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Fidelity kernel for training iterations/training data points (#178)
Summary: Pull Request resolved: #178 We added the fidelity kernels from Section 5.3 in https://arxiv.org/abs/1903.04703. Reviewed By: Balandat Differential Revision: D15695576 fbshipit-source-id: ccdc33640dc5f266816c6d0198445d5b2635c837
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‎botorch/models/fidelity_kernels/__init__.py‎

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#! /usr/bin/env python3
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# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved
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from .downsampling_kernel import DownsamplingKernel
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from .exponential_decay_kernel import ExpDecayKernel
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__all__ = ["ExpDecayKernel", "DownsamplingKernel"]

‎botorch/models/fidelity_kernels/downsampling_kernel.py‎

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#!/usr/bin/env python3
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# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved
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from typing import Optional
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import torch
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from gpytorch.constraints import Interval, Positive
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from gpytorch.kernels import Kernel
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from gpytorch.priors import Prior
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from torch import Tensor
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class DownsamplingKernel(Kernel):
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r"""
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Computes a covariance matrix based on the down sampling kernel
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between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}` (we expect 'd = 1'):
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.. math::
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\begin{equation*}
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k_\text{ds}(\mathbf{x_1}, \mathbf{x_2}) = c +
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(1 - \mathbf{x_1})^{1 + \delta} * (1 - \mathbf{x_2})^{1 + \delta}.
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\end{equation*}
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where
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* :math:`c` is an :attr:`offset` parameter,
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`\delta` is an :attr:`power` parameter
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Args:
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:attr:`power_constraint` (Constraint, optional):
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Constraint to place on power parameter. Default: `Positive`.
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:attr:`power_prior` (:class:`gpytorch.priors.Prior`):
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Prior over the power parameter (default `None`).
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:attr:`offset_constraint` (Constraint, optional):
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Constraint to place on offset parameter. Default: `Positive`.
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:attr:`active_dims` (list):
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List of data dimensions to operate on.
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`len(active_dims)` should equal `num_dimensions`.
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"""
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def __init__(
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self,
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power_prior: Optional[Prior] = None,
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offset_prior: Optional[Prior] = None,
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power_constraint: Optional[Interval] = None,
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offset_constraint: Optional[Interval] = None,
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**kwargs
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):
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super().__init__(**kwargs)
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if power_constraint is None:
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power_constraint = Positive()
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if offset_constraint is None:
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offset_constraint = Positive()
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self.register_parameter(
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name="raw_power",
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parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1)),
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)
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self.register_parameter(
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name="raw_offset",
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parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1)),
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)
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if power_prior is not None:
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self.register_prior(
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"power_prior",
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power_prior,
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lambda: self.power,
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lambda v: self._set_power(v),
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)
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self.register_constraint("raw_power", power_constraint)
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if offset_prior is not None:
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self.register_prior(
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"offset_prior",
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offset_prior,
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lambda: self.offset,
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lambda v: self._set_offset(v),
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)
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self.register_constraint("raw_offset", offset_constraint)
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@property
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def power(self) -> Tensor:
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return self.raw_power_constraint.transform(self.raw_power)
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@power.setter
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def power(self, value: Tensor) -> None:
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self._set_power(value)
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def _set_power(self, value: Tensor) -> None:
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if not torch.is_tensor(value):
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value = torch.as_tensor(value).to(self.raw_power)
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self.initialize(raw_power=self.raw_power_constraint.inverse_transform(value))
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@property
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def offset(self) -> Tensor:
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return self.raw_offset_constraint.transform(self.raw_offset)
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@offset.setter
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def offset(self, value: Tensor) -> None:
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self._set_offset(value)
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def _set_offset(self, value: Tensor) -> None:
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if not torch.is_tensor(value):
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value = torch.as_tensor(value).to(self.raw_offset)
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self.initialize(raw_offset=self.raw_offset_constraint.inverse_transform(value))
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def forward(
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self,
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x1: Tensor,
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x2: Tensor,
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diag: Optional[bool] = False,
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last_dim_is_batch: Optional[bool] = False,
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**params
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) -> Tensor:
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offset = self.offset.view(*self.batch_shape, 1, 1)
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power = self.power.view(*self.batch_shape, 1, 1)
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if last_dim_is_batch:
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x1 = x1.transpose(-1, -2).unsqueeze(-1)
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x2 = x2.transpose(-1, -2).unsqueeze(-1)
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x1_ = 1 - x1
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x2_ = 1 - x2
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if diag:
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return (x1_ * x2_).sum(dim=-1).pow(power + 1) + offset
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if x1.dim() == 2 and x2.dim() == 2:
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return torch.addmm(
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offset, x1_.pow(power + 1), x2_.transpose(-2, -1).pow(power + 1)
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)
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else:
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return (
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torch.matmul(x1_.pow(power + 1), x2_.transpose(-2, -1).pow(power + 1))
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+ offset
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)

‎botorch/models/fidelity_kernels/exponential_decay_kernel.py‎

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#!/usr/bin/env python3
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# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved
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from typing import Optional
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import torch
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from gpytorch.constraints import Interval, Positive
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from gpytorch.kernels import Kernel
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from gpytorch.priors import Prior
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from torch import Tensor
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class ExpDecayKernel(Kernel):
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r"""
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Computes a covariance matrix based on the exponential decay kernel
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between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}` (we expect d = 1):
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.. math::
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\begin{equation*}
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k_\text{expdecay}(\mathbf{x_1}, \mathbf{x_2}) = w +
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\frac{\beta^{\alpha}}{(\mathbf{x_1} + \mathbf{x_2} + \beta)^{\alpha}}.
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\end{equation*}
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where
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* :math:`w` is an :attr:`offset` parameter, `\beta` is an :attr:'lenthscale'
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parameter `\alpha` is an :attr:`power` parameter
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Args:
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:attr:`lengthscale_constraint` (Constraint, optional):
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Constraint to place on lengthscale parameter. Default: `Positive`.
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:attr:`lengthscale_prior` (:class:`gpytorch.priors.Prior`):
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Prior over the lengthscale parameter (default `None`).
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:attr:`power_constraint` (Constraint, optional):
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Constraint to place on power parameter. Default: `Positive`.
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:attr:`power_prior` (:class:`gpytorch.priors.Prior`):
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Prior over the power parameter (default `None`).
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:attr:`offset_constraint` (Constraint, optional):
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Constraint to place on offset parameter. Default: `Positive`.
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:attr:`active_dims` (list):
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List of data dimensions to operate on.
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`len(active_dims)` should equal `num_dimensions`.
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"""
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def __init__(
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self,
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power_prior: Optional[Prior] = None,
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offset_prior: Optional[Prior] = None,
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power_constraint: Optional[Interval] = None,
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offset_constraint: Optional[Interval] = None,
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**kwargs
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):
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super().__init__(has_lengthscale=True, **kwargs)
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if power_constraint is None:
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power_constraint = Positive()
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if offset_constraint is None:
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offset_constraint = Positive()
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self.register_parameter(
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name="raw_power",
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parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1)),
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)
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self.register_parameter(
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name="raw_offset",
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parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1)),
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)
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if power_prior is not None:
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self.register_prior(
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"power_prior",
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power_prior,
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lambda: self.power,
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lambda v: self._set_power(v),
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)
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self.register_constraint("raw_power", offset_constraint)
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if offset_prior is not None:
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self.register_prior(
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"offset_prior",
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offset_prior,
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lambda: self.offset,
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lambda v: self._set_offset(v),
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)
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self.register_constraint("raw_offset", offset_constraint)
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@property
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def power(self) -> Tensor:
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return self.raw_power_constraint.transform(self.raw_power)
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@power.setter
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def power(self, value: Tensor) -> None:
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self._set_power(value)
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def _set_power(self, value: Tensor) -> None:
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if not torch.is_tensor(value):
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value = torch.as_tensor(value).to(self.raw_power)
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self.initialize(raw_power=self.raw_power_constraint.inverse_transform(value))
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@property
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def offset(self) -> Tensor:
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return self.raw_offset_constraint.transform(self.raw_offset)
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@offset.setter
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def offset(self, value: Tensor) -> None:
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self._set_offset(value)
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def _set_offset(self, value: Tensor) -> None:
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if not torch.is_tensor(value):
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value = torch.as_tensor(value).to(self.raw_offset)
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self.initialize(raw_offset=self.raw_offset_constraint.inverse_transform(value))
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def forward(self, x1: Tensor, x2: Tensor, **params) -> Tensor:
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offset = self.offset.view(*self.batch_shape, 1, 1)
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power = self.power.view(*self.batch_shape, 1, 1)
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x1_ = x1.div(self.lengthscale)
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x2_ = x2.div(self.lengthscale)
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diff = self.covar_dist(x1_, -x2_, **params)
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res = offset + (diff + 1).pow(-power)
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return res

‎test/models/fidelity_kernels/__init__.py‎

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#! /usr/bin/env python3
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# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved

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