SED:SED toolbox

Introduction

SED Toolbox

The SED toolbox is a versatile Matlab toolbox that implements

--TO BE UPDATED--

the popular Gaussian Process based kriging surrogate models. Kriging is in particular popular for approximating (and optimizing) deterministic computer experiments. Given a dataset the toolbox automatically fits a kriging surrogate model to it. Afterwards the kriging surrogate can be fully exploited instead of the (probably more expensive) simulation code.

The toolbox is aimed for solving complex applications (expensive simulation codes, physical experiments, ...) and for researching new kriging extensions and techniques.

Download

See: download page

Quick start guide

IMPORTANT: Before the toolbox can be used you have to include the toolbox in Matlab's search path. You can do this manually by running startup, or, if Matlab is started in the root toolbox directory, then startup will be run automatically.

startup

Now the toolbox is ready to be used. The blindDACE toolbox is designed in an object oriented (OO) fashion. It is strongly recommended to exploit the OO design directly, i.e., use the Kriging and Optimizer matlab classes. However, for convenience wrapper scripts (dacefit, predictor) are provided that emulate the DACE toolbox interface (see wrapper scripts for more information).

Assume you want to fit a dataset of n samples in d dimensions.

samples holds the input parameters n-by-d array (each row is one observation) and values is the corresponding n-by-1 array containing the output values. lb and ub are 1-by-d arrays defining the lower bounds and upper bounds, respectively, needed to optimize the hyperparameters (theta). In addition, a set of starting values for theta has to be specified (i.e., theta0 is also an 1-by-d array)

As of version 0.2 of the blindDACE toolbox a script is provided, blinddacefit, that just takes your dataset (a samples and values matrix) and returns a fitted kriging object, all other parameters (theta0, etc.) are set to some sensible defaults.

For more flexibility the full example code to fit the dataset is:

...
% Generate kriging options structure
opts = getDefaultOptions();
opts.hpBounds = [lb ; ub]; % hyperparameter optimization bounds

% configure the optimization algorithm (only one optimizer is included)
% the Matlab Optimization toolbox is REQUIRED
optimopts.GradObj = 'on';
optimopts.DerivativeCheck = 'off';
optimopts.Diagnostics = 'off';
optimopts.Algorithm = 'active-set';
opts.hpOptimizer = MatlabOptimizer( dim, 1, optimopts );

% build and fit Kriging object
k = Kriging( opts, theta0, 'regpoly0', @corrgauss );
k = k.fit( samples, values );

% k represents the approximation and can now be used, e.g.,
[y mse] = k.predict( [1 2] )
...

See the included demo.m script for more example code on how to use the blindDACE toolbox (including more advanced features such as using blind kriging or how to use regression instead of interpolation). For more information on the classes and their methods please refer to the source files.

SED toolbox interface

The SED toolbox provides

--TO BE UPDATED--

two scripts dacefit.m and predictor.m that emulate the behavior of the DACE toolbox ([1]). Note, that full compatibility between blindDACE and the DACE toolbox is not provided. The scripts merely aim to ease the transition from the DACE toolbox to the blindDACE toolbox.

Example code:

krige = dacefit(samples, values, 'regpoly0', 'corrgauss', theta0, lb, ub )
y = predictor([1 2], krige)

Obviously, a lot less code is used to copy the setup described above. However, less code means less flexibility (e.g., blind kriging and regression kriging are not available using the wrapper scripts). Hence, it is suggested to learn the object oriented interface of SED and use it instead.

Contribute

Suggestions on how to improve the SED toolbox are always welcome. For more information please see the feedback page.