# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
# pyre-strict
from copy import deepcopy
from functools import partial
from typing import Any, Callable, List, Optional, Union
import torch
from ax.utils.common.typeutils import checked_cast, not_none
from ax.utils.sensitivity.derivative_gp import posterior_derivative
from botorch.models.model import Model
from botorch.posteriors.gpytorch import GPyTorchPosterior
from botorch.posteriors.posterior import Posterior
from botorch.sampling.normal import SobolQMCNormalSampler
from botorch.utils.sampling import draw_sobol_samples
from botorch.utils.transforms import unnormalize
from gpytorch.distributions import MultivariateNormal
[docs]def sample_discrete_parameters(
input_mc_samples: torch.Tensor,
discrete_features: Union[None, List[int]],
bounds: torch.Tensor,
num_mc_samples: int,
) -> torch.Tensor:
r"""Samples the input parameters uniformly at random for the discrete features.
Args:
input_mc_samples: The input mc samples tensor to be modified.
discrete_features: A list of integers (or None) of indices corresponding
to discrete features.
bounds: The parameter bounds.
num_mc_samples: The number of Monte Carlo grid samples.
Returns:
A modified input mc samples tensor.
"""
if discrete_features is None:
return input_mc_samples
all_low = bounds[0, discrete_features].to(dtype=torch.int).tolist()
all_high = (bounds[1, discrete_features]).to(dtype=torch.int).tolist()
for i, low, high in zip(discrete_features, all_low, all_high):
randint = partial(torch.randint, low=low, high=high + 1)
input_mc_samples[:, i] = randint(size=torch.Size([num_mc_samples]))
return input_mc_samples
[docs]class GpDGSMGpMean(object):
mean_gradients: Optional[torch.Tensor] = None
bootstrap_indices: Optional[torch.Tensor] = None
mean_gradients_btsp: Optional[List[torch.Tensor]] = None
def __init__(
self,
model: Model,
bounds: torch.Tensor,
derivative_gp: bool = False,
kernel_type: Optional[str] = None,
Y_scale: float = 1.0,
num_mc_samples: int = 10**4,
input_qmc: bool = False,
dtype: torch.dtype = torch.double,
num_bootstrap_samples: int = 1,
discrete_features: Optional[List[int]] = None,
) -> None:
r"""Computes three types of derivative based measures:
the gradient, the gradient square and the gradient absolute measures.
Args:
model: A BoTorch model.
bounds: Parameter bounds over which to evaluate model sensitivity.
derivative_gp: If true, the derivative of the GP is used to compute
the gradient instead of backward.
kernel_type: Takes "rbf" or "matern", set only if `derivative_gp` is true.
Y_scale: Scale the derivatives by this amount, to undo scaling
done on the training data.
num_mc_samples: The number of MonteCarlo grid samples
input_qmc: If True, a qmc Sobol grid is use instead of uniformly random.
dtype: Can be provided if the GP is fit to data of type `torch.float`.
num_bootstrap_samples: If higher than 1, the method will compute the
dgsm measure `num_bootstrap_samples` times by selecting subsamples
from the `input_mc_samples` and return the variance and standard error
across all computed measures.
discrete_features: If specified, the inputs associated with the indices in
this list are generated using an integer-valued uniform distribution,
rather than the default (pseudo-)random continuous uniform distribution.
"""
# pyre-fixme[4]: Attribute must be annotated.
self.dim = checked_cast(tuple, model.train_inputs)[0].shape[-1]
self.derivative_gp = derivative_gp
self.kernel_type = kernel_type
# pyre-fixme[4]: Attribute must be annotated.
self.bootstrap = num_bootstrap_samples > 1
# pyre-fixme[4]: Attribute must be annotated.
self.num_bootstrap_samples = (
num_bootstrap_samples - 1
) # deduct 1 because the first is meant to be the full grid
if self.derivative_gp and (self.kernel_type is None):
raise ValueError("Kernel type has to be specified to use derivative GP")
self.num_mc_samples = num_mc_samples
if input_qmc:
# pyre-fixme[4]: Attribute must be annotated.
self.input_mc_samples = (
draw_sobol_samples(bounds=bounds, n=num_mc_samples, q=1, seed=1234)
.squeeze(1)
.to(dtype)
)
else:
self.input_mc_samples = unnormalize(
torch.rand(num_mc_samples, self.dim, dtype=dtype),
bounds=bounds,
)
# uniform integral distribution for discrete features
self.input_mc_samples = sample_discrete_parameters(
input_mc_samples=self.input_mc_samples,
discrete_features=discrete_features,
bounds=bounds,
num_mc_samples=num_mc_samples,
)
if self.derivative_gp:
posterior = posterior_derivative(
model, self.input_mc_samples, not_none(self.kernel_type)
)
else:
self.input_mc_samples.requires_grad = True
posterior = checked_cast(
GPyTorchPosterior, model.posterior(self.input_mc_samples)
)
self._compute_gradient_quantities(posterior, Y_scale)
def _compute_gradient_quantities(
self, posterior: Union[GPyTorchPosterior, MultivariateNormal], Y_scale: float
) -> None:
if self.derivative_gp:
self.mean_gradients = checked_cast(torch.Tensor, posterior.mean) * Y_scale
else:
predictive_mean = posterior.mean
torch.sum(predictive_mean).backward()
self.mean_gradients = (
checked_cast(torch.Tensor, self.input_mc_samples.grad) * Y_scale
)
if self.bootstrap:
subset_size = 2
self.bootstrap_indices = torch.randint(
0, self.num_mc_samples, (self.num_bootstrap_samples, subset_size)
)
self.mean_gradients_btsp = [
torch.index_select(
checked_cast(torch.Tensor, self.mean_gradients), 0, indices
)
for indices in self.bootstrap_indices
]
[docs] def aggregation(
self, transform_fun: Callable[[torch.Tensor], torch.Tensor]
) -> torch.Tensor:
gradients_measure = torch.tensor(
[
torch.mean(transform_fun(not_none(self.mean_gradients)[:, i]))
for i in range(self.dim)
]
)
if not (self.bootstrap):
return gradients_measure
else:
gradients_measures_btsp = [gradients_measure.unsqueeze(0)]
for b in range(self.num_bootstrap_samples):
gradients_measures_btsp.append(
torch.tensor(
[
torch.mean(
transform_fun(
not_none(self.mean_gradients_btsp)[b][:, i]
)
)
for i in range(self.dim)
]
).unsqueeze(0)
)
gradients_measures_btsp = torch.cat(gradients_measures_btsp, dim=0)
return (
torch.cat(
[
gradients_measures_btsp.mean(dim=0).unsqueeze(0),
gradients_measures_btsp.var(dim=0).unsqueeze(0),
torch.sqrt(
gradients_measures_btsp.var(dim=0)
/ (self.num_bootstrap_samples + 1)
).unsqueeze(0),
],
dim=0,
)
.t()
.detach()
)
[docs] def gradient_measure(self) -> torch.Tensor:
r"""Computes the gradient measure:
Returns:
if `self.num_bootstrap_samples > 1`
Tensor: (values, var_mc, stderr_mc) x dim
else
Tensor: (values) x dim
"""
return self.aggregation(torch.as_tensor)
[docs] def gradient_absolute_measure(self) -> torch.Tensor:
r"""Computes the gradient absolute measure:
Returns:
if `self.num_bootstrap_samples > 1`
Tensor: (values, var_mc, stderr_mc) x dim
else
Tensor: (values) x dim
"""
return self.aggregation(torch.abs)
[docs] def gradients_square_measure(self) -> torch.Tensor:
r"""Computes the gradient square measure:
Returns:
if `num_bootstrap_samples > 1`
Tensor: (values, var_mc, stderr_mc) x dim
else
Tensor: (values) x dim
"""
return self.aggregation(torch.square)
[docs]class GpDGSMGpSampling(GpDGSMGpMean):
samples_gradients: Optional[torch.Tensor] = None
samples_gradients_btsp: Optional[List[torch.Tensor]] = None
def __init__(
self,
model: Model,
bounds: torch.Tensor,
num_gp_samples: int,
derivative_gp: bool = False,
kernel_type: Optional[str] = None,
Y_scale: float = 1.0,
num_mc_samples: int = 10**4,
input_qmc: bool = False,
gp_sample_qmc: bool = False,
dtype: torch.dtype = torch.double,
num_bootstrap_samples: int = 1,
) -> None:
r"""Computes three types of derivative based measures:
the gradient, the gradient square and the gradient absolute measures.
Args:
model: A BoTorch model.
bounds: Parameter bounds over which to evaluate model sensitivity.
num_gp_samples: If method is "GP samples", the number of GP samples has
to be set.
derivative_gp: If true, the derivative of the GP is used to compute the
gradient instead of backward.
kernel_type: Takes "rbf" or "matern", set only if `derivative_gp` is true.
Y_scale: Scale the derivatives by this amount, to undo scaling done on
the training data.
num_mc_samples: The number of Monte Carlo grid samples.
input_qmc: If True, a qmc Sobol grid is used instead of uniformly random.
gp_sample_qmc: If True, the posterior sampling is done using
`SobolQMCNormalSampler`.
dtype: Can be provided if the GP is fit to data of type `torch.float`.
num_bootstrap_samples: If higher than 1, the method will compute the
dgsm measure `num_bootstrap_samples` times by selecting subsamples
from the `input_mc_samples` and return the variance and standard error
across all computed measures.
Returns values of gradient_measure, gradient_absolute_measure and
gradients_square_measure change to the following:
if `num_bootstrap_samples > 1`:
Tensor: (values, var_gp, stderr_gp, var_mc, stderr_mc) x dim
else
Tensor: (values, var_gp, stderr_gp) x dim
"""
self.num_gp_samples = num_gp_samples
self.gp_sample_qmc = gp_sample_qmc
self.num_mc_samples = num_mc_samples
super().__init__(
model=model,
bounds=bounds,
derivative_gp=derivative_gp,
kernel_type=kernel_type,
Y_scale=Y_scale,
num_mc_samples=num_mc_samples,
input_qmc=input_qmc,
dtype=dtype,
num_bootstrap_samples=num_bootstrap_samples,
)
def _compute_gradient_quantities(
self, posterior: Union[Posterior, MultivariateNormal], Y_scale: float
) -> None:
if self.gp_sample_qmc:
sampler = SobolQMCNormalSampler(
sample_shape=torch.Size([self.num_gp_samples]), seed=0
)
samples = sampler(posterior)
else:
samples = posterior.rsample(torch.Size([self.num_gp_samples]))
if self.derivative_gp:
self.samples_gradients = samples * Y_scale
else:
samples_gradients = []
for j in range(self.num_gp_samples):
torch.sum(samples[j]).backward(retain_graph=True)
samples_gradients.append(
deepcopy(self.input_mc_samples.grad).unsqueeze(0)
)
self.input_mc_samples.grad.data.zero_()
self.samples_gradients = torch.cat(samples_gradients, dim=0) * Y_scale
if self.bootstrap:
subset_size = 2
self.bootstrap_indices = torch.randint(
0, self.num_mc_samples, (self.num_bootstrap_samples, subset_size)
)
self.samples_gradients_btsp = []
for j in range(self.num_gp_samples):
not_none(self.samples_gradients_btsp).append(
torch.cat(
[
torch.index_select(
not_none(self.samples_gradients)[j], 0, indices
).unsqueeze(0)
for indices in not_none(self.bootstrap_indices)
],
dim=0,
)
)
[docs] def aggregation(
self, transform_fun: Callable[[torch.Tensor], torch.Tensor]
) -> torch.Tensor:
gradients_measure_list = []
for j in range(self.num_gp_samples):
gradients_measure_list.append(
torch.tensor(
[
torch.mean(
transform_fun(not_none(self.samples_gradients)[j][:, i])
)
for i in range(self.dim)
]
).unsqueeze(0)
)
gradients_measure_list = torch.cat(gradients_measure_list, dim=0)
if not (self.bootstrap):
gradients_measure_mean_var = []
for i in range(self.dim):
gradients_measure_mean_var.append(
torch.tensor(
[
torch.mean(gradients_measure_list[:, i]),
torch.var(gradients_measure_list[:, i]),
torch.sqrt(
torch.var(gradients_measure_list[:, i])
/ self.num_gp_samples
),
]
).unsqueeze(0)
)
gradients_measure_mean_var = torch.cat(gradients_measure_mean_var, dim=0)
return gradients_measure_mean_var
else:
gradients_measure_list_btsp = []
for j in range(self.num_gp_samples):
gradients_measure_btsp = [gradients_measure_list[j].unsqueeze(0)] + [
torch.tensor(
[
torch.mean(
transform_fun(
not_none(self.samples_gradients_btsp)[j][b][:, i]
)
)
for i in range(self.dim)
]
).unsqueeze(0)
for b in range(self.num_bootstrap_samples)
]
gradients_measure_list_btsp.append(
torch.cat(gradients_measure_btsp, dim=0).unsqueeze(0)
)
gradients_measure_list_btsp = torch.cat(gradients_measure_list_btsp, dim=0)
var_per_bootstrap = torch.var(gradients_measure_list_btsp, dim=0)
gp_var = torch.mean(var_per_bootstrap, dim=0)
gp_se = torch.sqrt(gp_var / self.num_gp_samples)
var_per_gp_sample = torch.var(gradients_measure_list_btsp, dim=1)
mc_var = torch.mean(var_per_gp_sample, dim=0)
mc_se = torch.sqrt(mc_var / (self.num_bootstrap_samples + 1))
total_mean = gradients_measure_list_btsp.reshape(-1, self.dim).mean(dim=0)
gradients_measure_mean_vargp_segp_varmc_segp = torch.cat(
[
torch.tensor(
[total_mean[i], gp_var[i], gp_se[i], mc_var[i], mc_se[i]]
).unsqueeze(0)
for i in range(self.dim)
],
dim=0,
)
return gradients_measure_mean_vargp_segp_varmc_segp
[docs]def compute_derivatives_from_model_list(
model_list: List[Model],
bounds: torch.Tensor,
discrete_features: Optional[List[int]] = None,
**kwargs: Any,
) -> torch.Tensor:
"""
Computes average derivatives of a list of models on a bounded domain. Estimation
is according to the GP posterior mean function.
Args:
model_list: A list of m botorch.models.model.Model types for which to compute
the average derivative.
bounds: A 2 x d Tensor of lower and upper bounds of the domain of the models.
discrete_features: If specified, the inputs associated with the indices in
this list are generated using an integer-valued uniform distribution,
rather than the default (pseudo-)random continuous uniform distribution.
kwargs: Passed along to GpDGSMGpMean.
Returns:
A (m x d) tensor of gradient measures.
"""
indices = []
for model in model_list:
sens_class = GpDGSMGpMean(
model=model, bounds=bounds, discrete_features=discrete_features, **kwargs
)
indices.append(sens_class.gradient_measure())
return torch.stack(indices)
