laplace.baselaplace
#
ParametricLaplace
#
ParametricLaplace(model: Module, likelihood: Likelihood | str, sigma_noise: float | Tensor = 1.0, prior_precision: float | Tensor = 1.0, prior_mean: float | Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)
Bases: BaseLaplace
Parametric Laplace class.
Subclasses need to specify how the Hessian approximation is initialized, how to add up curvature over training data, how to sample from the Laplace approximation, and how to compute the functional variance.
A Laplace approximation is represented by a MAP which is given by the
model
parameter and a posterior precision or covariance specifying
a Gaussian distribution \(\mathcal{N}(\theta_{MAP}, P^{-1})\).
The goal of this class is to compute the posterior precision \(P\)
which sums as
Every subclass implements different approximations to the log likelihood Hessians, for example, a diagonal one. The prior is assumed to be Gaussian and therefore we have a simple form for \(\nabla^2_\theta \log p(\theta) \vert_{\theta_{MAP}} = P_0 \). In particular, we assume a scalar, layer-wise, or diagonal prior precision so that in all cases \(P_0 = \textrm{diag}(p_0)\) and the structure of \(p_0\) can be varied.
Source code in laplace/baselaplace.py
log_likelihood
#
Compute log likelihood on the training data after .fit()
has been called.
The log likelihood is computed on-demand based on the loss and, for example,
the observation noise which makes it differentiable in the latter for
iterative updates.
Returns:
-
log_likelihood
(Tensor
) –
prior_precision_diag
#
Obtain the diagonal prior precision \(p_0\) constructed from either a scalar, layer-wise, or diagonal prior precision.
Returns:
-
prior_precision_diag
(Tensor
) –
scatter
#
Computes the scatter, a term of the log marginal likelihood that
corresponds to L-2 regularization:
scatter
= \((\theta_{MAP} - \mu_0)^{T} P_0 (\theta_{MAP} - \mu_0) \).
Returns:
-
scatter
(Tensor
) –
log_det_prior_precision
#
Compute log determinant of the prior precision \(\log \det P_0\)
Returns:
-
log_det
(Tensor
) –
log_det_posterior_precision
#
Compute log determinant of the posterior precision \(\log \det P\) which depends on the subclasses structure used for the Hessian approximation.
Returns:
-
log_det
(Tensor
) –
log_det_ratio
#
Compute the log determinant ratio, a part of the log marginal likelihood.
Returns:
-
log_det_ratio
(Tensor
) –
posterior_precision
#
Compute or return the posterior precision \(P\).
Returns:
-
posterior_prec
(Tensor
) –
_glm_forward_call
#
_glm_forward_call(x: Tensor | MutableMapping, likelihood: Likelihood | str, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
for "glm" pred type.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
likelihood
(Likelihood or str in {'classification', 'regression', 'reward_modeling'}
) –determines the log likelihood Hessian approximation.
-
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
andlink_approx='mc'
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_predictive_samples
#
_glm_predictive_samples(f_mu: Tensor, f_var: Tensor, n_samples: int, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
using "glm" prediction
type.
Parameters:
-
f_mu
(Tensor or MutableMapping
) –glm predictive mean
(batch_size, output_shape)
-
f_var
(Tensor or MutableMapping
) –glm predictive covariances
(batch_size, output_shape, output_shape)
-
n_samples
(int
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs.
-
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
fit
#
Fit the local Laplace approximation at the parameters of the model.
Parameters:
-
train_loader
(DataLoader
) –each iterate is a training batch, either
(X, y)
tensors or a dict-like object containing keys as expressed byself.dict_key_x
andself.dict_key_y
.train_loader.dataset
needs to be set to access \(N\), size of the data set. -
override
(bool
, default:True
) –whether to initialize H, loss, and n_data again; setting to False is useful for online learning settings to accumulate a sequential posterior approximation.
-
progress_bar
(bool
, default:False
) –whether to show a progress bar; updated at every batch-Hessian computation. Useful for very large model and large amount of data, esp. when
subset_of_weights='all'
.
Source code in laplace/baselaplace.py
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|
square_norm
#
Compute the square norm under post. Precision with value-self.mean
as 𝛥:
Returns:
-
square_form
–
log_prob
#
log_prob(value: Tensor, normalized: bool = True) -> Tensor
Compute the log probability under the (current) Laplace approximation.
Parameters:
-
value
(Tensor
) – -
normalized
(bool
, default:True
) –whether to return log of a properly normalized Gaussian or just the terms that depend on
value
.
Returns:
-
log_prob
(Tensor
) –
Source code in laplace/baselaplace.py
log_marginal_likelihood
#
log_marginal_likelihood(prior_precision: Tensor | None = None, sigma_noise: Tensor | None = None) -> Tensor
Compute the Laplace approximation to the log marginal likelihood subject
to specific Hessian approximations that subclasses implement.
Requires that the Laplace approximation has been fit before.
The resulting torch.Tensor is differentiable in prior_precision
and
sigma_noise
if these have gradients enabled.
By passing prior_precision
or sigma_noise
, the current value is
overwritten. This is useful for iterating on the log marginal likelihood.
Parameters:
-
prior_precision
(Tensor
, default:None
) –prior precision if should be changed from current
prior_precision
value -
sigma_noise
(Tensor
, default:None
) –observation noise standard deviation if should be changed
Returns:
-
log_marglik
(Tensor
) –
Source code in laplace/baselaplace.py
__call__
#
__call__(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None, fitting: bool = False, **model_kwargs: dict[str, Any]) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here. When Laplace is done only on subset of parameters (i.e. some grad are disabled), only
nn
predictive is supported. -
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
whenjoint=False
in regression. In the case of last-layer Laplace with a diagonal or Kron Hessian, setting this toTrue
makes computation much(!) faster for large number of outputs. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used).
-
fitting
(bool
, default:False
) –whether or not this predictive call is done during fitting. Only useful for reward modeling: the likelihood is set to
"regression"
whenFalse
and"classification"
whenTrue
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
predictive_samples
#
predictive_samples(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
.
Can be used, for example, for Thompson sampling.
Parameters:
-
x
(Tensor or MutableMapping
) –input data
(batch_size, input_shape)
-
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here.
-
n_samples
(int
, default:100
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs. Only applies when
pred_type='glm'
. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
functional_variance
#
Compute functional variance for the 'glm'
predictive:
f_var[i] = Js[i] @ P.inv() @ Js[i].T
, which is a output x output
predictive covariance matrix.
Mathematically, we have for a single Jacobian
\(\mathcal{J} = \nabla_\theta f(x;\theta)\vert_{\theta_{MAP}}\)
the output covariance matrix
\( \mathcal{J} P^{-1} \mathcal{J}^T \).
Parameters:
-
Js
(Tensor
) –Jacobians of model output wrt parameters
(batch, outputs, parameters)
Returns:
-
f_var
(Tensor
) –output covariance
(batch, outputs, outputs)
Source code in laplace/baselaplace.py
functional_covariance
#
Compute functional covariance for the 'glm'
predictive:
f_cov = Js @ P.inv() @ Js.T
, which is a batchoutput x batchoutput
predictive covariance matrix.
This emulates the GP posterior covariance N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). Useful for joint predictions, such as in batched Bayesian optimization.
Parameters:
-
Js
(Tensor
) –Jacobians of model output wrt parameters
(batch*outputs, parameters)
Returns:
-
f_cov
(Tensor
) –output covariance
(batch*outputs, batch*outputs)
Source code in laplace/baselaplace.py
sample
#
sample(n_samples: int = 100, generator: Generator | None = None) -> Tensor
Sample from the Laplace posterior approximation, i.e., \( \theta \sim \mathcal{N}(\theta_{MAP}, P^{-1})\).
Parameters:
-
n_samples
(int
, default:100
) –number of samples
-
generator
(Generator
, default:None
) –random number generator to control the samples
Returns:
-
samples
(Tensor
) –
Source code in laplace/baselaplace.py
DiagLaplace
#
DiagLaplace(model: Module, likelihood: Likelihood | str, sigma_noise: float | Tensor = 1.0, prior_precision: float | Tensor = 1.0, prior_mean: float | Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)
Bases: ParametricLaplace
Laplace approximation with diagonal log likelihood Hessian approximation
and hence posterior precision.
Mathematically, we have \(P \approx \textrm{diag}(P)\).
See BaseLaplace
for the full interface.
Source code in laplace/baselaplace.py
log_likelihood
#
Compute log likelihood on the training data after .fit()
has been called.
The log likelihood is computed on-demand based on the loss and, for example,
the observation noise which makes it differentiable in the latter for
iterative updates.
Returns:
-
log_likelihood
(Tensor
) –
prior_precision_diag
#
Obtain the diagonal prior precision \(p_0\) constructed from either a scalar, layer-wise, or diagonal prior precision.
Returns:
-
prior_precision_diag
(Tensor
) –
scatter
#
Computes the scatter, a term of the log marginal likelihood that
corresponds to L-2 regularization:
scatter
= \((\theta_{MAP} - \mu_0)^{T} P_0 (\theta_{MAP} - \mu_0) \).
Returns:
-
scatter
(Tensor
) –
log_det_prior_precision
#
Compute log determinant of the prior precision \(\log \det P_0\)
Returns:
-
log_det
(Tensor
) –
log_det_ratio
#
Compute the log determinant ratio, a part of the log marginal likelihood.
Returns:
-
log_det_ratio
(Tensor
) –
posterior_precision
#
Diagonal posterior precision \(p\).
Returns:
-
precision
(tensor
) –(parameters)
posterior_scale
#
Diagonal posterior scale \(\sqrt{p^{-1}}\).
Returns:
-
precision
(tensor
) –(parameters)
posterior_variance
#
Diagonal posterior variance \(p^{-1}\).
Returns:
-
precision
(tensor
) –(parameters)
fit
#
Fit the local Laplace approximation at the parameters of the model.
Parameters:
-
train_loader
(DataLoader
) –each iterate is a training batch, either
(X, y)
tensors or a dict-like object containing keys as expressed byself.dict_key_x
andself.dict_key_y
.train_loader.dataset
needs to be set to access \(N\), size of the data set. -
override
(bool
, default:True
) –whether to initialize H, loss, and n_data again; setting to False is useful for online learning settings to accumulate a sequential posterior approximation.
-
progress_bar
(bool
, default:False
) –whether to show a progress bar; updated at every batch-Hessian computation. Useful for very large model and large amount of data, esp. when
subset_of_weights='all'
.
Source code in laplace/baselaplace.py
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|
log_marginal_likelihood
#
log_marginal_likelihood(prior_precision: Tensor | None = None, sigma_noise: Tensor | None = None) -> Tensor
Compute the Laplace approximation to the log marginal likelihood subject
to specific Hessian approximations that subclasses implement.
Requires that the Laplace approximation has been fit before.
The resulting torch.Tensor is differentiable in prior_precision
and
sigma_noise
if these have gradients enabled.
By passing prior_precision
or sigma_noise
, the current value is
overwritten. This is useful for iterating on the log marginal likelihood.
Parameters:
-
prior_precision
(Tensor
, default:None
) –prior precision if should be changed from current
prior_precision
value -
sigma_noise
(Tensor
, default:None
) –observation noise standard deviation if should be changed
Returns:
-
log_marglik
(Tensor
) –
Source code in laplace/baselaplace.py
__call__
#
__call__(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None, fitting: bool = False, **model_kwargs: dict[str, Any]) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here. When Laplace is done only on subset of parameters (i.e. some grad are disabled), only
nn
predictive is supported. -
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
whenjoint=False
in regression. In the case of last-layer Laplace with a diagonal or Kron Hessian, setting this toTrue
makes computation much(!) faster for large number of outputs. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used).
-
fitting
(bool
, default:False
) –whether or not this predictive call is done during fitting. Only useful for reward modeling: the likelihood is set to
"regression"
whenFalse
and"classification"
whenTrue
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 |
|
_glm_forward_call
#
_glm_forward_call(x: Tensor | MutableMapping, likelihood: Likelihood | str, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
for "glm" pred type.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
likelihood
(Likelihood or str in {'classification', 'regression', 'reward_modeling'}
) –determines the log likelihood Hessian approximation.
-
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
andlink_approx='mc'
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_predictive_samples
#
_glm_predictive_samples(f_mu: Tensor, f_var: Tensor, n_samples: int, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
using "glm" prediction
type.
Parameters:
-
f_mu
(Tensor or MutableMapping
) –glm predictive mean
(batch_size, output_shape)
-
f_var
(Tensor or MutableMapping
) –glm predictive covariances
(batch_size, output_shape, output_shape)
-
n_samples
(int
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs.
-
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
log_prob
#
log_prob(value: Tensor, normalized: bool = True) -> Tensor
Compute the log probability under the (current) Laplace approximation.
Parameters:
-
value
(Tensor
) – -
normalized
(bool
, default:True
) –whether to return log of a properly normalized Gaussian or just the terms that depend on
value
.
Returns:
-
log_prob
(Tensor
) –
Source code in laplace/baselaplace.py
predictive_samples
#
predictive_samples(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
.
Can be used, for example, for Thompson sampling.
Parameters:
-
x
(Tensor or MutableMapping
) –input data
(batch_size, input_shape)
-
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here.
-
n_samples
(int
, default:100
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs. Only applies when
pred_type='glm'
. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
KronLaplace
#
KronLaplace(model: Module, likelihood: Likelihood | str, sigma_noise: float | Tensor = 1.0, prior_precision: float | Tensor = 1.0, prior_mean: float | Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, damping: bool = False, backend_kwargs: dict[str, Any] | None = None, asdl_fisher_kwargs: dict[str, Any] | None = None)
Bases: ParametricLaplace
Laplace approximation with Kronecker factored log likelihood Hessian approximation
and hence posterior precision.
Mathematically, we have for each parameter group, e.g., torch.nn.Module,
that \P\approx Q \otimes H.
See BaseLaplace
for the full interface and see
laplace.utils.matrix.Kron
and laplace.utils.matrix.KronDecomposed
for the structure of
the Kronecker factors. Kron
is used to aggregate factors by summing up and
KronDecomposed
is used to add the prior, a Hessian factor (e.g. temperature),
and computing posterior covariances, marginal likelihood, etc.
Damping can be enabled by setting damping=True
.
Source code in laplace/baselaplace.py
log_likelihood
#
Compute log likelihood on the training data after .fit()
has been called.
The log likelihood is computed on-demand based on the loss and, for example,
the observation noise which makes it differentiable in the latter for
iterative updates.
Returns:
-
log_likelihood
(Tensor
) –
prior_precision_diag
#
Obtain the diagonal prior precision \(p_0\) constructed from either a scalar, layer-wise, or diagonal prior precision.
Returns:
-
prior_precision_diag
(Tensor
) –
scatter
#
Computes the scatter, a term of the log marginal likelihood that
corresponds to L-2 regularization:
scatter
= \((\theta_{MAP} - \mu_0)^{T} P_0 (\theta_{MAP} - \mu_0) \).
Returns:
-
scatter
(Tensor
) –
log_det_prior_precision
#
Compute log determinant of the prior precision \(\log \det P_0\)
Returns:
-
log_det
(Tensor
) –
log_det_ratio
#
Compute the log determinant ratio, a part of the log marginal likelihood.
Returns:
-
log_det_ratio
(Tensor
) –
posterior_precision
#
posterior_precision: KronDecomposed
Kronecker factored Posterior precision \(P\).
Returns:
-
precision
(`laplace.utils.matrix.KronDecomposed`
) –
log_marginal_likelihood
#
log_marginal_likelihood(prior_precision: Tensor | None = None, sigma_noise: Tensor | None = None) -> Tensor
Compute the Laplace approximation to the log marginal likelihood subject
to specific Hessian approximations that subclasses implement.
Requires that the Laplace approximation has been fit before.
The resulting torch.Tensor is differentiable in prior_precision
and
sigma_noise
if these have gradients enabled.
By passing prior_precision
or sigma_noise
, the current value is
overwritten. This is useful for iterating on the log marginal likelihood.
Parameters:
-
prior_precision
(Tensor
, default:None
) –prior precision if should be changed from current
prior_precision
value -
sigma_noise
(Tensor
, default:None
) –observation noise standard deviation if should be changed
Returns:
-
log_marglik
(Tensor
) –
Source code in laplace/baselaplace.py
__call__
#
__call__(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None, fitting: bool = False, **model_kwargs: dict[str, Any]) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here. When Laplace is done only on subset of parameters (i.e. some grad are disabled), only
nn
predictive is supported. -
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
whenjoint=False
in regression. In the case of last-layer Laplace with a diagonal or Kron Hessian, setting this toTrue
makes computation much(!) faster for large number of outputs. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used).
-
fitting
(bool
, default:False
) –whether or not this predictive call is done during fitting. Only useful for reward modeling: the likelihood is set to
"regression"
whenFalse
and"classification"
whenTrue
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_forward_call
#
_glm_forward_call(x: Tensor | MutableMapping, likelihood: Likelihood | str, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
for "glm" pred type.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
likelihood
(Likelihood or str in {'classification', 'regression', 'reward_modeling'}
) –determines the log likelihood Hessian approximation.
-
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
andlink_approx='mc'
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_predictive_samples
#
_glm_predictive_samples(f_mu: Tensor, f_var: Tensor, n_samples: int, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
using "glm" prediction
type.
Parameters:
-
f_mu
(Tensor or MutableMapping
) –glm predictive mean
(batch_size, output_shape)
-
f_var
(Tensor or MutableMapping
) –glm predictive covariances
(batch_size, output_shape, output_shape)
-
n_samples
(int
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs.
-
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
log_prob
#
log_prob(value: Tensor, normalized: bool = True) -> Tensor
Compute the log probability under the (current) Laplace approximation.
Parameters:
-
value
(Tensor
) – -
normalized
(bool
, default:True
) –whether to return log of a properly normalized Gaussian or just the terms that depend on
value
.
Returns:
-
log_prob
(Tensor
) –
Source code in laplace/baselaplace.py
predictive_samples
#
predictive_samples(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
.
Can be used, for example, for Thompson sampling.
Parameters:
-
x
(Tensor or MutableMapping
) –input data
(batch_size, input_shape)
-
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here.
-
n_samples
(int
, default:100
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs. Only applies when
pred_type='glm'
. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
LowRankLaplace
#
LowRankLaplace(model: Module, likelihood: Likelihood | str, backend: type[CurvatureInterface] = AsdfghjklHessian if find_spec('asdfghjkl') is not None else CurvatureInterface, sigma_noise: float | Tensor = 1, prior_precision: float | Tensor = 1, prior_mean: float | Tensor = 0, temperature: float = 1, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend_kwargs: dict[str, Any] | None = None)
Bases: ParametricLaplace
Laplace approximation with low-rank log likelihood Hessian (approximation).
The low-rank matrix is represented by an eigendecomposition (vecs, values).
Based on the chosen backend
, either a true Hessian or, for example, GGN
approximation could be used.
The posterior precision is computed as
\( P = V diag(l) V^T + P_0.\)
To sample, compute the functional variance, and log determinant, algebraic tricks
are usedto reduce the costs of inversion to the that of a \(K imes K\) matrix
if we have a rank of K.
Note that only AsdfghjklHessian
backend is supported. Install it via:
pip install git+https://git@github.com/wiseodd/asdl@asdfghjkl
See BaseLaplace
for the full interface.
Source code in laplace/baselaplace.py
log_likelihood
#
Compute log likelihood on the training data after .fit()
has been called.
The log likelihood is computed on-demand based on the loss and, for example,
the observation noise which makes it differentiable in the latter for
iterative updates.
Returns:
-
log_likelihood
(Tensor
) –
prior_precision_diag
#
Obtain the diagonal prior precision \(p_0\) constructed from either a scalar, layer-wise, or diagonal prior precision.
Returns:
-
prior_precision_diag
(Tensor
) –
scatter
#
Computes the scatter, a term of the log marginal likelihood that
corresponds to L-2 regularization:
scatter
= \((\theta_{MAP} - \mu_0)^{T} P_0 (\theta_{MAP} - \mu_0) \).
Returns:
-
scatter
(Tensor
) –
log_det_prior_precision
#
Compute log determinant of the prior precision \(\log \det P_0\)
Returns:
-
log_det
(Tensor
) –
log_det_ratio
#
Compute the log determinant ratio, a part of the log marginal likelihood.
Returns:
-
log_det_ratio
(Tensor
) –
posterior_precision
#
Return correctly scaled posterior precision that would be constructed as H[0] @ diag(H[1]) @ H[0].T + self.prior_precision_diag.
Returns:
-
H
(tuple(eigenvectors, eigenvalues)
) –scaled self.H with temperature and loss factors.
-
prior_precision_diag
(Tensor
) –diagonal prior precision shape
parameters
to be added to H.
log_marginal_likelihood
#
log_marginal_likelihood(prior_precision: Tensor | None = None, sigma_noise: Tensor | None = None) -> Tensor
Compute the Laplace approximation to the log marginal likelihood subject
to specific Hessian approximations that subclasses implement.
Requires that the Laplace approximation has been fit before.
The resulting torch.Tensor is differentiable in prior_precision
and
sigma_noise
if these have gradients enabled.
By passing prior_precision
or sigma_noise
, the current value is
overwritten. This is useful for iterating on the log marginal likelihood.
Parameters:
-
prior_precision
(Tensor
, default:None
) –prior precision if should be changed from current
prior_precision
value -
sigma_noise
(Tensor
, default:None
) –observation noise standard deviation if should be changed
Returns:
-
log_marglik
(Tensor
) –
Source code in laplace/baselaplace.py
__call__
#
__call__(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None, fitting: bool = False, **model_kwargs: dict[str, Any]) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here. When Laplace is done only on subset of parameters (i.e. some grad are disabled), only
nn
predictive is supported. -
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
whenjoint=False
in regression. In the case of last-layer Laplace with a diagonal or Kron Hessian, setting this toTrue
makes computation much(!) faster for large number of outputs. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used).
-
fitting
(bool
, default:False
) –whether or not this predictive call is done during fitting. Only useful for reward modeling: the likelihood is set to
"regression"
whenFalse
and"classification"
whenTrue
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_forward_call
#
_glm_forward_call(x: Tensor | MutableMapping, likelihood: Likelihood | str, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
for "glm" pred type.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
likelihood
(Likelihood or str in {'classification', 'regression', 'reward_modeling'}
) –determines the log likelihood Hessian approximation.
-
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
andlink_approx='mc'
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_predictive_samples
#
_glm_predictive_samples(f_mu: Tensor, f_var: Tensor, n_samples: int, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
using "glm" prediction
type.
Parameters:
-
f_mu
(Tensor or MutableMapping
) –glm predictive mean
(batch_size, output_shape)
-
f_var
(Tensor or MutableMapping
) –glm predictive covariances
(batch_size, output_shape, output_shape)
-
n_samples
(int
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs.
-
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
square_norm
#
Compute the square norm under post. Precision with value-self.mean
as 𝛥:
Returns:
-
square_form
–
log_prob
#
log_prob(value: Tensor, normalized: bool = True) -> Tensor
Compute the log probability under the (current) Laplace approximation.
Parameters:
-
value
(Tensor
) – -
normalized
(bool
, default:True
) –whether to return log of a properly normalized Gaussian or just the terms that depend on
value
.
Returns:
-
log_prob
(Tensor
) –
Source code in laplace/baselaplace.py
predictive_samples
#
predictive_samples(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
.
Can be used, for example, for Thompson sampling.
Parameters:
-
x
(Tensor or MutableMapping
) –input data
(batch_size, input_shape)
-
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here.
-
n_samples
(int
, default:100
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs. Only applies when
pred_type='glm'
. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
FullLaplace
#
FullLaplace(model: Module, likelihood: Likelihood | str, sigma_noise: float | Tensor = 1.0, prior_precision: float | Tensor = 1.0, prior_mean: float | Tensor = 0.0, temperature: float = 1.0, enable_backprop: bool = False, dict_key_x: str = 'input_ids', dict_key_y: str = 'labels', backend: type[CurvatureInterface] | None = None, backend_kwargs: dict[str, Any] | None = None)
Bases: ParametricLaplace
Laplace approximation with full, i.e., dense, log likelihood Hessian approximation
and hence posterior precision. Based on the chosen backend
parameter, the full
approximation can be, for example, a generalized Gauss-Newton matrix.
Mathematically, we have \(P \in \mathbb{R}^{P \times P}\).
See BaseLaplace
for the full interface.
Source code in laplace/baselaplace.py
log_likelihood
#
Compute log likelihood on the training data after .fit()
has been called.
The log likelihood is computed on-demand based on the loss and, for example,
the observation noise which makes it differentiable in the latter for
iterative updates.
Returns:
-
log_likelihood
(Tensor
) –
prior_precision_diag
#
Obtain the diagonal prior precision \(p_0\) constructed from either a scalar, layer-wise, or diagonal prior precision.
Returns:
-
prior_precision_diag
(Tensor
) –
scatter
#
Computes the scatter, a term of the log marginal likelihood that
corresponds to L-2 regularization:
scatter
= \((\theta_{MAP} - \mu_0)^{T} P_0 (\theta_{MAP} - \mu_0) \).
Returns:
-
scatter
(Tensor
) –
log_det_prior_precision
#
Compute log determinant of the prior precision \(\log \det P_0\)
Returns:
-
log_det
(Tensor
) –
log_det_ratio
#
Compute the log determinant ratio, a part of the log marginal likelihood.
Returns:
-
log_det_ratio
(Tensor
) –
posterior_scale
#
Posterior scale (square root of the covariance), i.e., \(P^{-\frac{1}{2}}\).
Returns:
-
scale
(tensor
) –(parameters, parameters)
posterior_covariance
#
Posterior covariance, i.e., \(P^{-1}\).
Returns:
-
covariance
(tensor
) –(parameters, parameters)
posterior_precision
#
Posterior precision \(P\).
Returns:
-
precision
(tensor
) –(parameters, parameters)
log_marginal_likelihood
#
log_marginal_likelihood(prior_precision: Tensor | None = None, sigma_noise: Tensor | None = None) -> Tensor
Compute the Laplace approximation to the log marginal likelihood subject
to specific Hessian approximations that subclasses implement.
Requires that the Laplace approximation has been fit before.
The resulting torch.Tensor is differentiable in prior_precision
and
sigma_noise
if these have gradients enabled.
By passing prior_precision
or sigma_noise
, the current value is
overwritten. This is useful for iterating on the log marginal likelihood.
Parameters:
-
prior_precision
(Tensor
, default:None
) –prior precision if should be changed from current
prior_precision
value -
sigma_noise
(Tensor
, default:None
) –observation noise standard deviation if should be changed
Returns:
-
log_marglik
(Tensor
) –
Source code in laplace/baselaplace.py
__call__
#
__call__(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None, fitting: bool = False, **model_kwargs: dict[str, Any]) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here. When Laplace is done only on subset of parameters (i.e. some grad are disabled), only
nn
predictive is supported. -
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
whenjoint=False
in regression. In the case of last-layer Laplace with a diagonal or Kron Hessian, setting this toTrue
makes computation much(!) faster for large number of outputs. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used).
-
fitting
(bool
, default:False
) –whether or not this predictive call is done during fitting. Only useful for reward modeling: the likelihood is set to
"regression"
whenFalse
and"classification"
whenTrue
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_forward_call
#
_glm_forward_call(x: Tensor | MutableMapping, likelihood: Likelihood | str, joint: bool = False, link_approx: LinkApprox | str = LinkApprox.PROBIT, n_samples: int = 100, diagonal_output: bool = False) -> Tensor | tuple[Tensor, Tensor]
Compute the posterior predictive on input data x
for "glm" pred type.
Parameters:
-
x
(Tensor or MutableMapping
) –(batch_size, input_shape)
if tensor. If MutableMapping, must contain the said tensor. -
likelihood
(Likelihood or str in {'classification', 'regression', 'reward_modeling'}
) –determines the log likelihood Hessian approximation.
-
link_approx
(('mc', 'probit', 'bridge', 'bridge_norm')
, default:'mc'
) –how to approximate the classification link function for the
'glm'
. Forpred_type='nn'
, only 'mc' is possible. -
joint
(bool
, default:False
) –Whether to output a joint predictive distribution in regression with
pred_type='glm'
. If set toTrue
, the predictive distribution has the same form as GP posterior, i.e. N([f(x1), ...,f(xm)], Cov[f(x1), ..., f(xm)]). IfFalse
, then only outputs the marginal predictive distribution. Only available for regression and GLM predictive. -
n_samples
(int
, default:100
) –number of samples for
link_approx='mc'
. -
diagonal_output
(bool
, default:False
) –whether to use a diagonalized posterior predictive on the outputs. Only works for
pred_type='glm'
andlink_approx='mc'
.
Returns:
-
predictive
(Tensor or tuple[Tensor]
) –For
likelihood='classification'
, a torch.Tensor is returned with a distribution over classes (similar to a Softmax). Forlikelihood='regression'
, a tuple of torch.Tensor is returned with the mean and the predictive variance. Forlikelihood='regression'
andjoint=True
, a tuple of torch.Tensor is returned with the mean and the predictive covariance.
Source code in laplace/baselaplace.py
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|
_glm_predictive_samples
#
_glm_predictive_samples(f_mu: Tensor, f_var: Tensor, n_samples: int, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
using "glm" prediction
type.
Parameters:
-
f_mu
(Tensor or MutableMapping
) –glm predictive mean
(batch_size, output_shape)
-
f_var
(Tensor or MutableMapping
) –glm predictive covariances
(batch_size, output_shape, output_shape)
-
n_samples
(int
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs.
-
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)
Source code in laplace/baselaplace.py
log_prob
#
log_prob(value: Tensor, normalized: bool = True) -> Tensor
Compute the log probability under the (current) Laplace approximation.
Parameters:
-
value
(Tensor
) – -
normalized
(bool
, default:True
) –whether to return log of a properly normalized Gaussian or just the terms that depend on
value
.
Returns:
-
log_prob
(Tensor
) –
Source code in laplace/baselaplace.py
predictive_samples
#
predictive_samples(x: Tensor | MutableMapping[str, Tensor | Any], pred_type: PredType | str = PredType.GLM, n_samples: int = 100, diagonal_output: bool = False, generator: Generator | None = None) -> Tensor
Sample from the posterior predictive on input data x
.
Can be used, for example, for Thompson sampling.
Parameters:
-
x
(Tensor or MutableMapping
) –input data
(batch_size, input_shape)
-
pred_type
(('glm', 'nn')
, default:'glm'
) –type of posterior predictive, linearized GLM predictive or neural network sampling predictive. The GLM predictive is consistent with the curvature approximations used here.
-
n_samples
(int
, default:100
) –number of samples
-
diagonal_output
(bool
, default:False
) –whether to use a diagonalized glm posterior predictive on the outputs. Only applies when
pred_type='glm'
. -
generator
(Generator
, default:None
) –random number generator to control the samples (if sampling used)
Returns:
-
samples
(Tensor
) –samples
(n_samples, batch_size, output_shape)