setup_LightRuleFit() combines decision rules from LightGBM trees with a regularized GLMNET model. The tree stage defines rule features; the linear stage estimates their contribution to the prediction.
2026-10-08 02:53:45 Checking data is ready for training... ✔ [check_supervised]
2026-10-08 02:53:45 ▶ [train]2026-10-08 02:53:45 Training set: 100 cases x 2 features. [summarize_supervised]2026-10-08 02:53:45 Test set: 50 cases x 2 features. [summarize_supervised]2026-10-08 02:53:45 //CPU (auto-selected) | serial | 1 worker: algorithm 1 thread, tuning 1, outer resampling 1 (as set) [msg_resources]2026-10-08 02:53:45 Shared memory (auto): not sharing training data (3.4 kB) -- this run transfers nothing to workers. [report_shared_memory]2026-10-08 02:53:45 Training LightRuleFit Regression... [train]2026-10-08 02:53:46 Checking data is ready for training... ✔ [check_supervised]
2026-10-08 02:53:46 Checking data is ready for training... ✔ [check_supervised]
2026-10-08 02:53:46 ▶ [train]2026-10-08 02:53:46 Training set: 100 cases x 2 features. [summarize_supervised]2026-10-08 02:53:46 //CPU (auto-selected) | serial | 1 worker: algorithm 1 thread, tuning 1, outer resampling 1 (as set) [msg_resources]2026-10-08 02:53:47 Training LightGBM Regression... [train]2026-10-08 02:53:47 Checking data is ready for training... ✔ [check_supervised]
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
<SupervisedReview>
LightRuleFit (LightGBM rules + GLMNET) was used for regression. R-squared was 0.57 on the training set and 0.54 on the test set.
100 training and 50 test cases; 2 predictors (50.0 training cases per predictor).
Performance
Training Test Training - test
MAE 0.927 1.072 -0.145
MSE 1.301 1.751 -0.450
RMSE 1.141 1.323 -0.182
R² 0.574 0.543 0.031
Baseline comparisons
MSE 1.751 vs 3.925 (training mean); loss reduction 2.174 (95% CI 1.391 to 2.957): better
MAE 1.072 vs 1.721 (training mean); loss reduction 0.649 (95% CI 0.447 to 0.851): better
R² 0.543 vs -0.023 (training mean)
Findings
* SINGLE_SPLIT (note): Performance was estimated on a single split, with 50 test cases. The test intervals reflect the number of test cases, not how much the estimate would change with a different split.
Suggestion: Use outer resampling to test on every case and to measure variation between splits; repeat it when cases are few.
* TEST_PRECISION (note): Test mean squared error is 1.751 (95% CI 1.092 to 2.411), from 50 test cases.
* BASELINE_MSE (note): Test mean squared error of 1.751 (mean reduction from the baseline's 3.925: 2.174, 95% CI 1.391 to 2.957) is better than predicting the training mean for every case.
Limitations
- Whether the model is useful depends on the question it addresses, the costs of different errors, and how its predictions will be used; performance metrics cannot establish this.
- Preprocessing, decomposition and tuning done by rtemis are fitted on the training cases of each split and only applied to its test cases. Steps taken before the data was passed to rtemis -- selecting or filtering predictors, transforming or removing cases using all the data, or choosing among models by their test performance -- can bias evaluation; this review cannot determine whether that happened.
- Performance estimates apply to cases from the population the data was drawn from; performance on a different population or setting may differ.
get_varimp(mod)
<VariableImportance>Coefficient (coefficient, 35 entries): The lasso coefficient of each rule extracted from the boosted trees, on the scale of the linear predictor; a rule is an indicator, so its coefficient does not depend on predictor units.
alpha_glmnet and lambda_glmnet control the regularized linear stage. Tree-stage parameters control the candidate rule set. A boosting stage that makes no split cannot supply decision rules and produces a corrective error.
Rule coefficients describe the fitted representation. Their interpretation depends on rule overlap, the regularization, and the data distribution. Held-out performance and explanations provide complementary information.
