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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 the N given data points, f_a is the parametrized function and a the set of function parameters.

Use the expression parameter 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's BOBYQA (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 the set interpolation points parameter is set to true.)

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 of 4 + 3 * ln(n), where n is 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 the set population size parameter is set to true.)

use local random seed​

CMA-ES optimization parameter:

This parameter indicates if a local random seed should be used for randomization. Using the same value for local random seed will produce the same randomization.

local random seed​

CMA-ES optimization parameter:

This parameter specifies the local random seed.

(This parameter is only available if the use local random seed parameter is set to true.)

active cma​

CMA-ES optimization parameter:

If set to true, 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 to 1 means 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.

stop error​

CMA-ES optimization parameter:

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