Acquisition Functions#

class pyvbmc.acquisition_functions.AbstractAcqFcn[source]#

Bases: ABC

Abstract acquisition function for VBMC.

Notes

A subclass that sets acq_info["compute_var_log_joint"] = True is given the posterior uncertainty of the expected log joint before each search: active_sample then writes its variance per GP hyperparameter sample to optim_state["var_log_joint_samples"], shape (Ns,) and a scalar when Ns == 1, and the covariance of the mixture components’ integrals to optim_state["cov_log_joint_components"], shape (Ns, K, K). The built-in acquisitions leave the flag disabled and neither entry exists for them.

__call__(Xs: ndarray, gp: GP, vp: VariationalPosterior, function_logger: FunctionLogger, optim_state: dict)[source]#

Calculate the acquisition function for the given inputs.

Parameters:

Xsnp.ndarray: Input points.
gpgpr.GP: The GaussianProcess of the VBMC instance this function is called from.
vpVariationalPosterior: The VariationalPosterior of the VBMC instance this function is called from.
function_loggerFunctionLogger: The FunctionLogger of the VBMC instance this function is called from.
optim_statedict: The optim_state of the VBMC instance this function is called from.

Returns:

acqnp.ndarray: The output of the acquisition function, shape (N,) where N is the number of input points.

get_info()[source]#

Return a dict with information about the acquisition function.

Returns:

acq_infodict: A dict containing information about the acquisition function.

class pyvbmc.acquisition_functions.AcqFcn[source]#

Bases: AbstractAcqFcn

Acquisition function for prospective uncertainty search.

class pyvbmc.acquisition_functions.AcqFcnIMIQR(quantile=0.75)[source]#

Bases: AbstractAcqFcn

Integrated Median Interquantile Range (IMIQR) acquisition function.

Approximates the Integrated Median Interquantile Range (IMIQR) via importance samples from the GP surrogate.

Parameters:

quantilefloat, optional: The upper quantile \(p_u\) of the interquantile range, a number strictly between 0.5 and 1; the default 0.75 gives \(u = \Phi^{-1}(0.75)\).

is_log_added(**kwargs)[source]#

Importance sampling proposal log density, added part.

The added term in the importance sampling proposal log density: The full proposal log density is is_log_full = is_log_base + is_log_added. Added part for VIQR/IMIQR is \(\log [2 \sinh(u f_s)]\), where \(f_s\) is the GP predictive standard deviation at the input points.

Parameters:

f_s2np.ndarray: The predicted posterior variance at the points of interest.

Returns:

ynp.ndarray: The added log density term at the points of interest.

is_log_base(x, **kwargs)[source]#

Importance sampling proposal log density, base part.

The base density of the importance sampling proposal distribution, used for computing i.s. weights (in addition to the full proposal density). The full proposal log density is is_log_full = is_log_base + is_log_added. IMIQR approximates an expectation w.r.t. to the (exponentiated) GP using importance sampling, so this base log density is the GP mean, f_mu.

Parameters:

f_munp.ndarray: The gp posterior mean at the points of interest.

Returns:

f_munp.ndarray: The log density of the target against which the i.s. expectation is taken. Here, just the log density as modeled by the GP.

is_log_full(x, **kwargs)[source]#

Importance sampling full proposal log density.

The full proposal log density, used for MCMC sampling: is_log_full = is_log_base + is_log_added.

Parameters:

f_munp.ndarray: The gp posterior mean at the points of interest. Either [f_s2 and f_mu] or gp must be provided.
f_s2np.ndarray, optional: The predicted posterior variance at the points of interest. Either [f_s2 and f_mu] or gp must be provided.
gpgpyreg.GaussianProcess, optional: The GP modeling the log-density. Either [f_s2 and f_mu] or gp must be provided.

Returns:

ynp.ndarray: The full log density of the importance sampling proposal distribution at the points of interest. Of the same shape as f_s2.

Raises:

ValueError: If [f_s2 or f_mu] are not provided, and gp is not provided.

class pyvbmc.acquisition_functions.AcqFcnLog[source]#

Bases: AbstractAcqFcn

Acquisition function for prospective uncertainty search (log-valued).

class pyvbmc.acquisition_functions.AcqFcnNoisy[source]#

Bases: AbstractAcqFcn

Acquisition function for noisy prospective uncertainty search.

class pyvbmc.acquisition_functions.AcqFcnVIQR(quantile=0.75, loss='iqr')[source]#

Bases: AbstractAcqFcn

Variational Interquantile Range (VIQR) acquisition function.

Approximates the Integrated Median Interquantile Range (IMIQR) by simple Monte Carlo using samples from the Variational Posterior.

Parameters:

quantilefloat, optional

The upper quantile \(p_u\) of the interquantile range, a number strictly between 0.5 and 1; the default 0.75 gives \(u = \Phi^{-1}(0.75)\).

loss{“iqr”, “iqr_reduction”}, optional

The loss whose expectation under the variational posterior the acquisition minimizes. Both losses share the same look-ahead predictive standard deviation \(s_{\Xi \cup \theta_*}(\theta_a)\) at the importance points \(\theta_a\): the GP posterior after a hypothetical observation at the candidate \(\theta_*\), which does not depend on the value observed there.

"iqr" (default): the log integrated interquantile range after the observation, \(\log \sum_a 2 \sinh(u\, s_{\Xi \cup \theta_*}(\theta_a))\), the VIQR of [1].
"iqr_reduction": minus the log of the integrated reduction of the interquantile range, \(-\log \sum_a w_a [\sinh(u\, s_\Xi(\theta_a)) - \sinh(u\, s_{\Xi \cup \theta_*}(\theta_a))]\). It has the same minimizer as "iqr" over any fixed candidate set. The log of the reduction spans orders of magnitude where the log of the residual range is nearly flat, which matters to the tolerance-based termination of the search optimizer.

\(w_a\) are the importance weights, normalized over the hyperparameter samples and the importance points together (so the reduction acquisition carries a constant, \(\log (N_s N_a)\) for \(N_s\) hyperparameter samples and \(N_a\) importance points, that does not move the minimizer) and uniform under the simple Monte Carlo of VIQR. The reduction is non-negative, so "iqr_reduction" is +inf where the candidate reduces the interquantile range at no importance point.

References

[1]

Acerbi, L. (2020). “Variational Bayesian Monte Carlo with Noisy Likelihoods.” Advances in Neural Information Processing Systems 33.

LOSSES = ('iqr', 'iqr_reduction')#

is_log_added(**kwargs)[source]#

Importance sampling proposal log density, added part.

Parameters:

f_s2np.ndarray: The predicted posterior variance at the points of interest.

Returns:

ynp.ndarray: The added log density term at the points of interest. Of the same shape as f_s2.

is_log_base(x, **kwargs)[source]#

Importance sampling proposal log density, base part.

The base density of the importance sampling proposal distribution, used for computing i.s. weights (in addition to the full proposal density). The full proposal log density is is_log_full = is_log_base + is_log_added. VIQR approximates an expectation w.r.t. to the VP using simple Monte Carlo, so this base density is constant (log=0).

Parameters:

xnp.ndarray: The input points, shape (N, D) where N is the number of points and D is the dimension.
f_s2np.ndarray: The predicted posterior variance at the points of interest.

Returns:

znp.ndarray: The log base part of the importance sampling weights (zeros), shape f_s2.

is_log_full(x, **kwargs)[source]#

Importance sampling full proposal log density.

The full proposal log density, used for MCMC sampling: is_log_full = is_log_base + is_log_added.

Parameters:

f_s2np.ndarray, optional: The predicted posterior variance at the points of interest. Either f_s2 or gp must be provided.
gpgpyreg.GaussianProcess, optional: The GP modeling the log-density. Either f_s2 or gp must be provided.

Returns:

ynp.ndarray: The full log density of the importance sampling proposal distribution at the points of interest. Of the same shape as f_s2.

Raises:

ValueError: If neither f_s2 nor gp are provided.

class pyvbmc.acquisition_functions.AcqFcnVanilla[source]#

Bases: AbstractAcqFcn

Acquisition function via vanilla uncertainty sampling.

Acquisition Functions

Contents

Acquisition Functions#