InteractionFeatures input transform (#2560)

Summary:
Pull Request resolved: #2560

InteractionFeatures input transform to compute first-order interactions between inputs.

Used for feature importance work in conjunction with (warped) linear models.

Reviewed By: sdaulton

Differential Revision: D63673008

botorch/models/transforms/input.py

@@ -24,7 +24,7 @@
 import torch
 from botorch.exceptions.errors import BotorchTensorDimensionError
 from botorch.exceptions.warnings import UserInputWarning
-from botorch.models.transforms.utils import subset_transform
+from botorch.models.transforms.utils import interaction_features, subset_transform
 from botorch.models.utils import fantasize
 from botorch.utils.rounding import approximate_round, OneHotArgmaxSTE, RoundSTE
 from gpytorch import Module as GPyTorchModule
@@ -1246,6 +1246,30 @@ def transform(self, X: Tensor) -> Tensor:
         return appended_X.view(*X.shape[:-2], -1, appended_X.shape[-1])
 
 
+class InteractionFeatures(AppendFeatures):
+    r"""A transform that appends the first-order interaction terms $x_i * x_j$ for
+    all or a subset of the input variables."""
+
+    def __init__(
+        self,
+        indices: Optional[list[int]] = None,
+    ) -> None:
+        r"""Initializes the InteractionFeatures transform.
+
+        Args:
+            indices: Indices of the subset of dimensions to compute interaction
+                features on.
+        """
+
+        super().__init__(
+            f=interaction_features,
+            indices=indices,
+            transform_on_train=True,
+            transform_on_eval=True,
+            transform_on_fantasize=True,
+        )
+
+
 class FilterFeatures(InputTransform, Module):
     r"""A transform that filters the input with a given set of features indices.
 

botorch/models/transforms/utils.py

@@ -126,3 +126,20 @@ def f(self, X: Tensor) -> Tensor:
         return Y
 
     return f
+
+
+def interaction_features(X: Tensor) -> Tensor:
+    """Computes the interaction features between the inputs.
+    Args:
+        X: A `batch_shape x q x d`-dim tensor of inputs.
+        indices: The input dimensions to generate interaction features for.
+    Returns:
+        A `n x q x 1 x (d * (d-1) / 2))`-dim tensor of interaction features.
+    """
+    dim = X.shape[-1]
+    row_idcs, col_idcs = torch.triu_indices(dim, dim, offset=1)
+    return (
+        (X.unsqueeze(-1) @ X.unsqueeze(-2))
+        .triu(diagonal=1)[..., row_idcs, col_idcs]
+        .unsqueeze(-2)
+    )

test/models/transforms/test_input.py

@@ -19,6 +19,7 @@
     InputPerturbation,
     InputStandardize,
     InputTransform,
+    InteractionFeatures,
     Log10,
     Normalize,
     OneHotToNumeric,
@@ -1502,6 +1503,45 @@ def f2(x: Tensor, n_f: int = 1) -> Tensor:
             self.assertEqual(X_transformed.shape, torch.Size((10, 4)))
 
 
+class TestInteractionFeatures(BotorchTestCase):
+    def test_interaction_features(self) -> None:
+        interaction = InteractionFeatures()
+        X = torch.arange(6, dtype=torch.float).reshape(2, 3)
+        X_tf = interaction(X)
+        self.assertTrue(X_tf.shape, torch.Size([2, 6]))
+
+        # test correct output values
+        self.assertTrue(
+            torch.equal(
+                X_tf,
+                Tensor(
+                    [[0.0, 1.0, 2.0, 0.0, 0.0, 2.0], [3.0, 4.0, 5.0, 12.0, 15.0, 20.0]]
+                ),
+            )
+        )
+        X = torch.arange(6, dtype=torch.float).reshape(2, 3)
+        interaction = InteractionFeatures(indices=[1, 2])
+        X_tf = interaction(X)
+        self.assertTrue(
+            torch.equal(
+                X_tf,
+                Tensor([[0.0, 1.0, 2.0, 2.0], [3.0, 4.0, 5.0, 20.0]]),
+            )
+        )
+        with self.assertRaisesRegex(
+            IndexError, "index 2 is out of bounds for dimension 0 with size 2"
+        ):
+            interaction(torch.rand(4, 2))
+
+        # test batched evaluation
+        interaction = InteractionFeatures()
+        X_tf = interaction(torch.rand(4, 2, 4))
+        self.assertTrue(X_tf.shape, torch.Size([4, 2, 10]))
+
+        X_tf = interaction(torch.rand(5, 7, 3, 4))
+        self.assertTrue(X_tf.shape, torch.Size([5, 7, 3, 10]))
+
+
 class TestFilterFeatures(BotorchTestCase):
     def test_filter_features(self) -> None:
         with self.assertRaises(ValueError):