Acquisition Functions

class pyvbmc.acquisition_functions.AbstractAcqFcn

Bases: ABC

Abstract acquisition function for VBMC.

__call__(Xs: ndarray, gp: GP, vp: VariationalPosterior, function_logger: FunctionLogger, optim_state: dict)

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()

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

Bases: AbstractAcqFcn

Acquisition function for prospective uncertainty search.

class pyvbmc.acquisition_functions.AcqFcnIMIQR(quantile=0.75)

Bases: AbstractAcqFcn

Integrated Median Interquantile Range (IMIQR) acquisition function.

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

is_log_added(**kwargs)

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 :math: \log [\sinh(u * f_s)]`, where f_s is the GP predictive variance 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)

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)

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

Bases: AbstractAcqFcn

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

class pyvbmc.acquisition_functions.AcqFcnNoisy

Bases: AbstractAcqFcn

Acquisition function for noisy prospective uncertainty search.

class pyvbmc.acquisition_functions.AcqFcnVIQR(quantile=0.75)

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.

is_log_added(**kwargs)

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 :math: \log [\sinh(u * f_s)]`, where f_s is the GP predictive variance 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. Of the same shape as f_s2.

is_log_base(x, **kwargs)

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)

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

Bases: AbstractAcqFcn

Acquisition function via vanilla uncertainty sampling.