Support for priors in OAK Kernel (#2535)

Summary:
Pull Request resolved: #2535

Added support for registering priors to the coefficients of the OrthogonalAdditiveKernel. Useful for incentivizing sparsity in the additive components, and improve identifiability between first- and second-order components.

Differential Revision: D61730632

botorch/models/kernels/orthogonal_additive_kernel.py

@@ -11,10 +11,15 @@
 from botorch.exceptions.errors import UnsupportedError
 from gpytorch.constraints import Interval, Positive
 from gpytorch.kernels import Kernel
+from gpytorch.priors import Prior
 
 from torch import nn, Tensor
 
 _positivity_constraint = Positive()
+SECOND_ORDER_PRIOR_ERROR_MSG = (
+    "Second order is disabled, but there is a prior on the second order coefficients. "
+    "Please remove the second order prior or enable second order terms."
+)
 
 
 class OrthogonalAdditiveKernel(Kernel):
@@ -40,6 +45,9 @@ def __init__(
         dtype: Optional[torch.dtype] = None,
         device: Optional[torch.device] = None,
         coeff_constraint: Interval = _positivity_constraint,
+        offset_prior: Optional[Prior] = None,
+        coeffs_1_prior: Optional[Prior] = None,
+        coeffs_2_prior: Optional[Prior] = None,
     ):
         """
         Args:
@@ -55,6 +63,9 @@ def __init__(
         """
         super().__init__(batch_shape=batch_shape)
         self.base_kernel = base_kernel
+        if not second_order and coeffs_2_prior is not None:
+            raise AttributeError(SECOND_ORDER_PRIOR_ERROR_MSG)
+
         # integration nodes, weights for [0, 1]
         tkwargs = {"dtype": dtype, "device": device}
         z, w = leggauss(deg=quad_deg, a=0, b=1, **tkwargs)
@@ -82,6 +93,29 @@ def __init__(
                 else None
             ),
         )
+        if offset_prior is not None:
+            self.register_prior(
+                "offset_prior",
+                offset_prior,
+                self._offset_param,
+                self._offset_closure,
+            )
+        if coeffs_1_prior is not None:
+            self.register_prior(
+                "coeffs_1_prior",
+                coeffs_1_prior,
+                self._coeffs_1_param,
+                self._coeffs_1_closure,
+            )
+        if coeffs_2_prior is not None:
+            self.register_prior(
+                "coeffs_2_prior",
+                coeffs_2_prior,
+                self._coeffs_2_param,
+                self._coeffs_2_closure,
+            )
+
+        # for second order interactions, we only
         if second_order:
             self._rev_triu_indices = torch.tensor(
                 _reverse_triu_indices(dim),
@@ -140,6 +174,56 @@ def coeffs_2(self) -> Optional[Tensor]:
         else:
             return None
 
+    def _coeffs_1_param(self, m):
+        return m.coeffs_1
+
+    def _coeffs_2_param(self, m):
+        return m.coeffs_2
+
+    def _offset_param(self, m):
+        return m.offset
+
+    def _coeffs_1_closure(self, m, v):
+        return m._set_coeffs_1(v)
+
+    def _coeffs_2_closure(self, m, v):
+        return m._set_coeffs_2(v)
+
+    def _offset_closure(self, m, v):
+        return m._set_offset(v)
+
+    def _set_coeffs_1(self, value):
+        if not torch.is_tensor(value):
+            value = torch.as_tensor(value).to(self.raw_coeffs_1)
+        self.initialize(raw_coeffs_1=self.coeff_constraint.inverse_transform(value))
+
+    def _set_coeffs_2(self, value):
+        if not isinstance(value, Tensor) or value.tril().abs().sum() == 0:
+            raise ValueError(
+                "Second order coefficients must be provided as an "
+                "upper-triangular matrix."
+            )
+        triu_indices = torch.triu_indices(self.dim, self.dim, offset=1)
+        value = value[..., triu_indices[0], triu_indices[1]].to(self.raw_coeffs_2)
+        self.initialize(raw_coeffs_2=self.coeff_constraint.inverse_transform(value))
+
+    def _set_offset(self, value):
+        if not torch.is_tensor(value):
+            value = torch.as_tensor(value).to(self.raw_offset)
+        self.initialize(raw_offset=self.coeff_constraint.inverse_transform(value))
+
+    @coeffs_1.setter
+    def coeffs_1(self, value):
+        self._set_coeffs_1(value)
+
+    @coeffs_2.setter
+    def coeffs_2(self, value):
+        self._set_coeffs_2(value)
+
+    @offset.setter  # offsetter, lol
+    def offset(self, value):
+        self._set_offset(value)
+
     def forward(
         self,
         x1: Tensor,

test/models/kernels/test_orthogonal_additive_kernel.py

@@ -6,10 +6,15 @@
 
 import torch
 from botorch.exceptions.errors import UnsupportedError
-from botorch.models.kernels.orthogonal_additive_kernel import OrthogonalAdditiveKernel
+from botorch.models.kernels.orthogonal_additive_kernel import (
+    OrthogonalAdditiveKernel,
+    SECOND_ORDER_PRIOR_ERROR_MSG,
+)
 from botorch.utils.testing import BotorchTestCase
 from gpytorch.kernels import MaternKernel, RBFKernel
 from gpytorch.lazy import LazyEvaluatedKernelTensor
+from gpytorch.priors import LogNormalPrior
+from gpytorch.priors.torch_priors import GammaPrior, HalfCauchyPrior
 from torch import nn, Tensor
 
 
@@ -118,6 +123,112 @@ def test_kernel(self):
                 tol = 1e-5
                 self.assertTrue(((K_ortho @ oak.w).squeeze(-1) < tol).all())
 
+    def test_priors(self):
+        d = 5
+        dtypes = [torch.float, torch.double]
+        batch_shapes = [(), (2,), (7, 2)]
+        for dtype in dtypes:
+            for batch_shape in batch_shapes:
+                # test with default args and batch_shape = None in second_order
+                offset_prior = HalfCauchyPrior(0.1)
+                coeffs_1_prior = LogNormalPrior(0, 1)
+                coeffs_2_prior = GammaPrior(3, 6)
+                oak = OrthogonalAdditiveKernel(
+                    RBFKernel(),
+                    dim=d,
+                    batch_shape=None,
+                    second_order=True,
+                    offset_prior=offset_prior,
+                    coeffs_1_prior=coeffs_1_prior,
+                    coeffs_2_prior=coeffs_2_prior,
+                )
+
+                self.assertIsInstance(oak.offset_prior, HalfCauchyPrior)
+                self.assertIsInstance(oak.coeffs_1_prior, LogNormalPrior)
+                self.assertEqual(oak.coeffs_1_prior.scale, 1)
+                self.assertEqual(oak.coeffs_2_prior.concentration, 3)
+
+                oak = OrthogonalAdditiveKernel(
+                    RBFKernel(),
+                    dim=d,
+                    batch_shape=None,
+                    second_order=True,
+                    coeffs_1_prior=None,
+                    coeffs_2_prior=coeffs_2_prior,
+                )
+                self.assertEqual(oak.coeffs_2_prior.concentration, 3)
+                with self.assertRaisesRegex(
+                    AttributeError,
+                    "'OrthogonalAdditiveKernel' object has no attribute "
+                    "'coeffs_1_prior",
+                ):
+                    _ = oak.coeffs_1_prior
+                    # test with batch_shape = None in second_order
+                    oak = OrthogonalAdditiveKernel(
+                        RBFKernel(),
+                        dim=d,
+                        batch_shape=batch_shape,
+                        second_order=True,
+                        coeffs_1_prior=coeffs_1_prior,
+                    )
+            with self.assertRaisesRegex(AttributeError, SECOND_ORDER_PRIOR_ERROR_MSG):
+                OrthogonalAdditiveKernel(
+                    RBFKernel(),
+                    dim=d,
+                    batch_shape=None,
+                    second_order=False,
+                    coeffs_2_prior=GammaPrior(1, 1),
+                )
+        # test no prior
+        oak = OrthogonalAdditiveKernel(
+            RBFKernel(), dim=d, batch_shape=None, second_order=True
+        )
+
+    def test_set_coeffs(self):
+        d = 5
+        dtype = torch.double
+        oak = OrthogonalAdditiveKernel(
+            RBFKernel(),
+            dim=d,
+            batch_shape=None,
+            second_order=True,
+            dtype=dtype,
+        )
+        constraint = oak.coeff_constraint
+        coeffs_1 = torch.arange(d).to(dtype)
+        coeffs_2 = torch.ones((d * d)).reshape(d, d).triu().to(dtype)
+        oak.coeffs_1 = coeffs_1
+        oak.coeffs_2 = coeffs_2
+
+        self.assertAllClose(
+            oak.raw_coeffs_1,
+            constraint.inverse_transform(coeffs_1),
+        )
+        # raw_coeffs_2 has length d * (d-1) / 2
+        self.assertAllClose(
+            oak.raw_coeffs_2, constraint.inverse_transform(torch.ones(10).to(dtype))
+        )
+
+        batch_shapes = torch.Size([2]), torch.Size([5, 2])
+        for batch_shape in batch_shapes:
+            dtype = torch.double
+            oak = OrthogonalAdditiveKernel(
+                RBFKernel(),
+                dim=d,
+                batch_shape=batch_shape,
+                second_order=True,
+                dtype=dtype,
+            )
+            constraint = oak.coeff_constraint
+            coeffs_1 = torch.arange(d).to(dtype)
+            coeffs_2 = torch.ones((d * d)).reshape(d, d).triu().to(dtype)
+            oak.coeffs_1 = coeffs_1
+            oak.coeffs_2 = coeffs_2
+
+            self.assertEqual(oak.raw_coeffs_1.shape, batch_shape + torch.Size([5]))
+            # raw_coeffs_2 has length d * (d-1) / 2
+            self.assertEqual(oak.raw_coeffs_2.shape, batch_shape + torch.Size([10]))
+
 
 def isposdef(A: Tensor) -> bool:
     """Determines whether A is positive definite or not, by attempting a Cholesky