# ApproxBuilder¶

## Introduction¶

The ApproxBuilder block trains an approximation model in the SmartSelection or manual mode using two input samples containing the values of variables and responses. After training, the block outputs the binary model, block finish status and a human readable model summary. It can also save the model to disk and export the model to a variety of other formats compatible with third-party programs and tools.

## Configuration¶

Usually configuration of an ApproxBuilder block requires the following steps:

• Congifure smart or manual training. For details, see section Training Modes.
• Provide the training data and additional information on variables and responses. For details, see section Training Data.
• Obtain the results. The block outputs the approximation model to the model port. It also outputs a human-readable model summary to info port after successfully training a model.

Optionally, you can:

### Training Modes¶

The ApproxBuilder block supports two training modes: SmartSelection (default) and manual. In the SmartSelection mode, pSeven automatically selects and tunes the approximation technique in order to obtain the most accurate approximation model. Manual training mode is intended for expert users who want to use specific training options and control the model quality manually.

If needed, you can configure both modes in the same block and then switch between them. The block saves all settings you specify, but only settings for the selected mode apply when it runs. For example, if you select a specific training technique in the manual mode, and then switch to the SmartSelection mode and run the workflow, the technique setting is ignored.

Tip

Approximation technique and a few other options can be specified manually even in the SmartSelection mode, using the Advanced options… hint. These option settings apply to SmartSelection only, manual mode ignores them.

To switch between SmartSelection and manual training mode from Run, you can add a workflow parameter which selects the mode: see the Parameter checkbox near the mode switch in the configuration dialog. In particular, this parameter can be useful when you configure a workflow for other users, as they will be able to switch modes without opening the block’s configuration dialog. This scenario assumes that your users do not edit the ApproxBuilder block configuration, so you should also add required hints in the SmartSelection mode and set required options in the manual mode (the block saves all these settings). For a more flexible configuration, you can also add required manual mode options to workflow parameters — then your users will be able to apply custom options from Run after they select the manual training mode.

#### SmartSelection¶

SmartSelection is a method which automatically selects an approximation technique and its options to obtain the most accurate model for a given problem. You can provide more details about the training data, specify the properties the model should possess, or training features to control the time-quality trade-off with the help of hints. These hints are divided into three groups accordingly: data features, model requirements, and training features. You can also add custom settings using the Advanced options hint.

To add a hint, click anywhere inside the Hints pane 1 or use the button 2 to open the list 3 with available hints.

For hints which require additional settings, a dialog appears when you select the hint from a list. When you finish adding a hint, it shows up on the Hints pane and becomes disabled (grayed out) in the list.

• Linear dependency — the dependency specified by the training sample is supposed to be linear.
• Quadratic dependency — the dependency specified by the training sample is supposed to be quadratic.
• Discontinuous dependency — the dependency specified by the training sample is supposed to be discontinuous.
• Dependent outputs… — specifies the type of dependency between different outputs. The following options are available for this hint:
• All dependent: different components of the output are treated as possibly dependent.
• Partial linear: before training, pSeven will search for linear dependencies between outputs in the training data. If such dependencies are found, pSeven will train a model which keeps these dependencies.
• Tensor structure — input points in the training sample are placed in a grid-like pattern. This is usually the case when inputs are generated by some factorial technique for design of experiments.

Model requirements hints add specific requirements for the trained model:

• Acceptable quality… — the metric and acceptable level of prediction error used to validate the model. With this hint, model training is stopped once the acceptable value of the metric is reached.
• Smooth model — the built model should be smooth (reduces noise).
• Accuracy evaluation – the built model should support accuracy evaluation.
• Exact fit — the built model should fit training data points exactly.
• Do not store training sample — training sample should not be stored inside the model (by default, the training sample is stored inside the model). Enabling the hint reduces the size of the model stored on disk, in particular, when tensor techniques are used. You can also use this hint, for example, if you want to transfer the model but not its training data.
• Enable NaN prediction — the built model should predict NaN output values in areas near those points of the training sample that contain NaN output values.
• Do not store internal validation data — the final model should not contain cross-validation data samples (by default, SmartSelection runs cross-validation for the final model and saves model outputs obtained in all cross-validation sessions, so you can review this data later). Adding this hint can reduce the model size. Note that a model trained with this hint can still contain internal validation statistics, if cross-validation is selected as the method to estimate quality of intermediate models (see the Validation type… hint).

Training features hints are used to tune the training process:

• Validation type… — specifies the method to estimate quality of intermediate models which SmartSelection creates during training:
• Auto (default): automatically selects one of the following methods, basing on data properties and other settings. Prefers validation on a test sample when it is available, otherwise can automatically split the sample into the train and test subsets, or use internal validation as the least preferred method. This is the default SmartSelection behavior, which is also used if you do not add the Validation type… hint. Note that in case when SmartSelection automatically switches to internal validation, the model will contain internal validation statistics even if you add the Do not store internal validation data hint (this hint removes only the cross-validation data samples).
• Internal validation: uses cross-validation. With this setting, you can also use the Advanced option… hint to specify the number of data subsets and training sessions in cross-validation.
• Test set: validates models on the test sample data. Test data is required for this method.
• Split training sample to train/test subsets: automatically splits the sample into two subsets, one of which is used to train models, and the other to validate them. You can change size of the training subset using the Training subset ratio slider. This method is similar to using the Split data… command to create the train and test samples (see Split Data), and then performing validation on the test set.
• Randomized training — enable randomization in certain internal training algorithms. Randomized training can produce models that are slightly different.
• Fixed random seed… — use a fixed seed in those training algorithms that support randomized training. This hint makes the behavior of randomized algorithms fully deterministic (controlled by the seed value).
• Training time limit… — specifies a recommended time limit for the model training. Note that if such a limit is specified, it may be generally detrimental to model quality.
• Try output transformations — decides whether to apply log transformation to the outputs data in the training sample. Using the hint means that two models will be trained and compared: one with log transformation applied to training sample outputs and the other without the transformation. This comparison is done only for outputs which have output transformation set to "auto".

You can also use the Advanced option… hint to specify some training options manually. Selecting this hint brings up the Advanced option dialog with option settings.

Available options are:

• MaxParallel: sets the maximum number of parallel threads to use for training. The value can be any positive integer. Note that it is not recommended to set it higher than the number of physical CPU cores, otherwise you can experience a performance degradation.
• Technique: specifies the approximation technique to use.
• SubmodelTraining: selects whether to train submodels in parallel or sequentially.
• IVSubsetCount: specifies the number of cross-validation subsets. See GTApprox/IVSubsetCount for details.
• IVTrainingCount: sets the number of training sessions in cross-validation. See GTApprox/IVTrainingCount for details.
• InputDomainType: specifies the input domain for the model. See GTApprox/InputDomainType for details.

You can select more than one hint. If you add hints which are in conflict, the block highlights them in red and prohibits applying such configuration.

A detailed description of SmartSelection features is available in the Smart Training section of the GTApprox guide.

#### Manual Training¶

To configure the block for manual training, switch the mode selector to Manual and set option values as required. See section Options for the complete options reference.

A guide to manual configuration is available in the Manual Training section of the GTApprox guide.

### Training Data¶

ApproxBuilder trains an approximation model using the data received to the x_sample (variables) and f_sample (responses) input ports. See the Sample-Based Approximation tutorial, sections Loading the Sample and Preparing the Sample for details on reading the sample data from a file and splitting the sample to be further sent to the ApproxBuilder block.

You can also use the following input ports to provide details on model variables and responses:

• sample_names: adds names to model inputs and outputs.
• sample_quantities: specifies physical quantities of variables and responses.
• sample_units: specifies measurement units.

Values sent to these ports must be StringVector of length equal to the total number of columns in the matrices received to the x_sample and f_sample ports. The order of vector elements follows the order of columns in training samples, with variables coming first. All names in the vector received to sample_names must be unique.

For example, suppose you are training a model of an I-beam under load, which has 3 inputs and 1 output — so the x_sample input receives a matrix with 3 columns, and f_sample receives a matrix with 1 column. The details on this model’s inputs and outputs could be:

• sample_names: ("S", "L", "F", "B"). Note that all names must be unique, and certain characters are prohibited in names (see the details below).
• sample_descriptions: ("I-beam cross-section area.", "I-beam length.", "The load applied to the beam.", "Bending stress.").
• sample_quantities: ("area", "length", "mass", "stress").
• sample_units: ("m.m", "m", "kg", "MPa").

These details are saved to the trained model and are shown when you view the model in Analyze or load it into the Approximation model block. They are also kept when you export the model code, for example, as a Functional Mock-up Unit for Co-Simulation.

Names in the vector received to the sample_names port must satisfy the following rules:

• Name must not be empty.
• All names must be unique. The same name for an input and an output is also prohibited.
• The only whitespace character allowed in names is the ASCII space, so \t, \n, \r, and various Unicode whitespace characters are prohibited.
• Name cannot contain leading or trailing spaces, and cannot contain two or more consecutive spaces.
• Name cannot contain leading or trailing dots, and cannot contain two or more consecutive dots, since dots in pSeven are used as name separators.
• Parts of the name separated by dots must not begin or end with a space, so the name cannot contain '. ' or ' .'.
• Name cannot contain control characters and Unicode separators.
• Name cannot contain characters from this set: :"/\|?*.

Additional training data can be sent to the following optional input ports:

• output_noise_variance — noise variance for training outputs. See Data with Errorbars.
• weights — point weights (relative importance measure) in the training sample. See Sample Weighting.
• output_transformation — the type of transformation to apply to the training sample outputs before training the model. See GTApprox/OutputTransformation.

If you use the SmartSelection mode, you can optionally provide a test sample to the x_test and f_test inputs. This sample is then used to calculate quality metrics when SmartSelection estimates model quality. The test sample has the same structure as the training sample.

### Initial Model¶

If you are using the GBRT or MoA technique in the manual mode, ApproxBuilder can train a model incrementally. You can select an initial model in block’s configuration, and the block uses input data to improve this model.

Note

The SmartSelection training mode does not support initial models. If you specify an initial model in the SmartSelection mode, training can start, but the initial model is ignored. pSeven shows a warning in the Issues pane in this case.

The block can accept the initial model as a file on disk. It can also accept the path to the model file to the initial_model_path port, or receive the file to the initial_model port instead of loading it from disk.

Note that the number of inputs and outputs in the initial model should conform to the number of components in the variable and response parts of the training sample. For example, if the initial model has 3 inputs and 1 output, the x_sample input should receive a matrix with 3 columns, and f_sample — a matrix with 1 column.

### Saving the Model¶

You can save the approximation model to disk in the binary GTApprox model format specific to pSeven (.gtapprox). The steps are as follows:

• Open the ApproxBuilder block configuration.
• Click in the Output model pane to bring up the Configure file dialog.
• In the File origin pane select the Project origin.
• In the File path field, input the name for the model, for example ./model.gtapprox.
• Leave other settings default and click to close the dialog.

As a result, the saved model (model.gtapprox) is found in your project directory after the workflow finishes. Note that a path which begins with ./ is a relative path where the dot . represents the project directory.

### Model Export¶

To set up model export, use the following ports:

• export_format — specifies the model export format.
• export_path — sets the path where to save the exported model file on disk.
• export_model — outputs a temporary file with the exported model.

The export_model port is intended to send the model to another block in the workflow — for example, some block which evaluates the model. You can reconfigure it to output a file which is saved to disk, but it means that the block will always export to the same file, overwriting it if you export multiple models.

A more flexible way to specify the export file location is using the export_path port. The path is a StringScalar value which you can either assign to this port or send it from another block. To assign the value, you can click in the value field to bring up the Select file dialog where you select file location. In this case, pSeven generates a correct path automatically. If you set the path manually or send it from another block in the workflow, note the following:

• It is recommended to use the forward slash / as the path separator both in Windows and Linux versions of pSeven.
• The path can be absolute or relative. Relative paths are interpreted as relative to the project directory. You can add a leading dot . to explicitly note that the path is relative, for example ./MyModels/SomeExportedModel (the dot represents the project directory).
• You can omit file extension: the block automatically adds a correct extension for the selected format.
• If the specified file already exists, it will be replaced.
• If you specify a path leading to a directory which does not exist, this directory will be automatically created by the block when it runs.

Available export formats are:

• Executable: command-line executable for the platform, on which pSeven currently runs (.exe for Windows and .bin for Linux). Note that it is not possible to export an executable file for another platform — for example, you cannot export a Windows executable under Linux.

• Excel document with a linked DLL: an Excel document with macros (.xlsm), which evaluates the model stored into a complementary DLL. In addition to the Excel document and two model DLLs (for the 32-bit and 64-bit Excel editions), this format also provides a file containing the code of a VBA wrapper (.bas) for the model DLL, and C source (.c) of the DLL. Export to this format is supported only in the Windows version of pSeven.

For convenience, the DLL names are based on the name of the Excel document. However, DLL names (hence, the Excel document name) are also used in the VBA macros code. Due to this, the document name must contain only characters, which can be represented in the system locale’s encoding (see Language for non-Unicode programs in Windows’ language settings). For compatibility across different local versions of Windows, it is recommended to use English characters only.

• FMU for Co-Simulation 1.0: FMI model (Functional Mock-up Unit, .fmu) in the Co-Simulation format, with source and binary.

• FMU for Model Exchange 1.0: FMI model (Functional Mock-up Unit, .fmu) in the Model Exchange format, with source and binary.

• FMU for Co-Simulation 1.0 (source only): FMI model in the Co-Simulation format, with source only.

• FMU for Model Exchange 1.0 (source only): FMI model in the Model Exchange format, with source only.

• C# source (experimental): source code (.cs) to compile the model with C# compiler.

• C# library (experimental): a compiled .NET DLL (.dll). Note that using this export format requires a C# compiler installed (pSeven does not include a C# compiler).

• In Windows: requires .NET Framework or another package which provides the C# compiler (csc.exe). pSeven finds the compiler automatically; if there are several versions installed, the latest is used. If you want to select a specific version, you can set the CSHARP_COMPILER_ROOT environment variable. Its value should be the full path to the directory which contains csc.exe.
• In Linux: requires the dotnet command line tool which is a part of .NET Core SDK. The following environment variables are also required: CSHARP_COMPILER_ROOT must contain the path to the compiler executable (csc.dll), and CSHARP_LIBRARIES_ROOT must contain the full path to the directory where the System.dll and System.Private.CoreLib.dll libraries are located. Finally, the dotnet executable should be added to PATH.
• C source for standalone program: C source code with the main() function, which you can compile to a complete command-line program.

• C header for library: the header for a model compiled to a shared library (DLL or .so).

• C source for library: C header and model implementation, which you can compile to a shared library (DLL or .so).

• C source for MEX: source code for a MATLAB MEX file.

• Octave script: model code compatible with MATLAB.

Note

If you select the Excel export format, the export_model port outputs a ZIP archive (.zip) containing all exported files (Excel document, DLL files, VBA wrapper code and model C source).

Note

An FMI model in either format (Co-Simulation or Model Exchange) can be exported as a FMU with a binary, or as a source-only FMU.

The binary FMU is ready to use, but it is platform-dependent: you can use it only on the same platform where it has been exported. For example, it is not possible to export a FMU with a Windows binary if you are running pSeven on Linux. However, this FMU also contains source code, so you can recompile it for any platform.

The source-only FMU does not contain any binaries, so you will always have to compile it in order to obtain a working FMU.

## Options¶

GTApprox/Accelerator

Five-position switch to control the trade-off between speed and accuracy.

Value: integer in range $$[1, 5]$$ 1

This option controls training time by changing some internal technique parameters. Possible values are from 1 (low speed, highest quality) to 5 (high speed, lower quality).

For the GBRT and HDA techniques, GTApprox/Accelerator also changes values of some public technique-specific options (the dependent options). User changes to dependent options always override settings made by GTApprox/Accelerator: if you set both GTApprox/Accelerator and some dependent option, GTApprox will use your value of this dependent option, not the value automatically set by GTApprox/Accelerator.

Changed in version 5.1: GTApprox/GBRTMaxDepth and GTApprox/GBRTNumberOfTrees added to dependent options.

Dependent GBRT options are GTApprox/GBRTMaxDepth and GTApprox/GBRTNumberOfTrees. GTApprox/Accelerator sets them as follows:

GTApprox/Accelerator 1 2 3 4 5
GTApprox/GBRTMaxDepth 10 10 10 6 6
GTApprox/GBRTNumberOfTrees 500 400 300 200 100

Settings made by GTApprox/Accelerator for HDA depend on input sample size. There are two cases:

• Ordinary sample size (the sample contains less than 10 000 points).
• Big sample size (the sample contains 10 000 points or more).

In the case of ordinary sized sample, dependent options are GTApprox/HDAFDGauss, GTApprox/HDAMultiMax, GTApprox/HDAMultiMin and GTApprox/HDAPhaseCount. GTApprox/Accelerator sets them as follows:

GTApprox/Accelerator 1 2 3 4 5
GTApprox/HDAFDGauss 1 1 0 0 0
GTApprox/HDAMultiMax 10 6 4 4 2
GTApprox/HDAMultiMin 5 4 2 2 1
GTApprox/HDAPhaseCount 10 7 5 1 1

In the case of big sized sample, dependent options are GTApprox/HDAFDGauss, GTApprox/HDAHessianReduction, GTApprox/HDAMultiMax, GTApprox/HDAMultiMin, GTApprox/HDAPhaseCount, GTApprox/HDAPMax, and GTApprox/HDAPMin. GTApprox/Accelerator sets them as follows:

GTApprox/Accelerator 1 2 3 4 5
GTApprox/HDAFDGauss 0 0 0 0 0
GTApprox/HDAHessianReduction 0.3 0.3 0 0 0
GTApprox/HDAMultiMax 3 2 2 2 1
GTApprox/HDAMultiMin 1 1 1 1 1
GTApprox/HDAPhaseCount 5 5 3 1 1
GTApprox/HDAPMax 150 150 150 150 150
GTApprox/HDAPMin 150 150 150 150 150
GTApprox/AccuracyEvaluation

Require accuracy evaluation.

Value: True or False False

If this option is True, then, in addition to the approximation, constructed model will contain a function providing an estimate of the approximation error as a function on the design space.

See Evaluation of accuracy in given point chapter for details.

GTApprox/CategoricalVariables

Specifies discrete (categorical) input variables.

Value: a list of zero-based indexes of input variables [] (no discrete variables)

New in version 6.3.

Treat listed variables as discrete (categorical). These variables can take only predefined values (levels). For every discrete variable, each unique value from the training sample becomes a level. Note that a discrete variable never takes a value not found in the training sample, and a model with discrete variables cannot be evaluated for values of discrete variables that was not found in the training sample.

See section Categorical Variables for more details.

Note that if you specify tensor factors for the TA and TGP techniques manually, you can select categorical variables with GTApprox/TensorFactors instead of specifying GTApprox/CategoricalVariables. Using both these options at the same time is not recommended since they can conflict; see section Categorical Variables for TA, iTA and TGP techniques for more details.

GTApprox/Componentwise

Perform componentwise approximation (independent outputs).

Value: True, False, Auto Auto

Deprecated since version 6.3: kept for compatibility, use GTApprox/DependentOutputs instead.

Prior to 6.3, this option was used to enable componentwise approximation which was disabled by default.

Since 6.3, componentwise approximation is enabled by default, and can be disabled with GTApprox/DependentOutputs. Now if GTApprox/Componentwise is default (Auto), GTApprox/DependentOutputs takes priority. If GTApprox/Componentwise is not default while GTApprox/DependentOutputs is Auto, then GTApprox/Componentwise takes priority. In case when values of these two options conflict, the block raises an error. However, this conflict is ignored if the output is 1-dimensional.

GTApprox/DependentOutputs

Specify the type of dependency between output components.

Value: Boolean, PartialLinear, or Auto Auto

New in version 6.3.

Changed in version 6.15: added the linear dependencies mode (PartialLinear).

Selects which approximation mode to use when training a model with multidimensional output (see section Output Dependency Modes for details).

• True: treat different components of the output as possibly dependent, do not use componentwise approximation.
• False: assume that output components are independent and use componentwise approximation.
• PartialLinear: before training, search for linear dependencies between outputs in the training data. If such dependencies are found, train a model which keeps the dependencies. In this case, the submodels of independent outputs are trained in the componentwise mode.
• Auto (default): use componentwise approximation unless it is explicitly disabled by GTApprox/Componentwise.

When GTApprox/DependentOutputs is default (Auto), componentwise approximation is enabled unless GTApprox/Componentwise is set to a non-default value, which takes priority. As a result, if GTApprox/DependentOutputs is Auto but GTApprox/Componentwise is False, componentwise approximation is disabled. This is done to avoid conflicts with older versions. Note that GTApprox/Componentwise is a deprecated option that is kept for version compatibility only and should not be used since 6.3.

Note

The TBL technique ignores this option since it is a simple table function.

GTApprox/Deterministic

Controls the behavior of randomized initialization algorithms in certain techniques.

Value: True or False True

New in version 5.0.

Several model training techniques in GTApprox feature randomized initialization of their internal parameters. These techniques include:

• GBRT, which can select random subsamples of the full training set when creating regression trees (see section Stochastic Boosting).
• HDA and HDAGP, which use randomized initialization of approximator parameters.
• MoA, if the approximation technique for its local models is set to HDA, HDAGP or SGP using GTApprox/MoATechnique, or the same selection is done automatically.
• SGP, which uses randomized selection of base points when approximating the full covariance matrix of the points from the training sample (Nystrom method).
• TA, if for some of its factors the HDA technique is specified manually or is selected automatically (see GTApprox/TensorFactors).

The determinacy of randomized techniques can be controlled in the following way:

• If GTApprox/Deterministic is on (deterministic training mode, default), a fixed seed is used in all randomized initialization algorithms. The seed is set by GTApprox/Seed. This makes the technique behavior reproducible — for example, two models trained in deterministic mode with the same data, same GTApprox/Seed and other settings will be exactly the same, since a training algorithm is initialized with the same parameters.
• Alternatively, if GTApprox/Deterministic is off (non-deterministic training mode), a new seed is generated internally every time you train a model. As a result, models trained with randomized techniques may slightly differ even if all settings and training samples are the same. In this case, GTApprox/Seed is ignored. The generated seed that was actually used for initialization can be found in model info, so later the training run can still be reproduced exactly by switching to the deterministic mode and setting GTApprox/Seed to this value.

In case of randomized techniques, repeated non-deterministic training runs may be used to try obtaining a more accurate approximation, because results will be slightly different. On the contrary, deterministic techniques always produce exactly the same model given the same training data and settings, and are not affected by GTApprox/Deterministic and GTApprox/Seed. Deterministic techniques include:

GTApprox/EnableTensorFeature

Enable automatic selection of the TA and iTA techniques.

Value: True or False True

New in version 1.9.2: allows the automatic selection of the iTA technique. Previously affected only the TA technique selection.

If True, makes TA and iTA techniques available for auto selection. If False, neither TA nor iTA will ever be selected automatically based on decision tree. Has no effect if any approximation technique is selected manually using the GTApprox/Technique option.

Note

This option does not enable the automatic selection of the TGP technique.

GTApprox/ExactFitRequired

Require the model to fit sample data exactly.

Value: True or False False

If this option is True, the model fits the points of the training sample exactly — that is, model responses in the points which were included in the training sample are equal to the response values in the training sample.

If GTApprox/ExactFitRequired is False then no fitting condition is imposed, and the approximation can be either fitting or non-fitting depending on the training data. Typical example: if GTApprox finds that the sample is noisy, it does not create an exact-fitting model to avoid overtraining.

Note that the exact fit mode is not supported by some approximation techniques. In particular, it is incompatible with the robust version of GP-based techniques (see GTApprox/GPLearningMode). For details on other techniques, see their descriptions in the Techniques section.

Changed in version 4.2: added the exact fit mode support to the TA technique (see TA).

Changed in version 6.15: the HDAGP technique, which does not support the exact fit mode, now raises an error if GTApprox/ExactFitRequired is on. Previously HDAGP silently ignored this option.

Changed in version 6.15: it is no longer possible to train a model with GTApprox/ExactFitRequired on and GTApprox/GPLearningMode set to "Robust". Now this combination is explicitly prohibited and raises an error.

For more information on the effects of this option, see section Exact Fit.

GTApprox/GBRTColsampleRatio

Column subsample ratio.

Works only for GBRT technique.

Value: floating point number in range $$(0, 1]$$ 1.0

New in version 5.1.

The GBRT technique uses random subsamples of the full training set when training weak estimators (regression trees). GTApprox/GBRTColsampleRatio specifies the fraction of columns (input features) to be included in a subsample: for example, setting it to 0.5 will randomly select half of the input features to form a subsample.

For more details, see section Stochastic Boosting.

GTApprox/GBRTMaxDepth

Maximum regression tree depth.

Works only for GBRT technique.

Value: non-negative integer 0

New in version 5.1.

Sets the maximum depth allowed for each regression tree (GBRT weak estimator). Greater depth results in a more complex final model.

Default (0) means that the tree depth will be set by GTApprox/Accelerator as follows:

GTApprox/Accelerator 1 2 3 4 5
GTApprox/GBRTMaxDepth 10 10 10 6 6

For example, if both options are default (GTApprox/GBRTMaxDepth is 0 and GTApprox/Accelerator is 1), actual depth setting is 10.

For more details, see section Model Complexity.

GTApprox/GBRTMinChildWeight

Minimum total weight of points in a regression tree leaf.

Works only for GBRT technique.

Value: non-negative floating point number 1

New in version 5.1.

The GBRT technique stops growing a branch of a regression tree if the total weight of points assigned to a leaf becomes less than GTApprox/GBRTMinChildWeight. If the sample is not weighted, this is the same as limiting the number of points in a leaf. Zero minimum weight means that no such limit is imposed.

For more details, see section Leaf Weighting.

GTApprox/GBRTMinLossReduction

Minimum significant reduction of loss function.

Works only for GBRT technique.

Value: non-negative floating point number 0

New in version 5.1.

The GBRT technique stops growing a branch of a regression tree if the reduction of loss function (model’s mean square error over the training set) becomes less than GTApprox/GBRTMinLossReduction.

For more details, see section Model Complexity.

GTApprox/GBRTNumberOfTrees

The number of regression trees in the model.

Works only for GBRT technique.

Value: non-negative integer 0

New in version 5.1.

Sets the number of weak estimators (regression trees) in a GBRT model, the same as the number of gradient boosting stages. Greater number results in a more complex final model.

Changed in version 5.2: 0 is allowed and means auto setting.

Default (0) means that the number of trees will be set by GTApprox/Accelerator as follows:

GTApprox/Accelerator 1 2 3 4 5
GTApprox/GBRTNumberOfTrees 500 400 300 200 100

For example, if both options are default (GTApprox/GBRTNumberOfTrees is 0 and GTApprox/Accelerator is 1), the actual number of trees is 500.

For more details, see section Model Complexity.

Note that in incremental training the default (0) number of trees is not affected by GTApprox/Accelerator but depends on the number of trees in the initial model and training sample sizes — see Incremental Training for details.

GTApprox/GBRTShrinkage

Shrinkage step, or learning rate

Works only for GBRT technique.

Value: floating point number in range $$(0, 1]$$ 0.3

New in version 5.1.

GBRT scales each weak estimator by a factor of GTApprox/GBRTShrinkage, resulting in a kind of regularization with smaller step values.

For more details, see section Shrinkage.

GTApprox/GBRTSubsampleRatio

Row subsample ratio

Works only for GBRT technique.

Value: floating point number in range $$(0, 1]$$ 1.0

New in version 5.1.

The GBRT technique uses random subsamples of the full training set when training weak estimators (regression trees). GTApprox/GBRTSubsampleRatio specifies the fraction of rows (sample points) to be included in a subsample: for example, setting it to 0.5 will randomly select half of the points to form a subsample.

For more details, see section Stochastic Boosting.

GTApprox/GPInteractionCardinality

Allowed orders of additive covariance function.

Works for GP, SGP and HDAGP techniques.

Value: list of unique unsigned integers in range $$[1, dim(X)]$$ each [] (equivalent to [1, n], $$n = dim(X)$$)

New in version 1.10.3.

This option takes effect only when using the additive covariance function (GTApprox/GPType is set to Additive), otherwise it is ignored. In particular, the TGP technique always ignores this option since its covariance function is always Wlp.

The additive covariance function is a sum of products of one-dimensional covariance functions, where each additive component (a summand) depends on a subset of initial input variables. GTApprox/GPInteractionCardinality defines the degree of interaction between input variables by specifying allowed subset sizes, which are in fact the allowed values of covariance function order.

All values in the list should be unique, and neither of them can be greater than the number of input components, excluding constant inputs (the effective dimension of the input part of the training sample).

Consider an n-dimensional $$X$$ sample with $$m$$ variable and $$n-m$$ constant components (sample matrix columns). Valid GTApprox/GPInteractionCardinality settings then would be:

• [1, n]: simplified syntax, implicitly converts to [1, m].
• [1, 2, ... m-1, m, m+1, ... k], where $$m < k \le n$$: treated as a consecutive list of interactions up to cardinality k, implicitly converts to [1, 2, ... m-1, m]. Note that in this case all values from 1 to m have to be included in the list, otherwise it is considered invalid.
• [i1, i2, ... ik], where $$i_j \le m$$: valid list of interaction cardinalities, no conversion needed.
GTApprox/GPLearningMode

Give priority to either model accuracy or robustness

Value: Accurate, Robust, or Auto Auto

New in version 1.9.6.

Changed in version 6.15: added the Auto value which is now default (was Accurate).

This option affects the Gaussian processes-based techniques: GP, TGP, and TA (with GP factors). These techniques can use different versions of the training algorithm. The so-called accurate version aims to minimize model errors, but in many cases can result in various adverse effects related to overtraining. The robust version prevents overtraining at the cost of a possible decrease in model accuracy; this version is also incompatible with the exact fit mode (see GTApprox/ExactFitRequired).

Using the robust version is recommended. The Auto setting selects the robust version unless the exact fit requirement is specified. Only if GTApprox/ExactFitRequired is on, Auto defaults to Accurate.

GTApprox/GPLinearTrend

Deprecated since version 3.2: kept for compatibility only, use GTApprox/GPTrendType instead.

Since version 3.2 this option is deprecated by a more advanced GTApprox/GPTrendType option which allows to select linear, quadratic, or none trend type.

GTApprox/GPMeanValue

Specifies mean of model output mean values

Works for GP , SGP, HDAGP and TGP techniques.

Value: list of floating point numbers [] (automatic estimate)

Model output mean values are essential for constructing GP approximation. These values may be defined by user or estimated using the given sample (the bigger and more representative is the sample, the better is the estimate of model output mean values). Model output mean values misspecification leads to decrease in approximation accuracy: the larger the error in output mean values, the worse is the final approximation model. If left default (empty list), model output mean values are estimated using the given sample.

Option value is a list of floating point numbers. This list should either be empty or contain a number of elements equal to output dataset dimensionality.

GTApprox/GPPower

The value of p in the p-norm which is used to measure the distance between input vectors

Works for GP, SGP, HDAGP and TGP techniques.

Value: floating point number in range $$[1, 2]$$ 2.0

The main component of the GP based regression is the covariance function measuring the similarity between two input points. The covariance between two input uses p-norm of the difference between coordinates of these input points. The case p = 2 corresponds to the usual gaussian covariance function (better suited for modelling of smooth functions) and the case p = 1 corresponds to laplacian covariance function (better suited for modelling of non-smooth functions).

For the GP technique, this option takes effect only if GTApprox/GPType is Wlp or Additive. The TGP technique is always affected by GTApprox/GPPower, since it always uses the common covariance function (denoted Wlp) and disregards the GTApprox/GPType setting.

GTApprox/GPTrendType

Specifies the trend type.

Works for GP, SGP, HDAGP and TGP techniques.

Value: None, Linear, Quadratic, or Auto Auto

New in version 3.2.

This option allows to take into account specific (linear or quadratic) behavior of the modeled dependency by selecting which type of trend to use.

• None — no trend.
• Linear — linear trend.
• Quadratic — polynomial trend with constant, linear and pure quadratic terms (no interaction terms, no feature selection).
• Auto — automatic selection, defaults to no trend unless GTApprox/GPLinearTrend is on (provides compatibility with the deprecated GTApprox/GPLinearTrend option).
GTApprox/GPType

Select the kernel function type for the Gaussian processes-based techniques (GP, SGP, and HDAGP, excluding TGP).

Value: Additive, Mahalanobis, Wlp, or Periodic Wlp

New in version 1.10.3: additive covariance function.

New in version 6.16: periodic covariance function.

Selects the kernel function used in Gaussian processes. Available kernels:

• Additive: summarized coordinate-wise products of 1-dimensional Gaussian covariance functions. With this setting, GTApprox/GPInteractionCardinality may be used to set the degree of interaction between input variables.
• Mahalanobis: squared exponential covariance function with Mahalanobis distance.
• Wlp: common exponential Gaussian covariance function with weighted $$L_p$$ distance.
• Periodic: periodic covariance function. Using this kernel potentially allows you to create an approximation model with periodic extrapolation.

If Additive is set, but the $$X$$ sample is 1-dimensional, then the additive covariance function is implicitly replaced with the common covariance function (denoted Wlp), and the GTApprox/GPInteractionCardinality option value is ignored.

Note

The TGP technique ignores this option and always uses the common covariance function (denoted Wlp).

GTApprox/Heteroscedastic

Treat input sample as a sample containing heteroscedastic noise.

Value: True, False, or Auto Auto

New in version 1.9.0.

If this option is True, the builder assumes that heteroscedastic noise variance is present in the input sample. Default value (Auto) currently means that option is False.

This option has certain limitations:

• It is valid for GP and HDAGP techniques only. For other techniques the value is ignored (treated as always False).
• Heteroscedasticity is incompatible with covariance functions other than Wlp: if GTApprox/Heteroscedastic is True and GTApprox/GPType is not Wlp, exception will be thrown.
• If noise variance is given, the GTApprox/Heteroscedastic option is ignored and non-variational GP (or HDAGP) technique is used.

See corresponding Heteroscedastic data section for details.

GTApprox/HDAFDGauss

Include Gaussian functions into functional dictionary used in construction of approximations

Works for HDA and HDAGP techniques.

Value: No, Ordinary or Auto Auto

In order to construct an approximation, the linear expansion in functions from special functional dictionary is used. This option controls whether Gaussian functions should be included into functional dictionary used in construction of approximation.

In general, using Gaussian functions as building blocks for construction of approximation can lead to significant increase in accuracy, especially in the case when the approximable function is bell-shaped. However, it may also significantly increase training time.

GTApprox/HDAFDLinear

Include linear functions into functional dictionary used in construction of approximations

Works for HDA and HDAGP techniques.

Value: No, Ordinary or Auto Auto

Changed in version 6.14: added the Auto value which is now default (was Ordinary).

In order to construct an approximation, the linear expansion in functions from special functional dictionary is used. This option controls whether linear functions should be included into functional dictionary used in construction of approximation or not.

In general, using linear functions as building blocks for construction of approximation can lead to increase in accuracy, especially in the case when the approximable function has significant linear component. However, it may also increase training time.

GTApprox/HDAFDSigmoid

Include sigmoid functions into functional dictionary used in construction of approximations

Works for HDA and HDAGP techniques.

Value: No, Ordinary or Auto Auto

Changed in version 6.14: added the Auto value which is now default (was Ordinary).

In order to construct an approximation, the linear expansion in functions from special functional dictionary is used. This option controls whether sigmoid-like functions should be included into functional dictionary used in construction of approximation or not.

In general, using sigmoid-like functions as building blocks for construction of approximation can lead to increase in accuracy, especially in the case when the approximable function has square-like or discontinuity regions. However, it may also lead to significant increase in training time.

GTApprox/HDAHessianReduction

Maximum proportion of data used in evaluating Hessian matrix

Works for HDA and HDAGP techniques.

Value: floating point number in range $$[0, 1]$$ 0.0

New in version 1.6.1.

This option shrinks maximum amount of data points for Hessian estimation (used in high-precision algorithm). If the value is 0, the whole set of points is used in Hessian estimation, otherwise, if the value is in range $$(0;1]$$, only a part (smaller than HDAHessianReduction of the whole set) is used. Reduction is used only in case of samples bigger than 1250 input points (if number of points is smaller than 1250, this option is ignored and Hessian is estimated by the whole train sample).

Note

In some cases, the high-precision algorithm can be disabled automatically, regardless of the GTApprox/HDAHessianReduction value. This happens if:

1. $$(dim(X) + 1) \cdot p \ge 4000$$, where dim(X) is the dimension of the input vector X and p is a total number of basis functions, or
2. $$dim(X) \ge 25$$, where dim(X) is the dimension of the input vector X, or
3. there are no sufficient computational resources to use the high precision algorithm.
GTApprox/HDAMultiMax

Maximum number of basic approximators constructed during one approximation phase.

Works for HDA and HDAGP techniques.

Value: integer in range $$[$$GTApprox/HDAMultiMin$$, 1000]$$ or 0 0 (auto selection)

Changed in version 6.14: added 0 as a valid value for automatic selection, which is now default (was 10).

This option specifies the maximum number of basic approximators constructed during one approximation phase. Option value is a positive integer which must be greater than or equal to the value of GTApprox/HDAMultiMin option. This option sets upper limit to the number of basic approximators, but does not require this limit to be reached (approximation algorithm stops constructing basic approximators as soon as construction of subsequent basic approximator does not increase accuracy). In general, the bigger the value of GTApprox/HDAMultiMax is, the more accurate is the constructed approximator. However, increasing the value may lead to significant training time increase and/or overtraining in some cases.

GTApprox/HDAMultiMin

Minimum number of basic approximators constructed during one approximation phase.

Works for HDA and HDAGP techniques.

Value: integer in range $$[1,$$ GTApprox/HDAMultiMax$$]$$ or 0 0 (auto selection)

Changed in version 6.14: added 0 as a valid value for automatic selection, which is now default (was 5).

This option specifies the minimum number of basic approximators constructed during one approximation phase. Option value is a positive integer which must be less than or equal to the value of GTApprox/HDAMultiMax option. In general, the bigger the value of GTApprox/HDAMultiMin is, the more accurate is the constructed approximator. However, increasing the value may lead to significant training time increase and/or overtraining in some cases.

GTApprox/HDAPhaseCount

Maximum number of approximation phases.

Works for HDA and HDAGP techniques.

Value: integer in range $$[1, 50]$$ or 0 0 (auto)

Changed in version 6.14: added 0 as a valid value for automatic selection, which is now default (was 10).

This option specifies the maximum possible number of approximation phases. It sets upper limit to that number only, and does not require the limit to be reached (approximation algorithm stops performing new phases as soon as the subsequent approximation phase does not increase accuracy). In general, the more approximation phases, the more accurate approximator is built. However, increasing maximum number of approximation phases may lead to significant training time increase and/or overtraining in some cases.

GTApprox/HDAPMax

Maximum allowed approximator complexity.

Works for HDA and HDAGP techniques.

Value: integer in range $$[$$GTApprox/HDAPMin$$, 5000]$$ or 0 0 (auto)

Changed in version 6.14: added 0 as a valid value for automatic selection, which is now default (was 150).

This option specifies the maximum allowed complexity of the approximator. Its value must be greater than or equal to the value of the GTApprox/HDAPMin option. The approximation algorithm selects the approximator with optimal complexity pOpt from the range $$[$$GTApprox/HDAPMin, GTApprox/HDAPMax$$]$$. Optimality here means that, depending on the complexity of approximable function behavior and the size of the available training sample, constructed approximator with complexity pOpt fits this function in the best possible way compared to other approximators with complexity in range $$[$$GTApprox/HDAPMin, GTApprox/HDAPMax$$]$$. Thus the GTApprox/HDAPMax value should be big enough in order to select the approximator with complexity being the most appropriate for the considered problem. Note, however, that increasing the GTApprox/HDAPMax value may lead to significant increase in training time and/or overtraining in some cases.

GTApprox/HDAPMin

Minimum allowed approximator complexity.

Works for HDA and HDAGP techniques.

Value: integer in range $$[0,$$ GTApprox/HDAPMax$$]$$ 0 (auto)

Changed in version 6.14: 0 is now a special value which enables automatic selection.

This option specifies the minimum allowed complexity of the approximator. Its value must be less than or equal to the value of the GTApprox/HDAPMax option. The approximation algorithm selects the approximator with optimal complexity pOpt from the range $$[$$GTApprox/HDAPMin, GTApprox/HDAPMax$$]$$. Optimality here means that, depending on the complexity of approximable function behavior and the size of the available training sample, constructed approximator with complexity pOpt fits this function in the best possible way compared to other approximators with complexity in range $$[$$GTApprox/HDAPMin, GTApprox/HDAPMax$$]$$. Thus the GTApprox/HDAPMin value should not be too big in order to select the approximator with complexity being the most appropriate for the considered problem. Note that increasing the GTApprox/HDAPMin value may lead to significant increase in training time and/or overtraining in some cases.

GTApprox/InputDomainType

Specifies the input domain for the model.

Value: unbound, box, or auto unbound

New in version 6.16.

By default, a GTApprox model has an unlimited input domain — that is, model functions are defined everywhere, and model outputs are always numeric values. Such model fits the training sample data but tends to linear extrapolation outside the input space region covered by the training sample.

This option limits the input domain by adding input constraints to the model. The model then returns NaN outputs when inputs do not satisfy the constraints (the input point is outside the domain).

The input domain type can be:

• unbound (default) — unlimited input domain, the same as in all pSeven versions prior to 6.16.
• box — a domain limited to the training sample’s bounding box, determined automatically by GTApprox.
• auto — a domain which is an intersection of:
• the training sample’s bounding box, and
• the region bound by an ellipsoid which envelops the training sample.

If you use a limited input domain, the auto type is recommended because it “cuts empty corners” from the sample’s bounding box, so the input constraints represent the training data better.

Note

Models trained with the Piecewise Linear Approximation (PLA) technique have a limited input domain by default. These default constraints are more strict than the sample’s bounding box and the enveloping ellipsoid, so GTApprox/InputDomainType has no effect for PLA.

Note

Another option which adds input constraints to the model is GTApprox/OutputNanMode (when set to predict).

GTApprox/InputNanMode

Specifies how to handle non-numeric values in the input part of the training sample.

Value: raise, ignore raise

New in version 6.8.

GTApprox cannot obtain any information from non-numeric (NaN or infinity) values of variables. This option controls its behavior when such values are encountered. Default (raise) means to raise an error and cancel training; ignore means to exclude data points with non-numeric values from the sample and continue training.

GTApprox/InputsTolerance

Specifies up to which tolerance each input variable would be rounded.

Value: list of length $$dim(X)$$ of floating point numbers []

New in version 6.3.

If default, option does nothing. Otherwise each input variable in training sample is rounded up to specified tolerance. Note that this may lead to merge of some points.

See section Sample Cleanup for details.

GTApprox/InternalValidation

Enable or disable internal validation.

Value: True or False False

If this option is True then, in addition to the approximation, the constructed model contains a table of cross validation errors of different types, which may serve as a measure of accuracy of approximation.

See Model Validation chapter for details.

GTApprox/IVDeterministic

Controls the behavior of the pseudorandom algorithm selecting data subsets in cross validation.

Works only if GTApprox/InternalValidation is True.

Value: True or False True

New in version 5.0.

Cross validation involves partitioning the training sample into a number of subsets (defined by GTApprox/IVSubsetCount) and randomized combination of these subsets for each training (validation) session. Since the algorithm that combines subsets is pseudorandom, its behavior can be controlled in the following way:

• If GTApprox/IVDeterministic is True (deterministic cross validation mode, default), a fixed seed is used in the combination algorithm. The seed is set by GTApprox/IVSeed. This makes cross-validation reproducible — a different combination is selected for each session, but if you repeat a cross validation run, for each session it will select the same combination as the first run.
• Alternatively, if GTApprox/IVDeterministic is False (non-deterministic cross validation mode), a new seed is generated internally for every run, so cross validation results may slightly differ. In this case, GTApprox/IVSeed is ignored. The generated seed that was actually used in cross validation can be found in model info, so results can still be reproduced exactly by switching to the deterministic mode and setting GTApprox/IVSeed to this value.

Final model is never affected by GTApprox/IVDeterministic because it is always trained using the full sample.

GTApprox/IVSavePredictions

Save model values calculated during internal validation.

Works only if GTApprox/InternalValidation is True.

Value: True, False, or Auto Auto

New in version 2.0 Release Candidate 2.

If this option is True, internal validation information, in addition to error values, also contains raw validation data: model values calculated during internal validation, as well as validation inputs and outputs.

GTApprox/IVSeed

Fixed seed used in the deterministic cross validation mode.

Works only if GTApprox/InternalValidation is True.

Value: positive integer 15313

New in version 5.0.

Fixed seed for the pseudorandom algorithm that selects the combination of data subsets for each cross validation session. GTApprox/IVSeed has an effect only if GTApprox/IVDeterministic is on — see its description for more details.

GTApprox/IVSubsetCount

The number of cross validation subsets.

Works only if GTApprox/InternalValidation is True.

Value: 0 (auto) or an integer in range $$[2, |S|]$$, where $$|S|$$ is the size of the training set; also can not be less than GTApprox/IVTrainingCount 0 (auto)

The number of subsets (of approximately equal size) into which the training set is divided for the cross validation.

If left default, the number of cross validation subsets is selected automatically and will be equal to $$min(10, |S|)$$, where $$|S|$$ is the size of the training set.

GTApprox/IVTrainingCount

The number of training sessions in cross validation.

Works only if GTApprox/InternalValidation is True.

Value: integer in range $$[1,$$ GTApprox/IVSubsetCount$$]$$, or 0 (auto) 0 (auto)

The number of training sessions performed during the cross validation. Each training session includes the following steps:

1. Select one of the cross validation subsets.
2. Construct a complement of this subset which is the training sample excluding the selected subset.
3. Build a model using this complement as a training sample (so the selected subset is excluded from builder input).
4. Validate this model on the previously selected subset.

Repeat until the number of such sessions exceeds GTApprox/IVTrainingCount.

If left default, the number of cross validation sessions is selected automatically and will be equal to:

$N_{\rm tr} = \bigg\lceil\min\Big(|S|, \frac{100}{|S|}\Big)\bigg\rceil,$

where $$|S|$$ is the training sample size.

GTApprox/LinearityRequired

Require the model to be linear.

Value: True or False False

If this option is True, then the approximation is constructed as a linear function which fits the training data optimally. If option is False, then no condition related to linearity is imposed on the approximation: it can be either linear or non-linear depending on which fits training data best.

Note

The TGP technique does not support linear models: if GTApprox/Technique is TGP, GTApprox/LinearityRequired should be False.

GTApprox/LogLevel

Set minimum log level.

Value: Debug, Info, Warn, Error, Fatal Info

If this option is set, only messages with log level greater than or equal to the threshold are dumped into log.

GTApprox/MaxExpectedMemory

Maximum expected amount of memory (in GB) allowed for model training.

Value: positive integer or 0 (no limit) 0 (no limit)

New in version 6.4.

This option currently works for the GBRT technique only.

GTApprox/MaxExpectedMemory is intended to avoid the case when a long training process fails due to memory overflow, spending much time and giving no results. If GTApprox/MaxExpectedMemory is not default, GTApprox tries to estimate the expected memory usage at each stage of the training algorithm, and if the estimate exceeds the option value, the training is suspended: the process stops and returns a “partially trained” model which then can be trained incrementally (see Incremental Training).

With GTApprox/MaxExpectedMemory set it is also possible that the training sample is so big that it never can be processed with the allowed amount of memory; in this case, the training does not start.

If GTApprox/MaxExpectedMemory is default (0, no limit) or training technique is not GBRT, then GTApprox does not try to prevent memory overflow.

GTApprox/MaxAxisRotations

Use rotation transformations in the input space to iteratively improve model quality.

Value: positive integer (number of rotations) or -1 (auto) 0 (no rotations)

New in version 6.12.

This option enables a special training mode which can improve quality of models trained using Gaussian processes-based techniques (HDA, GP, HDAGP, and SGP) in some cases where the training sample is non-uniformly distributed. After training an initial model, it evaluates model gradients in the training points and uses the principal component analysis algorithm to create a model input projection matrix. Then it applies the input transformation and trains a new model which improves the initial one. The process is repeated until an internal quality criterion is satisfied or the maximum number of iterations is reached. The final model is a weighted combination of all models trained in the process.

Option values are:

• 0 (default): iterative training is disabled.
• -1 (auto): selects the number of iterations automatically with respect to the approximation technique, training dataset size, GTApprox/Accelerator value and the GTApprox/ExactFitRequired setting.
• Any other value sets the maximum allowed number of iterations explicitly. The process may finish before this maximum is reached, if the internal quality criterion is satisfied.

This option works with the HDA, GP, HDAGP, and SGP techniques only. Note that enabling it can significantly increase training time, since a new model is trained internally on each iteration.

GTApprox/MaxParallel

Sets the maximum number of parallel threads to use when training a model.

Value: integer in range $$[1, 100000]$$, or 0 (auto) 0 (auto)

New in version 5.0 Release Candidate 1.

ApproxBuilder can use parallel calculations to speed up model training. This option sets the maximum number of threads the block is allowed to create.

Changed in version 6.0: auto (0) sets the number of threads to 1 for small training samples.

Changed in version 6.12: auto (0) tries to detect hyper-threading CPUs in order to use only physical cores.

Changed in version 6.15: added the upper limit for the option value, previously was any positive integer.

Default (auto) behavior depends on the value of the OMP_NUM_THREADS environment variable.

If OMP_NUM_THREADS is set to a valid value, this value is the maximum number of threads by default. Note that OMP_NUM_THREADS must be set before you launch pSeven.

If OMP_NUM_THREADS is unset, set to 0 or an invalid value, the default maximum number of threads is equal to the number of cores detected by pSeven. However, there are two exceptions:

• Parallelization becomes inefficient in the case of a small training sample. For small training samples, only 1 thread is used by default.
• On hyper-threading CPUs using all logical cores has been found to negatively affect the training performance. If a hyper-threading CPU is detected, the default maximum number of threads is set to half the number of cores (to use only physical cores).

The behavior described above is only for the default (0) option value. If you set this option to a non-default value, it will be the maximum number of threads, regardless of the sample size and your CPU.

GTApprox/MoACovarianceType

Type of covariance matrix to use when creating the Gaussian Mixture Model for the Mixture of Approximators technique.

Value: Full, Tied, Diag, Spherical, BIC, or Auto. Auto

New in version 1.10.0.

• Full — all covariance matrices are positive semidefinite and symmetric.
• Tied — all covariance matrices are positive semidefinite, symmetric, and equal.
• Diag — all covariance matrices are diagonal.
• Spherical — diagonal matrix with equal elements on its diagonal.
• BIC — the type of covariance matrix and effective number of clusters are selected according to Bayesian Information Criterion.
• Auto — optimal covariance type for each possible number of clusters is chosen according to the clustering quality.

Changed in version 6.11: added the Auto value which is now default (previously default was BIC).

This option allows the user to control accuracy and training time of the MoA technique. For example, if it is known that design space consists of regions of regularity having similar structure it may be reasonable to use Tied matrix for Gaussian Mixture Models. Full has the slowest training time and Diag and Spherical have the fastest training time. In BIC mode Gaussian Mixture Models are constructed for all types of covariance matrices and numbers of clusters, the best one in sense of Bayesian Information Criterion (BIC) is chosen.

In Auto mode optimal covariance types are selected for each possible number of clusters according to the clustering quality based on the cluster’s tightness and separation assessment.

GTApprox/MoANumberOfClusters

Sets the number of design space clusters.

Works only for the Mixture of Approximators technique.

Value: list of positive integers, or an empty list (auto) [] (auto)

New in version 1.10.0.

New in version 1.11.0: empty list is also a valid value which selects the number of clusters automatically.

If set, the effective number of clusters is selected from the list according to Bayesian Information Criterion (BIC). To fix the number of clusters, you may specify a list containing a single positive integer.

Default ([]) selects the number of clusters automatically, based on the training sample size and input dimension.

GTApprox/MoAPointsAssignment

Select the technique for assigning points to clusters.

Works only for the Mixture of Approximators technique, see Design Space Decomposition.

Value: Probability or Mahalanobis. Probability

New in version 1.10.0.

• Probability corresponds to points assignment based on posterior probability.
• Mahalanobis corresponds to points assignment based on Mahalanobis distance.

For the Mahalanobis distance based technique, the confidence value $$\alpha$$ may be changed using the GTApprox/MoAPointsAssignmentConfidence option.

GTApprox/MoAPointsAssignmentConfidence

This option sets confidence value for points assignment technique based on Mahalanobis distance.

Works only for the Mixture of Approximators technique, see Design Space Decomposition.

Value: floating point number in range $$(0, 1)$$. 0.97

New in version 1.10.0.

This option allows to control size of clusters. The greater this value is the greater will be the cluster size.

GTApprox/MoATechnique

This option specifies approximation technique for local models.

Works only for Mixture of Approximators.

Value: SPLT, HDA, GP, HDAGP, SGP, TA, iTA, TGP, RSM, or Auto. Auto

New in version 1.10.0.

The option allows to control local approximation technique. It sets the same technique for all local models.

GTApprox/MoATypeOfWeights

This option sets the type of weighting used for “gluing” local approximations.

Works only for Mixture of Approximators, see Calculating Model Output.

Value: Probability or Sigmoid. Probability

New in version 1.10.0.

• Probability corresponds to weights based on posterior probability.
• Sigmoid corresponds to weights based on sigmoid function.

Sigmoid weighting can be fine-tuned with GTApprox/MoAWeightsConfidence.

GTApprox/MoAWeightsConfidence

This option sets confidence for sigmoid based weights.

Works only for Mixture of Approximators, see Calculating Model Output.

Value: floating point number in range $$(0, 1)$$; must be greater than GTApprox/MoAPointsAssignmentConfidence 0.99

New in version 1.10.0.

This options controls smoothness of weights. The greater this value is the smoother will be weights providing more smooth approximation.

GTApprox/OutputNanMode

Specifies how to handle non-numeric values in the output part of the training sample.

Value: raise, ignore, or predict raise

New in version 6.8.

By convention, NaN output values signify undefined function behavior. This option controls whether the model should try to predict undefined behavior. If set to predict, NaN values in training sample outputs are accepted, and the model will return NaN values in regions that are close to those points, for which the training sample contained NaN output values. Default (raise) means that NaN output values are not accepted and GTApprox raises an exception and cancels training if they are found; ignore means that such points are excluded from the sample, and training continues.

Note

This option adds specific input constraints to the model. These constraints are combined with the constraints added by GTApprox/InputDomainType.

GTApprox/OutputTransformation

Apply transformation to the training sample outputs before training the model.

Value: a StringScalar or StringVector specifying the transformation none (no transformations)

New in version 6.13 Service Pack 1.

This option is intended to improve accuracy of models trained on data where values of some outputs are exponentially distributed. For such outputs, a log transformation can reduce the distribution skew, resulting in a more accurate approximation. The model is trained on the transformed data and automatically applies the reverse transformation when evaluated.

Transformations are denoted by strings with the following meanings:

• auto — use statistical tests to determine whether transformation should be applied to an output.
• lnp1 — apply log transformation of the form $$y^* = \text{sgn}(y) \cdot \ln(|y| + 1)$$, where $$\text{sgn}$$ is the sign function.
• none — disable transformation, values of outputs are passed to the model builder as is.

Note that the strings used in this option’s value (auto, lnp1, and none) are case-sensitive.

If option value is a StringScalar, the same setting is applied to all outputs. For example, setting this option to auto means that the block will analyze all sample outputs and automatically apply the log transformation to those outputs which are statistically similar to an exponential distribution.

The StringVector form can be used to apply a specific setting to each output. The length of this vector must be equal to the number of columns in the matrix received to the f_sample port (the output part of the training sample). Each element of the vector specifies the transform for the respective output column. For example, if there are 3 training outputs, ("auto", "lnp1", "none") means that the block will analyze the first output in order to decide whether to apply the transformation to it, log transformation is always applied to the second output, and all transformations are disabled for the third one.

Note

If you start training with an initial model, which was trained with the GBRT technique and uses output transformation, GTApprox/OutputTransformation must be set either to "auto" or to the same value as the one you used when training the initial model.

GTApprox/RSMCategoricalVariables

Specifies categorical variables.

Value: a list of zero-based indexes of input variables [] (no categorical variables)

Deprecated since version 6.3: kept for compatibility only, use GTApprox/CategoricalVariables instead.

Prior to 6.3 this option listed categorical variables for the RSM technique specifically. With the improved support for categorical variables added in 6.3, there is now the general GTApprox/CategoricalVariables that deprecates GTApprox/RSMCategoricalVariables and overrides it unless these options come into a conflict.

GTApprox/RSMElasticNet/L1_ratio

Specifies ratio between L1 and L2 regularization.

Works only for Response Surface Model technique.

Value: list of floats in range $$[0, 1]$$. []

Each element of the list sets the trade-off between L1 and L2 regularization: 1 means L1 regularization only, while 0 means L2 regularization only. The best value among given is chosen via cross-validation procedure. If none is given (default) RSM with pure L1 regularization is constructed.

GTApprox/RSMFeatureSelection

Specifies the regularization and term selection procedures.

Works only for Response Surface Model technique.

Value: LS, RidgeLS, MultipleRidgeLS, ElasticNet, or StepwiseFit RidgeLS

The technique to use for regularization and term selection:

• LS — ordinary least squares (no regularization, no term selection).
• RidgeLS — least squares with Tikhonov regularization (no term selection).
• MultipleRidgeLS — multiple ridge regression that also filters non-important terms.
• ElasticNet — linear combination of L1 and L2 regularizations.
• StepwiseFit — ordinary least squares regression with stepwise inclusion/exclusion for term selection.
GTApprox/RSMMapping

Specifies mapping type for data pre-processing.

Works only for Response Surface Model technique.

Value: None, MapStd or MapMinMax MapStd

The technique to use for data pre-processing:

• None - no data pre-processing.
• MapStd - linear mapping of standard deviation for each variable to $$[-1, 1]$$ range.
• MapMinMax - linear mapping of values for each variable to $$[-1, 1]$$ range.
GTApprox/RSMStepwiseFit/inmodel

Selects the starting model for stepwise-fit regression.

Works only for Response Surface Model technique, see GTApprox/RSMFeatureSelection.

Value: IncludeAll, ExcludeAll, Auto Auto

Changed in version 6.14: added the Auto setting, which is now default instead of IncludeAll.

This option specifies the terms initially included in the model when stepwise-fit regression is used (GTApprox/RSMFeatureSelection is set to StepwiseFit).

• IncludeAll starts with a full model (all terms included).
• ExcludeAll assumes none of the terms are included at the starting step.
• Auto selects the type of the initial model automatically according to the number of terms. If the number of terms is low enough, regression starts with a full model (similar to IncludeAll); otherwise, if the number of terms is high, no terms are included in the initial model (similar to ExcludeAll).

Depending on the terms included in the initial model and the order in which terms are moved in and out, the method may build different models from the same set of potential terms.

GTApprox/RSMStepwiseFit/penter

Specifies p-value of inclusion for stepwise-fit regression.

Works only for Response Surface Model technique.

Value: floating point number in range $$(0,$$ GTApprox/RSMStepwiseFit/premove$$]$$ 0.05

Option value is the maximum p-value of F-test for a term to be added into the model. Generally, the higher the value, the more terms are included into the final model.

GTApprox/RSMStepwiseFit/premove

Specifies p-value of exclusion for stepwise-fit regression.

Works only for Response Surface Model technique.

Value: floating point number in range $$[$$GTApprox/RSMStepwiseFit/penter$$, 1)$$ 0.10

Option value is the minimum p-value of F-test for a term to be removed from the model. Generally, the higher the value, the more terms are included into the final model.

GTApprox/RSMType

Specifies the type of response surface model.

Works only for Response Surface Model technique.

Value: Linear, Interaction, Quadratic, or PureQuadratic Linear

Changed in version 6.8: default is Linear (was PureQuadratic).

This option restricts the type of terms that may be included into the regression model.

• Linear — only constant and linear terms may be included.
• Interaction — constant, linear, and interaction terms may be included.
• Quadratic — constant, linear, interaction, and quadratic terms may be included.
• PureQuadratic — only constant, linear, and quadratic terms may be included (interaction terms are excluded).
GTApprox/Seed

Fixed seed used in the deterministic training mode.

Value: positive integer 15313

New in version 5.0.

In the deterministic training mode, GTApprox/Seed sets the seed for randomized initialization algorithms in certain techniques. See GTApprox/Deterministic for more details.

GTApprox/SGPNumberOfBasePoints

The number of base points used to approximate the full covariance matrix of the points from the training sample.

Works only for Sparse Gaussian Process technique.

Value: integer in range $$[1, 4000]$$ 1000

Base points (subset of regressors) are selected randomly among points from the training sample and used for the reduced rank approximation of the full covariance matrix of the points from the training sample. Reduced rank approximation is done using Nystrom method for selected subset of regressors. Note that if the value of this option is greater than the dataset size, then GP technique is used instead of SGP.

GTApprox/SPLTContinuity

Required approximation smoothness.

Works only for 1D Splines with tension technique.

Value: C1 or C2 C2

If this option value is C2 (default), then the approximation curve is required to have continuous second derivative. If it is C1, only the first derivative is required to be continuous.

GTApprox/StoreTrainingSample

Save a copy of training data with the model.

Value: True, False, or Auto Auto

New in version 6.6.

If True, the trained model will store a copy of the training sample. If False, this attribute will be an empty list. The Auto setting currently defaults to False.

Note that in case of GBRT incremental training (see Incremental Training) setting GTApprox/StoreTrainingSample saves only the last (most recent) training sample on each training iteration.

GTApprox/SubmodelTraining

Select whether to train submodels in parallel or sequentially.

Value: Sequential, Parallel, or Auto Auto

New in version 6.14.

This option can be used to force or disable parallel training of submodels.

• Sequential: different submodels are never trained simultaneously. Parallel threads will be used only if the selected approximation technique supports parallelization internally (on the algorithm level).
• Parallel: parallel threads will be used to train multiple submodels simultaneously. If some submodel is trained by a technique which supports parallelization internally, it can use several threads if available.
• Auto (default): determines the mode to use automatically, depending on the approximation settings and properties of the training sample.

See Submodels and Parallel Training for details.

GTApprox/TADiscreteVariables

Specifies discrete input variables.

Value: a list of zero-based indexes of input variables [] (no discrete variables)

Deprecated since version 6.3: kept for compatibility only, use GTApprox/CategoricalVariables instead.

Prior to 6.3 this option specified discrete input variables for the TA technique specifically. With the improved support for categorical variables added in 6.3, there is now the general GTApprox/CategoricalVariables that deprecates GTApprox/TADiscreteVariables and overrides it unless these options come into a conflict.

GTApprox/TALinearBSPLExtrapolation

Use linear extrapolation for BSPL factors.

Works for Tensor Products of Approximations and Incomplete Tensor Products of Approximations techniques.

Value: True, False, or Auto Auto

New in version 1.9.4.

This option allows to switch extrapolation type for BSPL factors to linear. By default, BSPL factors extrapolate to constant. If GTApprox/TALinearBSPLExtrapolation is True, extrapolation will be linear in the range specified by the GTApprox/TALinearBSPLExtrapolationRange option, and fall back to constant outside this range.

• True: use linear extrapolation in the range specified by GTApprox/TALinearBSPLExtrapolationRange.
• False: do not use linear extrapolation (always use constant extrapolation).
• Auto: defaults to False.

This option affects only the Tensor Products of Approximations (including Incomplete Tensor Products of Approximations) models that contain BSPL factors. It does not affect non-BSPL factors at all, and if a Tensor Products of Approximations model is built using only non-BSPL factors, this option is ignored.

GTApprox/TALinearBSPLExtrapolationRange

Sets linear BSPL extrapolation range.

Works for Tensor Products of Approximations and Incomplete Tensor Products of Approximations techniques.

Value: floating point number in range $$(0, \infty)$$ 1.0

New in version 1.9.4.

Sets the range in which the BSPL factors extrapolation will be linear (see GTApprox/TALinearBSPLExtrapolation) relatively to the variable range of this factor in the training sample. This setting “expands” the sample range: let $$x_{min}$$ and $$x_{max}$$ be the minimum and maximum value of a variable found in the sample (BSPL factors are always 1-dimensional), then the extrapolation range is $$(x_{max} - x_{min}) \cdot (1 + 2r)$$, where $$r$$ is the GTApprox/TALinearBSPLExtrapolationRange option value (the range is expanded by $$(x_{max} - x_{min}) \cdot r$$ on each bound).

This option affects only the Tensor Products of Approximations (including Incomplete Tensor Products of Approximations) models that contain BSPL factors, and only if GTApprox/TALinearBSPLExtrapolation is set to True. It does not affect non-BSPL factors at all, and if a Tensor Approximation model is built using only non-BSPL factors, this option is ignored.

GTApprox/TAModelReductionRatio

Sets the ratio the model complexity should be reduced by.

Works for Tensor Products of Approximations and Incomplete Tensor Products of Approximations techniques.

Value: floating point number in range $$[1, \infty)$$ or 0 (auto) 0 (auto)

New in version 6.2.

Sets the ratio of the complexity (number of basis functions) of the default TA or iTA model to the desired complexity (for detailed description see Model Complexity Reduction). For example, if this option is set to 2 the number of basis function of the model will be 2 times less than the number of basis functions in the default model. This option affects only TA models with BSPL factors. All other factors ignore this option.

Using this option slightly increases model size but reduces memory consumption during model evaluation and the size of model exported to C and Octave. The accuracy of the model in most cases decreases.

Note, that the model complexity has a lower bound. This means that the reduction ratio has an upper bound. So, the actual reduction ratio can be smaller than the value of GTApprox/TAModelReductionRatio.

Default setting (0) means that no reduction is performed.

Setting GTApprox/TAModelReductionRatio greater than 1 does not guarantee exact fit, so this options is not compatible with GTApprox/ExactFitRequired set to True.

Note, that this option is not compatible with GTApprox/TAReducedBSPLModel, because both options reduce model complexity but use different algorithm to do this.

GTApprox/TAReducedBSPLModel

Deprecated since version 6.2: kept for compatibility only, use GTApprox/TAModelReductionRatio instead.

Since version 6.2 this option is deprecated by a more advanced GTApprox/TAModelReductionRatio option which allows to set the desired complexity of the final model.

GTApprox/Technique

Specify the approximation algorithm to use.

Value: RSM, SPLT, HDA, GP, SGP, HDAGP, TA, iTA, TGP, MoA, GBRT, PLA, TBL or Auto Auto

New in version 1.9.2: added the incomplete Tensor Approximation technique.

New in version 1.10.0: added the Mixture of Approximators technique.

New in version 3.0 Release Candidate 1: added the Tensor Gaussian Processes technique.

New in version 6.3: added the Piecewise Linear Approximation technique.

New in version 6.8: added the Table Function technique.

Changed in version 6.8: removed the deprecated Linear Regression (LR) technique. This technique is no longer supported; instead, use RSM with GTApprox/RSMType set to Linear.

This option allows user to explicitly specify an algorithm to be used in approximation. Its default value is Auto, meaning that the tool will automatically determine and use the best algorithm (except TGP and GBRT which are never selected automatically, and TA and iTA which are by default excluded from automatic selection — see GTApprox/EnableTensorFeature). Manual settings are:

Sample size requirements taking effect when the approximation technique is selected manually are described in section Sample Size Requirements.

Note

Smart training of GBRT technique can be time consuming even in case of small training samples. Details on smart training can be found in section Smart Training.

GTApprox/TensorFactors

Describes tensor factors to use in the Tensor Approximation technique.

Value: factorization vector in JSON format (see description) [] (automatic factorization)

This option allows user to specify his own factorization of the inpu when the TA technique is used. Can also be used with TGP, but does not allow to change factor techniques in this case, except specifying discrete variables. iTA and other techniques ignore this option completely.

Note

The incomplete tensor approximation (iTA) technique ignores factorization specified by GTApprox/TensorFactors because it always uses 1-dimensional BSPL factors. The tensor Gaussian processes (TGP) technique applies factorization, but in this case the option value cannot include technique labels (see below). The only valid label for TGP is DV, but it is better to use the GTApprox/CategoricalVariables option instead.

Option value is a list of user-defined tensor factors, each factor being a subset of input dataset components selected by user. A factor is defined by a list of component indices and optionally includes a label, specifying the approximation technique to use, as the last element of the list. Indices are zero-based, lists are comma-separated and enclosed in square brackets.

For example, [[0, 2], [1, "BSPL"]] specifies factorization of a 3-dimensional input dataset into two factors. The first factor includes the first and third components, and the approximation technique for this factor will be selected automatically (no technique specified by user). The second factor includes the second component, and splines (BSPL label) will be used in the approximation of this factor.

Technique label must be the last element of the list defining a factor. Valid labels are:

• Auto - automatic selection (same as no label).
• BSPL - use 1-dimensional cubic smoothing splines.
• GP - use Gaussian processes.
• SGP - use Sparse Gaussian Process (added in 6.2).
• HDA - use high dimensional approximation.
• LR - linear approximation (linear regression).
• LR0 - constant approximation (zero order linear regression).
• DV - discrete variable. The only valid label for the tensor Gaussian processes (TGP) technique. To specify discrete variable GTApprox/CategoricalVariables option can also be used. Interaction between these two options is described in section Categorical Variables for TA, iTA and TGP techniques.

Note

The splines technique (BSPL) is available only for 1-dimensional factors.

Note

For factors using sparse Gaussian processes (SGP) the number of base points is specified by GTApprox/SGPNumberOfBasePoints. Note that this number is the same for all SGP factors. If a factor’s cardinality is less than the number of base points then a warning is generated and the Gaussian processes (GP) technique is used for this factor instead.

Warning

The DV label may conflict with the GTApprox/CategoricalVariables option — see its description for details. For this reason, when using the TGP technique, GTApprox/CategoricalVariables should be used instead of specifying discrete variables using the DV label.

Factorization has to be full (has to include all components). If there is a component not included in any of the factors, it leads to an exception.

GTApprox/TrainingAccuracySubsetSize

Limits the number of points selected from the training set to calculate model accuracy on the training set.

Value: integer in range $$[1, 2^{32}-1]$$, or 0 (no limit). 100 000

New in version 1.9.0.

After a model has been built by GTApprox, it is evaluated on the input values from the training set to test model accuracy (calculate model errors, or the deviation of model output values from the original output values). The result is an integral characteristic named “Training Set Accuracy”, which is found in model info. For very large samples this test is time consuming and may significantly increase the build time. If the number of points in the training set exceeds the GTApprox/TrainingAccuracySubsetSize option value, some of the points will be dropped to make the test take less time, and training set accuracy statistic will be based only on the model errors calculated using the limited points subset (the size of which is equal to the GTApprox/TrainingAccuracySubsetSize option value). The number of points actually used in the test will also be found in model info.

If the sample size is less than GTApprox/TrainingAccuracySubsetSize value, this option in fact has no effect. In this case the number of points used in model accuracy test is equal to the number of points used to build the model (which may still be different from the number of points in the training set — for example, if the training set contains duplicate values).

When this option does take an effect, it always produces a warning to the model build log stating that only a limited subset of points selected from the training set will be used to calculate model accuracy.

To cancel the limit, set this option to 0. With this setting, the model will always be evaluated on the same set of points which were used to build the model.