"How to carry out symbolic regression?"

mzn

Is there any tutorials/examples on to how use RM to carry out symbolic regression?

IngoRM

Hi @mzn

Traditional approaches for symbolic regression often suffered from a phenomenon called feature bloat which is why they are hardly used any longer today.  They have been replaced by a combination of linear regression (for assigning coefficients) with automatic feature generation approaches.  In RapidMiner you would use a combination of the operators Generalized Linear Models with Automatic Feature Engineering for this.  The multi-objective optimization approach keeps the feature bloat in check and therefore reduces the risk for overfitting.  I have attached a small demo process below.

I gave a presentation in London last week which also covered this to some degree.  For this discussion I used similar data to the one in the example process mentioned above.  I attached a couple of relevant slides showing a simple linear regression model, a decision tree model, a GBT model, and a model consisting of linear regression combined with automatic feature engineering.  Like in symbolic regression, the resulting formula can be easily seen (in this case it was prediction(y) = 10,550 * |x| + 7,565 * x * |x|2 + 705 / |x| + 17,394.

Here are some relevant links:

• https://docs.rapidminer.com/latest/studio/operators/modeling/optimization/automatic_feature_engineering.html
• https://docs.rapidminer.com/latest/studio/operators/modeling/predictive/functions/generalized_linear_model.html
• https://rapidminer.com/resource/automatic-feature-engineering/ - check out the video from minute 30 on
  

And finally the little demo process below.

Hope this helps,
Ingo

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<parameter key="number_examples" value="3000"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="number_of_attributes" value="1"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attributes_lower_bound" value="-25.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attributes_upper_bound" value="25.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="gaussian_standard_deviation" value="10.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="largest_radius" value="10.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_local_random_seed" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="local_random_seed" value="1977"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="datamanagement" value="double_array"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="data_management" value="auto"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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<parameter key="use_local_random_seed" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="local_random_seed" value="1992"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="h2o:generalized_linear_model" compatibility="9.2.000" expanded="true" height="124" name="Generalized Linear Model" width="90" x="179" y="34"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="family" value="AUTO"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="link" value="family_default"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="solver" value="AUTO"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="reproducible" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="maximum_number_of_threads" value="4"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_regularization" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="lambda" value="1.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="lambda_search" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="number_of_lambdas" value="0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="lambda_min_ratio" value="0.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="early_stopping" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="stopping_rounds" value="3"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="stopping_tolerance" value="0.001"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="alpha" value="1.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="standardize" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="non-negative_coefficients" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="add_intercept" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="compute_p-values" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="remove_collinear_columns" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="missing_values_handling" value="MeanImputation"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="max_iterations" value="0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="specify_beta_constraints" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <list key="beta_constraints"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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<portSpacing port="sink_performance sink" spacing="0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </process><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="multiply" compatibility="9.2.000" expanded="true" height="103" name="Multiply (2)" width="90" x="715" y="34"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="model_simulator:apply_feature_set" compatibility="9.2.000" expanded="true" height="82" name="Apply Feature Set" width="90" x="849" y="187"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="handle missings" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="keep originals" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="originals special role" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="h2o:generalized_linear_model" compatibility="9.2.000" expanded="true" height="124" name="Generalized Linear Model (2)" width="90" x="983" y="187"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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<list key="application_parameters"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="create_view" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="concurrency:join" compatibility="9.2.000" expanded="true" height="82" name="Join" width="90" x="1251" y="442"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="remove_double_attributes" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="join_type" value="inner"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_id_attribute_as_key" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <list key="key_attributes"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="keep_both_join_attributes" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Generate Data" from_port="output" to_op="Add Noise" to_port="example set input"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Add Noise" from_port="example set output" to_op="Split Data (2)" to_port="example set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Split Data (2)" from_port="partition 1" to_op="Multiply" to_port="input"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Split Data (2)" from_port="partition 2" to_op="Generate ID" to_port="example set input"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Generate ID" from_port="example set output" to_op="Multiply (3)" to_port="input"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Multiply" from_port="output 1" to_op="Automatic Feature Engineering" to_port="example set in"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Multiply" from_port="output 2" to_op="Apply Feature Set" to_port="example set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Automatic Feature Engineering" from_port="feature set" to_op="Multiply (2)" to_port="input"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Multiply (2)" from_port="output 1" to_op="Apply Feature Set" to_port="feature set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Multiply (2)" from_port="output 2" to_op="Apply Feature Set (2)" to_port="feature set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Apply Feature Set" from_port="example set" to_op="Generalized Linear Model (2)" to_port="training set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Generalized Linear Model (2)" from_port="model" to_op="Apply Model (2)" to_port="model"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Multiply (3)" from_port="output 1" to_op="Apply Feature Set (2)" to_port="example set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Multiply (3)" from_port="output 2" to_op="Join" to_port="right"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Apply Feature Set (2)" from_port="example set" to_op="Apply Model (2)" to_port="unlabelled data"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Apply Model (2)" from_port="labelled data" to_op="Join" to_port="left"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Apply Model (2)" from_port="model" to_port="result 1"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Join" from_port="join" to_port="result 2"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <portSpacing port="source_input 1" spacing="0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <portSpacing port="sink_result 1" spacing="0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <portSpacing port="sink_result 2" spacing="315"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <portSpacing port="sink_result 3" spacing="0"/><br>&nbsp;&nbsp;&nbsp; </process><br>&nbsp; </operator><br></process><br>

Eliminating the Hidden Black Box in Machine Learning Models Only Modeling.pdf