Molecule Net Regression Eval

---
name: molecule-net-regression-eval
description: Evaluates the ability of graph-theoretic and machine learning models to predict continuous molecular properties (biological activity, physicochemical, and thermodynamic) from molecular structure. It tests generalization across diverse chemical spaces and compares classical feature-based approaches against deep learning baselines. Use when the user wants to benchmark on MoleculeNet (BACE, LogP Synthetic, LogP Experimental, ESOL, SAMPL), or asks about evaluating this task. Reports R^2.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2604.19840
  bibtex_key: niane2026graph
  confidence: high
---

# molecule-net-regression-eval

> Graph-Theoretic Models for the Prediction of Molecular Measurements — Niane et al. (2026) (arXiv:2604.19840, 2026)

## What this evaluates

Evaluates the ability of graph-theoretic and machine learning models to predict continuous molecular properties (biological activity, physicochemical, and thermodynamic) from molecular structure. It tests generalization across diverse chemical spaces and compares classical feature-based approaches against deep learning baselines.

## Datasets

- **MoleculeNet (BACE, LogP Synthetic, LogP Experimental, ESOL, SAMPL)** — total ?; splits: 5-fold cross-validation (-1)

## Metrics

- `R^2` **(primary)** — range: (-∞, 1]
  - Coefficient of determination: R^2 = 1 - (SS_res / SS_tot). Reports mean and 95% confidence interval across 5-fold CV folds.
- `RMSE` — range: ≥ 0
  - Root mean square error: sqrt(mean((y_true - y_pred)^2)).
- `MAE` — range: ≥ 0
  - Mean absolute error: mean(abs(y_true - y_pred)).
- `MSE` — range: ≥ 0
  - Mean squared error: mean((y_true - y_pred)^2).

## Input / output format

**Input**: Molecular structures (SMILES/graphs) processed into graph-theoretic indices (D(G), zeta(G)), additional topological descriptors, physicochemical properties, and/or Morgan fingerprints.

**Output**: Continuous numerical value corresponding to the target molecular property (e.g., pIC50, LogP, LogS, Delta G_hyd).

## Scoring recipe

```python
def compute_metrics(y_true, y_pred):
    ss_res = np.sum((y_true - y_pred) ** 2)
    ss_tot = np.sum((y_true - np.mean(y_true)) ** 2)
    r2 = 1 - (ss_res / ss_tot)
    rmse = np.sqrt(np.mean((y_true - y_pred) ** 2))
    mae = np.mean(np.abs(y_true - y_pred))
    mse = np.mean((y_true - y_pred) ** 2)
    return r2, rmse, mae, mse
# Evaluated via 5-fold cross-validation; report mean ± 95% CI across folds.
```

## Common pitfalls

- Direct comparison of absolute R² values with studies using different data splits (e.g., 80/20 holdout vs. 5-fold CV) is invalid due to distribution shifts.
- Small dataset sizes combined with high-dimensional feature spaces (e.g., 657 molecules vs. 1026 features) can cause severe overfitting if regularization/feature selection is omitted.
- Baseline graph-theoretic models trained on homogeneous datasets often fail to generalize to chemically diverse benchmarks, leading to artificially low R² scores.

## Evidence (verbatim from paper)

> All models were evaluated using 5-fold cross-validation with four metrics: the coefficient of determination ($R^{2}$), root mean square error (RMSE), mean absolute error (MAE), and mean squared error (MSE).

## Citation

```bibtex
@misc{niane2026graph,
  title={Graph-Theoretic Models for the Prediction of Molecular Measurements},
  author={Niane et al. (2026)},
  year={2026},
  note={arXiv:2604.19840}
}
```

- arXiv: 2604.19840