`elastic_net_regression`

Elastic net regression regressor supporting continuous and mixed-feature datasets. The library implements the regressor_protocol defined in the regression_protocols library and learns a linear model using cyclic coordinate descent with coefficient-wise soft-thresholding updates and an additional L2 term in order to minimize mean squared error plus a standard elastic net penalty.

API documentation

Open the ../../apis/library_index.html#elastic_net_regression link in a web browser.

Loading

To load this library, load the loader.lgt file:

| ?- logtalk_load(elastic_net_regression(loader)).

Testing

To test this library predicates, load the tester.lgt file:

| ?- logtalk_load(elastic_net_regression(tester)).

The unit test suite covers the default mixed-penalty behavior together with the boundary cases l1_ratio(0.0) and l1_ratio(1.0).

To run the performance benchmark suite, load the tester_performance.lgt file:

| ?- logtalk_load(elastic_net_regression(tester_performance)).

Features

Continuous and Mixed Features: Supports continuous attributes and categorical attributes.
Feature Scaling: Continuous attributes can be standardized using z-score scaling.
Missing Values: Missing numeric and categorical values represented using anonymous variables are encoded using explicit missing-value indicator features.
Unknown Values: Prediction requests containing categorical values that are not declared by the dataset raise a domain error.
Mixed Penalty: Combines coefficient-wise L1 shrinkage with an L2 penalty controlled by the regularization/1 and l1_ratio/1 options, including the ridge-like l1_ratio(0.0) and lasso-like l1_ratio(1.0) endpoints.
Standard Encoding Semantics: Categorical attributes are encoded using reference-level dummy coding derived from the declared dataset attribute values, with a trailing missing-value indicator feature, and each encoded coefficient is regularized independently.
Diagnostics Metadata: Learned regressors record model name, target, training example count, optimization stop reason, completed iterations, final parameter delta, encoded feature count, and effective options, accessible using the shared regression diagnostics predicates.
Model Export: Learned regressors can be exported as predicate clauses or written to a file.
Reference Benchmarks: Includes a dedicated performance suite reporting training time, RMSE, and MAE for both zero-penalty baselines and explicit elastic-net runs on sparse, mixed, categorical, and wide mixed datasets.

Regressor representation

The learned regressor is represented by default as:

elastic_net_regressor(Encoders, Bias, Weights, Diagnostics)

The exported predicate clauses therefore use the shape:

Functor(Encoders, Bias, Weights, Diagnostics)

Diagnostics syntax

The diagnostics/2 predicate returns a list of metadata terms with the form:

[
    model(elastic_net_regression),
    target(Target),
    training_example_count(TrainingExampleCount),
    options(Options),
    convergence(Status),
    iterations(Iterations),
    final_delta(FinalDelta),
    encoded_feature_count(FeatureCount)
]

Where:

model(elastic_net_regression) identifies the learning algorithm that produced the regressor.
target(Target) stores the target attribute name declared by the training dataset.
training_example_count(TrainingExampleCount) stores the number of examples used during training.
options(Options) stores the effective learning options after merging the user options with the library defaults.
convergence(Status) records the optimization stop condition. The current values are tolerance when the maximum Karush-Kuhn-Tucker optimality violation across the intercept and all encoded features is within the configured tolerance and maximum_iterations_exhausted when training stops because the iteration cap is reached.
iterations(Iterations) stores the number of coordinate-descent sweeps completed during training.
final_delta(FinalDelta) stores the maximum Karush-Kuhn-Tucker optimality violation measured during the final optimization check.
encoded_feature_count(FeatureCount) stores the number of numeric features induced by the encoder list, including missing-value indicator features.

Use the regression_protocols diagnostic/2 and regressor_options/2 helper predicates when you only need a single metadata term or the effective options.

Options

The learn/3 predicate accepts the following options:

maximum_iterations/1: Maximum number of coordinate-descent sweeps to run before stopping even if the tolerance criterion has not been met. The default is 2000.
tolerance/1: Convergence threshold for the maximum Karush-Kuhn-Tucker optimality violation in a full coordinate-descent sweep. Training stops early when both the intercept condition and all encoded-feature subgradient conditions are satisfied within this value. The default is 1.0e-7.
regularization/1: Overall penalty coefficient applied during optimization. Higher values increase shrinkage and can reduce overfitting. The default is 0.01.
l1_ratio/1: Fraction of the overall penalty assigned to the L1 part of the elastic net penalty. The remaining fraction is assigned to the L2 part. Accepted values are floats in the interval [0.0, 1.0], where 0.0 gives the ridge endpoint and 1.0 gives the lasso endpoint. The default is 0.5.
feature_scaling/1: Controls z-score standardization of continuous attributes before training and prediction. Accepted values are true and false. The default is true.

elastic_net_regression