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SPC-UQ/Cubic_Regression/README.md

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+# Toy Example: SPC-UQ on Cubic Regression
+
+This directory provides an implementation of several uncertainty quantification (UQ) methods on a synthetic cubic regression problem.
+
+The task is defined by
+
+    y = x³ + ε(x) - E[ε(x)]
+
+- Training set: 2,000 samples
+- Test set: 1,000 samples
+- In-distribution data: x ∈ [-4, 4]
+- Out-of-distribution data: x ∈ [-6, -4) ∪ (4, 6]
+
+## Running `run_cubic_tests.py`
+
+`run_cubic_tests.py` trains and evaluates different UQ models, and visualizes results.
+
+### Basic usage
+
+```bash
+python run_cubic_tests.py --num-epochs 5000 --data-noise log --UQ-model SPCregression
+```
+The benchmarks are lightweight and can run on **CPU-only devices**.  
+
+### Arguments
+
+- `--num-epochs`: Number of training epochs (default: 5000).
+- `--data-noise {norm, tri, log}`: Type of noise added to the data. `norm` is Gaussian, `tri` is a mixture distribution, and `log` is log-normal (default).
+- `--UQ-model {SPCregression, DeepEnsemble, EDLRegressor, EDLQuantileRegressor, QROC, ConformalRegressor}`: UQ model to run.
+
+After execution, the script prints RMSE, PICP and related metrics, and produces plots of prediction intervals and uncertainty.