[Bug] MultiTaskGP without data

[AdrianSosic]

🐛 Bug

The evaluation of the MultiTaskGP fails in cases where there is no training data available. The same situation works without problems for a SingleTaskGP, which conceptually should simply return values from the prior. However, the MultiTaskGP crashes with a ZeroDivisionError.

To reproduce

SingleTaskGP

import torch
from botorch.models.gp_regression import SingleTaskGP

N_train = 0
N_test = 10

train_X = torch.rand(N_train, 2, dtype=torch.float64)
train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)

test_X = torch.rand(N_test, 2, dtype=torch.float64)

model = SingleTaskGP(train_X, train_Y)
model.posterior(test_X).mean

MultiTaskGP

import torch
from botorch.models.multitask import MultiTaskGP

N_train = 0
N_test = 10

train_X1, train_X2 = torch.rand(N_train, 2), torch.rand(N_train, 2)
i1, i2 = torch.zeros(N_train, 1), torch.ones(N_train, 1)
train_X = torch.cat(
    [
        torch.cat([train_X1, i1], -1),
        torch.cat([train_X2, i2], -1),
    ]
)
train_Y = torch.randn(train_X.shape[0], 1)

test_X1, test_X2 = torch.rand(N_train, 2), torch.rand(N_train, 2)
i1, i2 = torch.zeros(N_train, 1), torch.ones(N_train, 1)
test_X = torch.cat(
    [
        torch.cat([test_X1, i1], -1),
        torch.cat([test_X2, i2], -1),
    ]
)

model = MultiTaskGP(train_X, train_Y, task_feature=-1)
model.posterior(test_X).mean

Stack trace/error message

ZeroDivisionError: integer division or modulo by zero

Expected Behavior

Just like the SingleTaskGP, the MultiTaskGP should return the prior values.

System information

Please complete the following information:

• BoTorch Version: 0.11.0
• GPyTorch Version: 1.11
• PyTorch Version: 2.3.0
• OS: macOS

[sdaulton]

Thanks for flagging this. This appears to be an issue in IndexKernel: specifically, InterpolatedLinearOperator doesn't work when left_interp_indices and right_interp_indices are empty tensors. Would you mind opening an issue in gpytorch?

[AdrianSosic]

Sure thing, done! Thanks for the help 🥇