IMSE

IMSPE(model, theta=None, Lambda=None, mult=None, covtype=None, nu=None, eps=np.float64(1.4901161193847656e-08))[source]

IMSPE of a given design.

Integrated Mean Square Prediction Error

Parameters:

X (hetgpy.hetGP.hetGP or hetgpy.homGP.homGP model.) – Alternatively, one can provide a matrix of unique designs considered
theta (ndarray_like) – lengthscales
Lambda (ndarray_like) – diagonal matrix for the noise
mult (ndarray_like) – number of replicates at each design
covtype (str) – either “Gaussian”, “Matern3_2” or “Matern5_2”
nu (float) – variance parameter
eps (float) – numerical nugget
Details
-------
homGP (One can provide directly a model of class hetGP or)
arguments (or provide design locations X and all other)

Wij(mu1, mu2=None, theta=None, type='Gaussian')[source]

Compute double integral of the covariance kernel over a [0,1]^d domain

Parameters:

mu1 (ndarray)like) – input locations considered
mu2 (ndarray)like) – input locations considered
theta (ndarray_like) – lengthscale hyperparameter of the kernel
type (str) – kernel type, one of "Gaussian", "Matern5_2" or "Matern3_2"

References

M. Binois, J. Huang, R. B. Gramacy, M. Ludkovski (2019), Replication or exploration? Sequential design for stochastic simulation experiments, Technometrics, 61(1), 7-23. Preprint available on arXiv:1710.03206.

allocate_mult(model=None, N=None, Wijs=None, use_Ki=False)[source]

Allocation of replicates on existing design locations, based on (29) from (Ankenman et al, 2010)

Parameters:

model (hetGP model) – hetGP model
N (int) – total budget of replication to allocate
Wijs (ndarray) – optional previously computed matrix of Wijs, see hetgpy.IMSE.Wij
use_Ki (bool) – should Ki from model be used?

Return type:

vector with approximated best number of replicates per design

References

Ankenman, B. Nelson, J. Staum (2010), Stochastic kriging for simulation metamodeling, Operations research, pp. 371–382, 58

deriv_crit_IMSPE(x, model, id=None, Wijs=None)[source]

Derivative of crit_IMSPE

Parameters:

x (ndarray_like) – matrix for the news design (size 1 x d)
model (hetGP or homGP) – model
id (None) – None (but included for compatibility with crit_IMSPE input structure so it can be used in minimize)
Wijs (ndarray_like) – optional previously computed matrix of Wijs, see Wij

Return type:

Derivative of the sequential IMSPE with respect to x

horizon(model, current_horizon=None, previous_ratio=None, target=None, Wijs=None, seed=None)[source]

Adapt the look-ahead horizon depending on the replicate allocation or a target ratio

Parameters:

model (hetGP or homGP model) – hetGP or homGP model
current_horizon (int) – horizon used for the previous iteration, see details
previous_ratio (float) – ratio before adding the previous new design
target (float) – scalar in [0,1] for desired n/N
Wijs (nd_array) – optional previously computed matrix of Wijs, see hetgpy.IMSE.Wij

Returns:

Randomly selected horizon for next iteration (adpative) if no target is provided,
otherwise returns the update horizon value.
Details
——-
If target is provided, along with previous_ratio and current_horizon
itemize{ – item the horizon is increased by one if more replicates are needed but a new ppint has been added at the previous iteration, item the horizon is decreased by one if new points are needed but a replicate has been added at the previous iteration, item otherwise it is unchanged.
}
If no target is provided, allocate_mult is used to obtain the best allocation of the existing replicates,
then the new horizon is sampled from the difference between the actual allocation and the best one, bounded below by 0.
See (Binois et al. 2017).

References

M. Binois, J. Huang, R. B. Gramacy, M. Ludkovski (2019), Replication or exploration? Sequential design for stochastic simulation experiments, Technometrics, 61(1), 7-23.cr Preprint available on arXiv:1710.03206.

lhs_EP(m, seed=None)[source]

From DiceDesign: FUNCTION PERFORMING ELEMENTARY PERMUTATION (EP) IN LHD USED IN SA ALGORITHMS

Parameters:: m (nd_arraylike) – the design
Returns:: out – list including design after EP, ligns and columns defining EP
Return type:: tuple

maximinSA_LHS(design, T0=10, c=0.95, it=2000, p=50, profile='GEOM', Imax=100, seed=None)[source]

Implementation of maximinSA_LHS from DiceDesign Only profile=”GEOM” is implemented (like in hetGP)

#####maximinSA_LHS##### #####Maximin LHS VIA SIMULATED ANNEALING OPTIMIZATION#####

mi(mu1, theta, type)[source]

Compute integral of the covariance kernel over a [0,1]^d domain

Parameters:

mu1 (ndarray_like) – input locations considered
theta (ndarray_like) – lengthscale hyperparameter of the kernel
type (str) – kernel type, one of "Gaussian", "Matern5_2" or "Matern3_2"

References

Replication or exploration? Sequential design for stochastic simulation experiments, Technometrics, 61(1), 7-23. Preprint available on arXiv:1710.03206.

phiP(design, p=50)[source]

Implementation of phiP.R from DiceDesign (necessary for maximinSA_LHS from DiceDesign which is used by IMSPE_search)

From DiceDesign: Compute the phiP criterion (Lp norm of the sum of the inverses of the design inter-point distances) Reference: Pronzato, L. and Muller, W.,2012, Design of computer experiments: space filling and beyond, Statistics and Computing, 22:681-701. A higher phiP corresponds to a more regular scaterring of design points

Parameters:

design (nd_arraylike) – design for a computer experiment
p (int) – the “p” in the Lp norm which is taken (default=50)

Returns:

fi_p – the phiP criterion

Return type:

np.float