = (
x[..., self._task_feature]
.view(batch_shape + torch.Size([-1, 1]))
.to(dtype=torch.long)
)
return x_basic, task_idcs
[docs] def forward(self, x: Tensor) -> MultivariateNormal:
x_basic, task_idcs = self._split_inputs(x)
# Compute base mean and covariance
mean_x = self.mean_module(x_basic)
covar_x = self.covar_module(x_basic)
# Compute task covariances
covar_i = self.task_covar_module(task_idcs)
# Combine the two in an ICM fashion
covar = covar_x.mul(covar_i)
return MultivariateNormal(mean_x, covar)
[docs]class FixedNoiseMultiTaskGP(MultiTaskGP):
r"""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`).
"""
def __init__(
self,
train_X: Tensor,
train_Y: Tensor,
train_Yvar: Tensor,
task_feature: int,
output_tasks: Optional[List[int]] = None,
rank: Optional[int] = None,
) -> None:
r"""Multi-Task GP model using an ICM kernel and known observatioon noise.
Args:
train_X: 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: A `n` or `b x n` (batch mode) tensor of training
observations.
train_Yvar: A `n` or `b x n` (batch mode) tensor of observation
noise standard errors.
task_feature: The index of the task feature
(`-d <= task_feature <= d`).
output_tasks: A list of task indices for which to compute model
outputs for. If omitted, return outputs for all task indices.
rank: 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)
"""
# We'll instatiate a MultiTaskGP and simply override the likelihood
super().__init__(
train_X=train_X,
train_Y=train_Y,
task_feature=task_feature,
output_tasks=output_tasks,
rank=rank,
)
self.likelihood = FixedNoiseGaussianLikelihood(noise=train_Yvar)
self.to(train_X)
