"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  They have been replaced by a combination of linear regression (for assigning coefficients) with automatic feature generation approaches.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>

mzn

Thanks a lot Ingo. I am interested in the following:
1. I have a set of data points (x1, x2, x3...) with a corresponding output (y1)
2. I need to derive a relation (in the form of an equation) that links x1, x2, x3 to y1 such that I can predict the output for any inputs variables.
3. Can I do this in RM? If yes, is there a simple example I/my graduate students can follow?
4. Your youtube videos are very helpful! Thanks!

IngoRM

Hi @mzn

Thanks for your kind words  

The process above is a cool example, but maybe not simple enough.  Pretty much machine learning models in RapidMiner can be used for this task, but maybe I would go with a simple linear regression first.  The process below shows a simple example for this.  If you use the Model Simulator like I do in this example, the students can even play around with some of the inputs and see how the model reacts.  You can see the Simulator in this video (around minute 6:40): https://academy.rapidminer.com/learn/video/auto-model-classification

More helpful videos on this can be found here: https://academy.rapidminer.com/catalog?label=search&value=regression

Hope this helps,
Ingo

<?xml version="1.0" encoding="UTF-8"?><process version="9.2.000"><br>&nbsp; <context><br>&nbsp;&nbsp;&nbsp; <input/><br>&nbsp;&nbsp;&nbsp; <output/><br>&nbsp;&nbsp;&nbsp; <macros/><br>&nbsp; </context><br>&nbsp; <operator activated="true" class="process" compatibility="9.2.000" expanded="true" name="Process"><br>&nbsp;&nbsp;&nbsp; <parameter key="logverbosity" value="init"/><br>&nbsp;&nbsp;&nbsp; <parameter key="random_seed" value="2001"/><br>&nbsp;&nbsp;&nbsp; <parameter key="send_mail" value="never"/><br>&nbsp;&nbsp;&nbsp; <parameter key="notification_email" value=""/><br>&nbsp;&nbsp;&nbsp; <parameter key="process_duration_for_mail" value="30"/><br>&nbsp;&nbsp;&nbsp; <parameter key="encoding" value="UTF-8"/><br>&nbsp;&nbsp;&nbsp; <process expanded="true"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="generate_data" compatibility="9.2.000" expanded="true" height="68" name="Generate Data" width="90" x="45" y="34"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="target_function" value="sum"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="number_examples" value="1000"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="number_of_attributes" value="5"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attributes_lower_bound" value="-10.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attributes_upper_bound" value="10.0"/><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="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="local_random_seed" value="1992"/><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; <operator activated="true" class="add_noise" compatibility="9.2.000" expanded="true" height="103" name="Add Noise" width="90" x="179" y="34"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="return_preprocessing_model" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="create_view" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attribute_filter_type" value="all"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attribute" value=""/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="attributes" value=""/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_except_expression" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="value_type" value="attribute_value"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_value_type_exception" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="except_value_type" value="time"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="block_type" value="attribute_block"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_block_type_exception" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="except_block_type" value="value_matrix_row_start"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="invert_selection" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="include_special_attributes" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="random_attributes" value="5"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="label_noise" value="0.05"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="default_attribute_noise" value="0.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <list key="noise"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="offset" value="0.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="linear_factor" value="1.0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_local_random_seed" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="local_random_seed" value="1992"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="split_data" compatibility="9.2.000" expanded="true" height="103" name="Split Data" width="90" x="313" y="187"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <enumeration key="partitions"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="ratio" value="0.7"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="ratio" value="0.3"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </enumeration><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="sampling_type" value="automatic"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_local_random_seed" value="false"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="local_random_seed" value="1992"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="linear_regression" compatibility="9.2.000" expanded="true" height="103" name="Linear Regression" width="90" x="447" y="34"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="feature_selection" value="none"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="alpha" value="0.05"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="max_iterations" value="10"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="forward_alpha" value="0.05"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="backward_alpha" value="0.05"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="eliminate_colinear_features" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="min_tolerance" value="0.05"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="use_bias" value="true"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <parameter key="ridge" value="1.0E-8"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </operator><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <operator activated="true" class="apply_model" compatibility="9.2.000" expanded="true" height="82" name="Apply Model" width="90" x="581" y="238"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <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="model_simulator:model_simulator" compatibility="9.2.000" expanded="true" height="103" name="Model Simulator" width="90" x="782" y="136"/><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" to_port="example set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Split Data" from_port="partition 1" to_op="Linear Regression" to_port="training set"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Split Data" from_port="partition 2" to_op="Apply Model" to_port="unlabelled data"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Linear Regression" from_port="model" to_op="Apply Model" to_port="model"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Linear Regression" from_port="exampleSet" to_op="Model Simulator" to_port="training data"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Apply Model" from_port="labelled data" to_op="Model Simulator" to_port="test data"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Apply Model" from_port="model" to_op="Model Simulator" to_port="model"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Model Simulator" from_port="simulator output" to_port="result 1"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <connect from_op="Model Simulator" from_port="model output" 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="105"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <portSpacing port="sink_result 2" spacing="0"/><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <portSpacing port="sink_result 3" spacing="0"/><br>&nbsp;&nbsp;&nbsp; </process><br>&nbsp; </operator><br></process>