Source code for botorch.models.pairwise_gp

#!/usr/bin/env python3
# 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.

Preference Learning with Gaussian Process

.. [Chu2005preference]
    Wei Chu, and Zoubin Ghahramani. Preference learning with Gaussian processes.
    Proceedings of the 22nd international conference on Machine learning. 2005.

.. [Brochu2010tutorial]
    Eric Brochu, Vlad M. Cora, and Nando De Freitas.
    A tutorial on Bayesian optimization of expensive cost functions,
    with application to active user modeling and hierarchical reinforcement learning.
    arXiv preprint arXiv:1012.2599 (2010).

from __future__ import annotations

import warnings
from copy import deepcopy
from typing import Any, Dict, List, Optional, Tuple, Union

import numpy as np
import torch
from botorch.acquisition.objective import PosteriorTransform
from botorch.exceptions import UnsupportedError
from botorch.models.likelihoods.pairwise import (
from botorch.models.model import FantasizeMixin, Model
from botorch.models.transforms.input import InputTransform
from botorch.posteriors.gpytorch import GPyTorchPosterior
from botorch.posteriors.posterior import Posterior
from gpytorch import settings
from gpytorch.constraints import GreaterThan, Interval
from gpytorch.distributions.multivariate_normal import MultivariateNormal
from gpytorch.kernels.rbf_kernel import RBFKernel
from gpytorch.kernels.scale_kernel import ScaleKernel
from gpytorch.means.constant_mean import ConstantMean
from gpytorch.mlls import MarginalLogLikelihood
from import GP
from gpytorch.priors.smoothed_box_prior import SmoothedBoxPrior
from gpytorch.priors.torch_priors import GammaPrior
from linear_operator.operators import LinearOperator, RootLinearOperator
from linear_operator.utils.cholesky import psd_safe_cholesky
from scipy import optimize
from torch import float32, float64, Tensor
from torch.nn.modules.module import _IncompatibleKeys

# Why we subclass GP even though it provides no functionality:
# if this subclassing is removed, we get the following GPyTorch error:
# "RuntimeError: All MarginalLogLikelihood objects must be given a GP object as
# a model. If you are using a more complicated model involving a GP, pass the
# underlying GP object as the model, not a full PyTorch module."
[docs]class PairwiseGP(Model, GP, FantasizeMixin): r"""Probit GP for preference learning with Laplace approximation A probit-likelihood GP that learns via pairwise comparison data, using a Laplace approximation of the posterior of the estimated utility values. By default it uses a scaled RBF kernel. Implementation is based on [Chu2005preference]_. Also see [Brochu2010tutorial]_ for additional reference. Note that in [Chu2005preference]_ the likelihood of a pairwise comparison is :math:`\left(\frac{f(x_1) - f(x_2)}{\sqrt{2}\sigma}\right)`, i.e. a scale is used in the denominator. To maintain consistency with usage of kernels elsewhere in BoTorch, we instead do not include :math:`\sigma` in the code (implicitly setting it to 1) and use ScaleKernel to scale the function. In the example below, the user/decision maker has stated that they prefer the first item over the second item and the third item over the second item, generating comparisons [0, 1] and [2, 1]. Example: >>> from botorch.models import PairwiseGP >>> import torch >>> datapoints = torch.Tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> comparisons = torch.Tensor([[0, 1], [2, 1]]) >>> model = PairwiseGP(datapoints, comparisons) """ _buffer_names = [ "datapoints", "comparisons", "D", "DT", "utility", "covar_chol", "likelihood_hess", "hlcov_eye", "covar", "covar_inv", ] def __init__( self, datapoints: Tensor, comparisons: Tensor, likelihood: Optional[PairwiseLikelihood] = None, covar_module: Optional[ScaleKernel] = None, input_transform: Optional[InputTransform] = None, **kwargs, ) -> None: r""" Args: datapoints: A `batch_shape x n x d` tensor of training features. comparisons: A `batch_shape x m x 2` training comparisons; comparisons[i] is a noisy indicator suggesting the utility value of comparisons[i, 0]-th is greater than comparisons[i, 1]-th. likelihood: A PairwiseLikelihood. covar_module: Covariance module. input_transform: An input transform that is applied in the model's forward pass. """ super().__init__() if input_transform is not None: # input transformation is applied in set_train_data self.input_transform = input_transform # Compatibility variables with fit_gpytorch_*: Dummy likelihood # Likelihood is tightly tied with this model and # it doesn't make much sense to keep it separate self.likelihood = ( PairwiseProbitLikelihood() if likelihood is None else likelihood ) for key in self._buffer_names: self.register_buffer(key, None) self.train_inputs = [] self.train_targets = None self.utility = None self.pred_cov_fac_need_update = True self.dim = None # See set_train_data for additional compatibility variables. # Not that the datapoints here are not transformed even if input_transform # is not None to avoid double transformation during model fitting. # self.transform_inputs is called in `forward` self.set_train_data(datapoints, comparisons, update_model=False) # Set optional parameters # Explicitly set jitter for numerical stability in psd_safe_cholesky self._jitter = kwargs.get("jitter", 1e-6) # Stopping creteria in scipy.optimize.fsolve used to find f_map in _update() # If None, set to 1e-6 by default in _update self._xtol = kwargs.get("xtol") # The maximum number of calls to the function in scipy.optimize.fsolve # If None, set to 100 by default in _update # If zero, then 100*(N+1) is used by default by fsolve; self._maxfev = kwargs.get("maxfev") # Set hyperparameters # Do not set the batch_shape explicitly so mean_module can operate in both mode # once fsolve used in _update can run in batch mode, we should explicitly set # the bacth shape here self.mean_module = ConstantMean() # Do not optimize constant mean prior for param in self.mean_module.parameters(): param.requires_grad = False # set covariance module # the default outputscale here is only a rule of thumb, meant to keep # estimates away from scale value that would make Phi(f(x)) saturate # at 0 or 1 if covar_module is None: os_lb, os_ub = 1e-2, 1e2 ls_prior = GammaPrior(1.2, 0.5) ls_prior_mode = (ls_prior.concentration - 1) / ls_prior.rate covar_module = ScaleKernel( RBFKernel( batch_shape=self.batch_shape, ard_num_dims=self.dim, lengthscale_prior=ls_prior, lengthscale_constraint=GreaterThan( lower_bound=1e-4, transform=None, initial_value=ls_prior_mode ), ), outputscale_prior=SmoothedBoxPrior(a=os_lb, b=os_ub), # make sure we won't get extreme values for the output scale outputscale_constraint=Interval( lower_bound=os_lb * 0.5, upper_bound=os_ub * 2.0, initial_value=1.0, ), ) if not isinstance(covar_module, ScaleKernel): raise UnsupportedError("PairwiseGP must be used with a ScaleKernel.") self.covar_module = covar_module self._x0 = None # will store temporary results for warm-starting if self.datapoints is not None and self.comparisons is not None:, device=self.datapoints.device) # Find f_map for initial parameters with transformed datapoints transformed_dp = self.transform_inputs(datapoints) self._update(transformed_dp) def __deepcopy__(self, memo) -> PairwiseGP: attrs = ( "datapoints", "comparisons", "covar", "covar_inv", "covar_chol", "likelihood_hess", "utility", "hlcov_eye", ) if any(getattr(self, attr) is not None for attr in attrs): # Temporarily remove non-leaf tensors so that pytorch allows deepcopy old_attr = {} for attr in attrs: old_attr[attr] = getattr(self, attr) setattr(self, attr, None) new_model = deepcopy(self, memo) # now set things back for attr in attrs: setattr(self, attr, old_attr[attr]) return new_model else: dcp = self.__deepcopy__ # make sure we don't fall into the infinite recursive loop self.__deepcopy__ = None new_model = deepcopy(self, memo) self.__deepcopy__ = dcp return new_model def _scaled_psd_safe_cholesky( self, M: Tensor, jitter: Optional[float] = None ) -> Tensor: r"""scale M by 1/outputscale before cholesky for better numerical stability""" scale = self.covar_module.outputscale.unsqueeze(-1).unsqueeze(-1) M = M / scale chol = psd_safe_cholesky(M, jitter=jitter) chol = chol * scale.sqrt() return chol def _has_no_data(self): r"""Return true if the model does not have both datapoints and comparisons""" return ( self.datapoints is None or len(self.datapoints.size()) == 0 or self.comparisons is None ) def _calc_covar(self, X1: Tensor, X2: Tensor) -> Union[Tensor, LinearOperator]: r"""Calculate the covariance matrix given two sets of datapoints""" covar = self.covar_module(X1, X2) return covar.to_dense() def _update_covar(self, datapoints: Tensor) -> None: r"""Update values derived from the data and hyperparameters covar, covar_chol, and covar_inv will be of shape batch_shape x n x n Args: datapoints: (Transformed) datapoints for finding f_max """ self.covar = self._calc_covar(datapoints, datapoints) self.covar_chol = self._scaled_psd_safe_cholesky( self.covar, jitter=self._jitter ) self.covar_inv = torch.cholesky_inverse(self.covar_chol) def _prior_mean(self, X: Tensor) -> Union[Tensor, LinearOperator]: r"""Return point prediction using prior only Args: X: A `batch_size x n' x d`-dim Tensor at which to evaluate prior Returns: Prior mean prediction """ return self.mean_module(X) def _prior_predict(self, X: Tensor) -> Tuple[Tensor, Tensor]: r"""Predict utility based on prior info only Args: X: A `batch_size x n' x d`-dim Tensor at which to evaluate prior Returns: pred_mean: predictive mean pred_covar: predictive covariance """ pred_mean = self._prior_mean(X) pred_covar = self._calc_covar(X, X) return pred_mean, pred_covar def _grad_posterior_f( self, utility: Union[Tensor, np.ndarray], datapoints: Tensor, D: Tensor, DT: Tensor, covar_chol: Tensor, covar_inv: Tensor, ret_np: bool = False, ) -> Union[Tensor, np.ndarray]: r"""Compute the gradient of S loss wrt to f/utility in [Chu2005preference]_. For finding f_map, which is negative of the log posterior, i.e., -log(p(f|D)) Derivative of (10) in [Chu2005preference]_. Also see [Brochu2010tutorial]_ page 26. This is needed for estimating f_map. Args: utility: A Tensor of shape `batch_size x n` datapoints: A Tensor of shape `batch_size x n x d` as in self.datapoints D: A Tensor of shape `batch_size x m x n` as in self.D DT: Transpose of D. A Tensor of shape `batch_size x n x m` as in self.DT covar_chol: A Tensor of shape `batch_size x n x n`, as in self.covar_chol covar_inv: A Tensor of shape `batch_size x n x n`, as in self.covar_inv ret_np: return a numpy array if true, otherwise a Tensor """ prior_mean = self._prior_mean(datapoints) if ret_np: utility = torch.tensor(utility, dtype=self.datapoints.dtype) prior_mean = prior_mean.cpu() b = self.likelihood.negative_log_gradient_sum(utility=utility, D=D) # g_ = covar_inv x (utility - pred_prior) p = (utility - prior_mean).unsqueeze(-1).to(covar_chol) g_ = torch.cholesky_solve(p, covar_chol).squeeze(-1) g = g_ + b if ret_np: return g.cpu().numpy() else: return g def _hess_posterior_f( self, utility: Union[Tensor, np.ndarray], datapoints: Tensor, D: Tensor, DT: Tensor, covar_chol: Tensor, covar_inv: Tensor, ret_np: bool = False, ) -> Union[Tensor, np.ndarray]: r"""Compute the hessian of S loss wrt utility for finding f_map. which is negative of the log posterior, i.e., -log(p(f|D)) Following [Chu2005preference]_ section 2.2.1. This is needed for estimating f_map Args: utility: A Tensor of shape `batch_size x n` datapoints: A Tensor of shape `batch_size x n x d` as in self.datapoints D: A Tensor of shape `batch_size x m x n` as in self.D DT: Transpose of D. A Tensor of shape `batch_size x n x m` as in self.DT covar_chol: A Tensor of shape `batch_size x n x n`, as in self.covar_chol covar_inv: A Tensor of shape `batch_size x n x n`, as in self.covar_inv ret_np: return a numpy array if true, otherwise a Tensor """ if ret_np: utility = torch.tensor(utility, dtype=self.datapoints.dtype) hl = self.likelihood.negative_log_hessian_sum(utility=utility, D=D) hess = hl + covar_inv return hess.numpy() if ret_np else hess def _update_utility_derived_values(self) -> None: r"""Calculate utility-derived values not needed during optimization Using subsitution method for better numerical stability Let `pred_cov_fac = (covar + hl^-1)`, which is needed for calculate predictive covariance = `K - k.T @ pred_cov_fac^-1 @ k` (Also see posterior mode in `forward`) Instead of inverting `pred_cov_fac`, let `hlcov_eye = (hl @ covar + I)` Then we can obtain `pred_cov_fac^-1 @ k` by solving for p in `(hl @ k) p = hlcov_eye` `hlcov_eye p = hl @ k` """ hl = self.likelihood_hess # "C" from page 27, [Brochu2010tutorial]_ hlcov = hl @ self.covar eye = torch.eye( hlcov.size(-1), dtype=self.datapoints.dtype, device=self.datapoints.device ).expand(hlcov.shape) self.hlcov_eye = hlcov + eye self.pred_cov_fac_need_update = False def _update(self, datapoints: Tensor, **kwargs) -> None: r"""Update the model by updating the covar matrix and MAP utility values Update the model by 1. Re-evaluating the covar matrix as the data or hyperparams may have changed 2. Approximating maximum a posteriori of the utility function f using fsolve Should be called after data or hyperparameters are changed to update f_map and related values self._xtol and self._maxfev are passed to fsolve as xtol and maxfev to control stopping criteria Args: datapoints: (transformed) datapoints for finding f_max """ xtol = 1e-6 if self._xtol is None else self._xtol maxfev = 100 if self._maxfev is None else self._maxfev # Using the latest param for covariance before calculating f_map self._update_covar(datapoints) # scipy newton raphson with torch.no_grad(): # warm start init_x0_size = self.batch_shape + torch.Size([self.n]) if self._x0 is None or torch.Size(self._x0.shape) != init_x0_size: sqrt_scale = ( self.covar_module.outputscale.sqrt() .unsqueeze(-1) .detach() .cpu() .numpy() ) # initialize x0 using std normal but clip by 3 std to keep it bounded x0 = np.random.standard_normal(init_x0_size).clip(min=-3, max=3) # scale x0 to be on roughly the right scale x0 = x0 * sqrt_scale else: x0 = self._x0 if len(self.batch_shape) > 0: # batch mode, do optimize.fsolve sequentially on CPU # TODO: enable vectorization/parallelization here x0 = x0.reshape(-1, self.n) dp_v = datapoints.view(-1, self.n, self.dim).cpu() D_v = self.D.view(-1, self.m, self.n).cpu() DT_v = self.DT.view(-1, self.n, self.m).cpu() ch_v = self.covar_chol.view(-1, self.n, self.n).cpu() ci_v = self.covar_inv.view(-1, self.n, self.n).cpu() x = np.empty(x0.shape) for i in range(x0.shape[0]): fsolve_args = (dp_v[i], D_v[i], DT_v[i], ch_v[i], ci_v[i], True) with warnings.catch_warnings(): warnings.filterwarnings("ignore", category=RuntimeWarning) x[i] = optimize.fsolve( x0=x0[i], func=self._grad_posterior_f, fprime=self._hess_posterior_f, xtol=xtol, maxfev=maxfev, args=fsolve_args, **kwargs, ) x = x.reshape(*init_x0_size) else: # fsolve only works on CPU fsolve_args = ( datapoints.cpu(), self.D.cpu(), self.DT.cpu(), self.covar_chol.cpu(), self.covar_inv.cpu(), True, ) with warnings.catch_warnings(): warnings.filterwarnings("ignore", category=RuntimeWarning) x = optimize.fsolve( x0=x0, func=self._grad_posterior_f, fprime=self._hess_posterior_f, xtol=xtol, maxfev=maxfev, args=fsolve_args, **kwargs, ) self._x0 = x.copy() # save for warm-starting f = torch.tensor(x, dtype=datapoints.dtype, device=datapoints.device) # To perform hyperparameter optimization, this need to be recalculated # when calling forward() in order to obtain correct gradients # self.likelihood_hess is updated here is for the rare case where we # do not want to call forward() self.likelihood_hess = self.likelihood.negative_log_hessian_sum( utility=f, D=self.D ) # Lazy update hlcov_eye, which is used in calculating posterior during training self.pred_cov_fac_need_update = True # fill in dummy values for hlcov_eye so that load_state_dict can function hlcov_eye_size = torch.Size((*self.likelihood_hess.shape[:-2], self.n, self.n)) self.hlcov_eye = torch.empty(hlcov_eye_size) # Take two newton step on the posterior MAP point to fill # in gradients for pytorch. Using 2 instead of 1 since empirically sometimes # the first step results in gradients in the order of 1e-7 while the 2nd step # allows it go down further to the order of 1e-12 and stay there. self.utility = self._util_newton_updates( datapoints, f.clone().requires_grad_(True), max_iter=2 ) def _transform_batch_shape(self, X: Tensor, X_new: Tensor) -> Tuple[Tensor, Tensor]: r"""Transform X and X_new into the same shape Transform the batch shape of X to be compatible with `X_new` to calculate the posterior. If X has the same batch size as `X_new`, return it as is. If one is in batch mode and the other one is not, convert both into batch mode. If both are in batch mode, this will only work if X_batch_shape can propagate to X_new_batch_shape Args: X: A `batch_shape x q x d`-dim or `(1 x) q x d`-dim Tensor X_new: A `batch_shape x q x d`-dim Tensor Returns: Transformed X and X_new pair """ X_bs = X.shape[:-2] # X batch shape X_new_bs = X_new.shape[:-2] # X_new batch shape if X_new_bs == X_bs: # if batch shapes match, there's no need to transform # X_new may or may not have batch_shape dimensions return X, X_new elif len(X_new_bs) < len(X_bs): # if X_new has fewer dimension, try to expand it to X's shape return X, X_new.expand(X_bs + X_new.shape[-2:]) else: # if X has fewer dimension, try to expand it to X_new's shape return X.expand(X_new_bs + X.shape[-2:]), X_new def _util_newton_updates(self, dp, x0, max_iter=1, xtol=None) -> Tensor: r"""Make `max_iter` newton updates on utility. This is used in `forward` to calculate and fill in gradient into tensors. Instead of doing utility -= H^-1 @ g, use substition method. See more explanation in _update_utility_derived_values. By default only need to run one iteration just to fill the the gradients. Args: dp: (Transformed) datapoints. x0: A `batch_size x n` dimension tensor, initial values. max_iter: Max number of iterations. xtol: Stop creteria. If `None`, do not stop until finishing `max_iter` updates. """ xtol = float("-Inf") if xtol is None else xtol D, DT, ch, ci = ( self.D, self.DT, self.covar_chol, self.covar_inv, ) covar = self.covar diff = float("Inf") i = 0 x = x0 eye = None while i < max_iter and diff > xtol: hl = self.likelihood.negative_log_hessian_sum(utility=x, D=D) self.likelihood_hess = hl cov_hl = covar @ hl if eye is None: eye = torch.diag_embed( torch.ones( cov_hl.shape[:-1], device=cov_hl.device, dtype=cov_hl.dtype ) ) cov_hl = cov_hl + eye # add 1 to cov_hl g = self._grad_posterior_f(x, dp, D, DT, ch, ci) cov_g = covar @ g.unsqueeze(-1) x_update = torch.linalg.solve(cov_hl, cov_g).squeeze(-1) x_next = x - x_update diff = torch.norm(x - x_next) x = x_next i += 1 return x def _check_strict_input(self, inputs, t_inputs, target_or_inputs): for input_, t_input in zip(inputs, t_inputs or (None,)): for attr in {"shape", "dtype", "device"}: expected_attr = getattr(t_input, attr, None) found_attr = getattr(input_, attr, None) if expected_attr != found_attr: msg = ( "Cannot modify {attr} of {t_or_i} " "(expected {e_attr}, found {f_attr})." ) msg = msg.format( attr=attr, e_attr=expected_attr, f_attr=found_attr, t_or_i=target_or_inputs, ) raise RuntimeError(msg) # ============== public APIs ============== @property def num_outputs(self) -> int: r"""The number of outputs of the model.""" return self._num_outputs @property def batch_shape(self) -> torch.Size: r"""The batch shape of the model. This is a batch shape from an I/O perspective, independent of the internal representation of the model (as e.g. in BatchedMultiOutputGPyTorchModel). For a model with `m` outputs, a `test_batch_shape x q x d`-shaped input `X` to the `posterior` method returns a Posterior object over an output of shape `broadcast(test_batch_shape, model.batch_shape) x q x m`. """ if self.datapoints is None: # this could happen in prior mode return torch.Size() else: return self.datapoints.shape[:-2]
[docs] def set_train_data( self, datapoints: Tensor = None, comparisons: Tensor = None, strict: bool = False, update_model: bool = True, ) -> None: r"""Set datapoints and comparisons and update model properties if needed Args: datapoints: A `batch_shape x n x d` dimension tensor X. If there are input transformations, assume the datapoints are not transformed comparisons: A tensor of size `batch_shape x m x 2`. (i, j) means f_i is preferred over f_j. strict: `strict` argument as in gpytorch.models.exact_gp for compatibility when using fit_gpytorch_model with input_transform. update_model: True if we want to refit the model (see _update) after re-setting the data. """ # When datapoints and/or comparisons are None, we are constructing # a prior-only model if datapoints is None or comparisons is None: return # following gpytorch.models.exact_gp.set_train_data if datapoints is not None: if torch.is_tensor(datapoints): inputs = (datapoints,) inputs = tuple( input_.unsqueeze(-1) if input_.ndimension() == 1 else input_ for input_ in inputs ) if strict: self._check_strict_input(inputs, self.train_inputs, "inputs") self.datapoints = inputs[0] # Compatibility variables with fit_gpytorch_* # alias for datapoints ("train_inputs") self.train_inputs = inputs if comparisons is not None: if strict: self._check_strict_input([comparisons], [self.train_targets], "targets") # convert to long so that it can be used as index and # compatible with Tensor.scatter_ self.comparisons = comparisons.long() # Compatibility variables with fit_gpytorch_* # alias for comparisons ("train_targets" here) self.train_targets = self.comparisons # Compatibility variables with optimize_acqf self._dtype = self.datapoints.dtype self._num_outputs = 1 # 1 latent value output per observation self.dim = self.datapoints.shape[-1] # feature dimensions self.n = self.datapoints.shape[-2] # num datapoints self.m = self.comparisons.shape[-2] # num pairwise comparisons # D is batch_size x m x n or num_comparison x num_datapoints. # D_k_i is the s_k(x_i) value as in equation (6) in [Chu2005preference]_ # D will usually be very sparse as well # TODO swap out scatter_ so that comparisons could be int instead of long # TODO: make D a sparse matrix once pytorch has better support for # sparse tensors D_size = torch.Size((*(self.batch_shape), self.m, self.n)) self.D = torch.zeros( D_size, dtype=self.datapoints.dtype, device=self.datapoints.device ) comp_view = self.comparisons.view(-1, self.m, 2).long() for i, sub_D in enumerate(self.D.view(-1, self.m, self.n)): sub_D.scatter_(1, comp_view[i, :, [0]], 1) sub_D.scatter_(1, comp_view[i, :, [1]], -1) self.DT = self.D.transpose(-1, -2) if update_model: transformed_dp = self.transform_inputs(datapoints) self._update(transformed_dp)
[docs] def load_state_dict( self, state_dict: Dict[str, Tensor], strict: bool = False ) -> _IncompatibleKeys: r"""Removes data related buffers from the `state_dict` and calls `super().load_state_dict` with `strict=False`. Args: state_dict: The state dict. strict: Boolean specifying whether or not given and instance-bound state_dicts should have identical keys. Only implemented for `strict=False` since buffers will filters out when calling `_load_from_state_dict`. Returns: A named tuple `_IncompatibleKeys`, containing the `missing_keys` and `unexpected_keys`. """ if strict: raise UnsupportedError("Passing strict=True is not supported.") return super().load_state_dict(state_dict=state_dict, strict=False)
def _load_from_state_dict( self, state_dict: Dict[str, Tensor], prefix: str, local_metadata: Dict[str, Any], strict: bool, missing_keys: List[str], unexpected_keys: List[str], error_msgs: List[str], ) -> None: super()._load_from_state_dict( state_dict={ k: v for k, v in state_dict.items() if k not in self._buffer_names }, prefix=prefix, local_metadata=local_metadata, strict=False, missing_keys=missing_keys, unexpected_keys=unexpected_keys, error_msgs=error_msgs, )
[docs] def forward(self, datapoints: Tensor) -> MultivariateNormal: r"""Calculate a posterior or prior prediction. During training mode, forward implemented solely for gradient-based hyperparam opt. Essentially what it does is to re-calculate the utility f using its analytical form at f_map so that we are able to obtain gradients of the hyperparameters. Args: datapoints: A `batch_shape x n x d` Tensor, should be the same as self.datapoints during training Returns: A MultivariateNormal object, being one of the followings: 1. Posterior centered at MAP points for training data (training mode) 2. Prior predictions (prior mode) 3. Predictive posterior (eval mode) """ # Training mode: optimizing if if self._has_no_data(): raise RuntimeError( "datapoints and comparisons cannot be None in training mode. " "Call .eval() for prior predictions, " "or call .set_train_data() to add training data." ) if datapoints is not self.datapoints: raise RuntimeError("Must train on training data") transformed_dp = self.transform_inputs(datapoints) # We pass in the untransformed datapoints into set_train_data # as we will be setting self.datapoints as the untransformed datapoints # self.transform_inputs will be called inside before calling _update() self.set_train_data(datapoints, self.comparisons, update_model=True) hl = self.likelihood_hess covar = self.covar # Apply matrix inversion lemma on eq. in page 27 of [Brochu2010tutorial]_ # (A + B)^-1 = A^-1 - A^-1 @ (I + BA^-1)^-1 @ BA^-1 # where A = covar_inv, B = hl hl_cov = hl @ covar eye = torch.eye( hl_cov.size(-1), dtype=self.datapoints.dtype, device=self.datapoints.device, ).expand(hl_cov.shape) hl_cov_I = hl_cov + eye # add I to hl_cov train_covar_map = covar - covar @ torch.linalg.solve(hl_cov_I, hl_cov) output_mean, output_covar = self.utility, train_covar_map # Prior mode elif settings.prior_mode.on() or self._has_no_data(): transformed_new_dp = self.transform_inputs(datapoints) # if we don't have any data yet, use prior GP to make predictions output_mean, output_covar = self._prior_predict(transformed_new_dp) # Posterior mode else: transformed_dp = self.transform_inputs(self.datapoints) transformed_new_dp = self.transform_inputs(datapoints).to(transformed_dp) # self.utility might be None if exception was raised and _update # was failed to be called during hyperparameter optimization # procedures (e.g., fit_gpytorch_mll_scipy) if self.utility is None: self._update(transformed_dp) if self.pred_cov_fac_need_update: self._update_utility_derived_values() X, X_new = self._transform_batch_shape(transformed_dp, transformed_new_dp) covar_chol, _ = self._transform_batch_shape(self.covar_chol, X_new) hl, _ = self._transform_batch_shape(self.likelihood_hess, X_new) hlcov_eye, _ = self._transform_batch_shape(self.hlcov_eye, X_new) # otherwise compute predictive mean and covariance covar_xnew_x = self._calc_covar(X_new, X) covar_x_xnew = covar_xnew_x.transpose(-1, -2) covar_xnew = self._calc_covar(X_new, X_new) p = self.utility - self._prior_mean(X) covar_inv_p = torch.cholesky_solve(p.unsqueeze(-1), covar_chol) pred_mean = (covar_xnew_x @ covar_inv_p).squeeze(-1) pred_mean = pred_mean + self._prior_mean(X_new) # [Brochu2010tutorial]_ page 27 # Preictive covariance fatcor: hlcov_eye = (K + C^-1) # fac = (K + C^-1)^-1 @ k = pred_cov_fac_inv @ covar_x_xnew # used substitution method here to calculate fac fac = torch.linalg.solve(hlcov_eye, hl @ covar_x_xnew) pred_covar = covar_xnew - (covar_xnew_x @ fac) output_mean, output_covar = pred_mean, pred_covar post = MultivariateNormal( mean=output_mean, # output_covar is sometimes non-PSD # perform a cholesky decomposition to check and amend covariance_matrix=RootLinearOperator( self._scaled_psd_safe_cholesky(output_covar, jitter=self._jitter) ), ) return post
# ============== botorch.models.model.Model interfaces ==============
[docs] def posterior( self, X: Tensor, output_indices: Optional[List[int]] = None, observation_noise: bool = False, posterior_transform: Optional[PosteriorTransform] = None, **kwargs: Any, ) -> Posterior: r"""Computes the posterior over model outputs at the provided points. Args: X: A `batch_shape x q x d`-dim Tensor, where `d` is the dimension of the feature space and `q` is the number of points considered jointly. output_indices: As defined in parent Model class, not used for this model. observation_noise: Ignored (since noise is not identifiable from scale in probit models). posterior_transform: An optional PosteriorTransform. Returns: A `Posterior` object, representing joint distributions over `q` points. """ self.eval() # make sure model is in eval mode if output_indices is not None: raise RuntimeError( "output_indices is not None. PairwiseGP should not be a" "multi-output model." ) post = self(X) posterior = GPyTorchPosterior(post) if posterior_transform is not None: return posterior_transform(posterior) else: return posterior
[docs] def condition_on_observations(self, X: Tensor, Y: Tensor, **kwargs: Any) -> Model: r"""Condition the model on new observations. Note that unlike other BoTorch models, PairwiseGP requires Y to be pairwise comparisons Args: X: A `batch_shape x n x d` dimension tensor X Y: A tensor of size `batch_shape x m x 2`. (i, j) means f_i is preferred over f_j Returns: A (deepcopied) `Model` object of the same type, representing the original model conditioned on the new observations `(X, Y)`. """ new_model = deepcopy(self) if self._has_no_data(): # If the model previously has no data, set X and Y as the data directly new_model.set_train_data(X, Y, update_model=True) else: # Can only condition on pairwise comparisons instead of the directly # observed values. Raise a RuntimeError if Y is not a tensor presenting # pairwise comparisons if Y.dtype in (float32, float64) or Y.shape[-1] != 2: raise RuntimeError( "Conditioning on non-pairwise comparison observations." ) # Reshaping datapoints and comparisons by batches Y_new_batch_shape = Y.shape[:-2] new_datapoints = self.datapoints.expand( Y_new_batch_shape + self.datapoints.shape[-2:] ) new_comparisons = self.comparisons.expand( Y_new_batch_shape + self.comparisons.shape[-2:] ) # Reshape X since Y may have additional batch dim. from fantasy models X = X.expand(Y_new_batch_shape + X.shape[-2:]) new_datapoints =,, dim=-2) shifted_comp = + self.n new_comparisons =, shifted_comp), dim=-2) # TODO: be smart about how we can update covar matrix here new_model.set_train_data(new_datapoints, new_comparisons, update_model=True) return new_model
[docs]class PairwiseLaplaceMarginalLogLikelihood(MarginalLogLikelihood): r"""Laplace-approximated marginal log likelihood/evidence for PairwiseGP See (12) from [Chu2005preference]_. """ def __init__(self, likelihood, model: GP): """ Args: likelihood: Used as in args to GPyTorch MarginalLogLikelihood model: Used as in args to GPyTorch MarginalLogLikelihood """ super().__init__(likelihood, model)
[docs] def forward(self, post: Posterior, comp: Tensor) -> Tensor: r"""Calculate approximated log evidence, i.e., log(P(D|theta)) Args: post: training posterior distribution from self.model comp: Comparisons pairs, see PairwiseGP.__init__ for more details Returns: The approximated evidence, i.e., the marginal log likelihood """ model = self.model likelihood = self.likelihood if comp is not model.comparisons: raise RuntimeError("Must train on training data") f_map = post.mean.squeeze(-1) log_likelihood = likelihood.log_p(utility=f_map, D=model.D) neg_log_likelihood_sum = -(torch.sum(log_likelihood, dim=-1)) # 1/2 f_map^T @ covar_inv @ f_map inv_prod = torch.cholesky_solve(f_map.unsqueeze(-1), model.covar_chol) log_prior = 0.5 * (f_map.unsqueeze(-2) @ inv_prod).squeeze(-1).squeeze(-1) log_posterior = neg_log_likelihood_sum + log_prior # log_posterior is the S loss function in [Chu2005preference]_ log_posterior = -log_posterior.clamp(min=0) mll = model.covar @ model.likelihood_hess mll = mll + torch.diag_embed( torch.ones(mll.shape[:-1], device=mll.device, dtype=mll.dtype) ) mll = -0.5 * torch.logdet(mll) mll = mll + log_posterior # Sum up mll first so that when adding parameter prior probs it won't # propagate and double count mll = mll.sum() # Add log probs of priors on the (functions of) parameters for _, module, prior, closure, _ in self.named_priors(): mll = mll.add(prior.log_prob(closure(module)).sum()) return mll