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Function Fitting

Synopsis

Fits a parametrized numeric function to a set of data points.

Description

This operator takes a parametrized numeric function and a set of data points and fits the function to the data points. It does so by minimizing the objective function

obj(a) = Σ(f_a(xk) - yk)²

where(xk, yk), k ∈ {1, ... , N}are theNgiven data points,f_ais the parametrized function andathe set of function parameters.

Use theexpressionparameter to specify a parametrized function. Variables that are not attributes in the input example set are automatically recognized and optimized as function parameters.

(Please note: This operator is in a beta state and its behavior may change in future releases.)

Input

training set

This input port expects an ExampleSet. It should hold the label and the variables used in the parametrized function.

Output

prediction

The training set with an additional prediction column. The prediction column is the result of applying the generated model to the data points.

parameters

Example set holding the optimized parameter values and the corresponding error.

model

Model holding the fitting information.

original

The training set is passed without any modifications through this port.

Parameters

Expression

The parametrized numeric function can be specified here. Use the calculator button to the right to open the'Edit Expression'window.

Optimization algorithm

The optimization algorithm used to minimize the objective function.

  • Michael J. D. Powell'sBOBYQA (Bound Optimization BY Quadratic Approximation)algorithm. This algorithm can be applied to problem dimensions>= 2.
  • CMA-ES (Covariance Matrix Adaptation Evolution Strategy)algorithm. This algorithm can be applied to problem dimensions>= 1.

Initial parameter values

The initial parameter values. If you specify bounds for the parameters, then the initial parameter values must lie within these bounds.

Parameter bounds

Bounds for the parameter values. Please assure that the initial values lie within these bounds.

Max iterations

The maximum number of iterations to be used for the model fitting.

Max evaluations

The maximum number of function evaluations to be used for the model fitting.

Set interpolation points

BOBYQA optimization parameter:

Check this parameter to manually set the number of interpolation points.

Interpolation points

BOBYQA optimization parameter:

The number of interpolation points used to locally approximate the objective function.

(This parameter is only available if theset interpolation pointsparameter is set totrue.)

Initial trust

BOBYQA optimization parameter:

The initial trust region radius.

Stop trust

BOBYQA optimization parameter:

Stopping criterion. The algorithm stops if the trust region radius drops below this threshold.

Sigma

CMA-ES optimization parameter:

The initial standard deviation for sampling new search points. Large values lead to a broader, small values to a more local search.

Set population size

CMA-ES optimization parameter:

Check this parameter to manually set the population size. By default the algorithm uses a population size of4 + 3 * ln(n), wherenis the number of optimized function parameters.

Population size

CMA-ES optimization parameter:

The number offspring used to explore the search space.

(This parameter is only available if theset population sizeparameter is set totrue.)

Use local random seed

CMA-ES optimization parameter:

This parameter indicates if alocal random seedshould be used for randomization. Using the same value forlocal random seedwill produce the same randomization.

Local random seed

CMA-ES optimization parameter:

This parameter specifies thelocal random seed.

(This parameter is only available if theuse local random seedparameter is set totrue.)

Active cma

CMA-ES optimization parameter:

If set totrue, the algorithm will use active covariance matrix adaption.

Diagonal only

CMA-ES optimization parameter:

Number of initial iterations with diagonal covariance matrix. Special case: Setting this parameter to1means keeping the covariance matrix always diagonal.

Feasible count

CMA-ES optimization parameter:

Number of times new random offspring is generated in case it is outside of the defined bounds.

Stop improvement

CMA-ES optimization parameter:

Stopping criterion. Algorithm stops if the error improvement is below the given threshold.

停止错误

CMA-ES optimization parameter:

Stopping criterion. Algorithm stops if the error is below the given threshold.