optimal_experimental_design
- pyapprox.expdesign.optimal_experimental_design(design_pts, fun, criteria, regression_type='lstsq', noise_multiplier=None, solver_opts=None, pred_factors=None, cvar_tol=None)[source]
Compute optimal experimental designs for models of the form
to be used with estimators, such as least-squares and quantile regression, to find approximate parameters
that are the solutions offor some loss function
- Parameters:
- design_ptsnp.ndarray (nvars,nsamples)
All possible experimental conditions
- design_factorscallable or np.ndarray
The function
with the signaturedesign_factors(z,p)->np.ndarray
where z are the design points and p are the unknown parameters of the function which will be estimated from data collected using the optimal design
A np.ndarray with shape (nsamples,nfactors) where each column is the jacobian of
for some- criteriastring
The optimality criteria. Supported criteria are
'A'
'D'
'C'
'I'
'R'
'G'
The criteria I,G and R require pred_factors to be provided. A, C and D optimality do not. R optimality requires cvar_tol to be provided.
See [KJHSIAMUQ2020] for a definition of these criteria
- regression_typestring
The method used to compute the coefficients of the linear model. This defines the loss function
. Currently supported options are'lstsq'
'quantile'
Both these options will produce the same design if noise_multiplier is None
- noise_multipliernp.ndarray (nsamples)
An array specifying the noise multiplier
at each design point- solver_optsdict
Options passed to the non-linear optimizer which solves the OED problem
- pred_factorscallable or np.ndarray
The function
with the signaturedesign_factors(z,p)->np.ndarray
where z are the prediction points and p are the unknown parameters
A np.ndarray with shape (nsamples,nfactors) where each column is the jacobian of
for some- cvar_tolfloat
The
quantile defining the R-optimality criteria. When , I and R optimal designs will be the same.
- Returns:
- final_design_ptsnp.ndarray (nvars,nfinal_design_pts)
The design points used in the experimental design
- nrepetitionsnp.ndarray (nfinal_design_pts)
The number of times to evaluate the model at each design point
References
[KJHSIAMUQ2020]D.P. Kouri, J.D. Jakeman, G. Huerta, Risk-Adapted Optimal Experimental Design.