Indian Air Quality Forecasting Eval

indian-air-quality-forecasting-eval

Air Quality Prediction Using LOESS-ARIMA and Multi-Scale CNN-BiLSTM with Residual-Gated Attention — Pahari et al. (2025) (arXiv:2510.22818, 2025)

What this evaluates

Evaluates the ability of hybrid time-series models to forecast urban air quality indices and specific pollutant concentrations (PM2.5, O3, CO, NOx) using historical environmental data and temporal features.

Datasets

• CPCB Indian Air Quality Dataset — total ?; splits: train (-1), val (-1), test (-1)

Metrics

• RMSE (primary) — range: other
  • Root Mean Square Error: $\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}$. Lower values indicate better predictive accuracy.
• R² — range: [0, 1]
  • Coefficient of Determination: $1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}{i})^{2}}{\sum{i=1}^{n}(y_{i}-\bar{y})^{2}}$. Measures proportion of variance explained; higher is better.
• MAE — range: other
  • Mean Absolute Error: $\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right|$. Lower values indicate better predictive accuracy.

Input / output format

Input: Hourly time-series sequences of pollutant concentrations (PM2.5, O3, CO, NOx) augmented with temporal features (hour, dayofweek, month, year) and a 1-year lag feature for PM2.5.

Output: Predicted concentration values for the target pollutant(s) at the next forecasting horizon.

Scoring recipe

def compute_metrics(y_true, y_pred):
    n = len(y_true)
    rmse = np.sqrt(np.mean((y_true - y_pred) ** 2))
    mae = np.mean(np.abs(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)
    return {'RMSE': rmse, 'R2': r2, 'MAE': mae}

Common pitfalls

• Pollutants have vastly different scales (e.g., O3/CO MSE ~1e-5 vs PM2.5 MSE ~8), so comparing raw MSE across pollutants is misleading without normalization.
• Time-series splits must be chronological to prevent data leakage; the paper does not explicitly state the train/val/test split ratio or dates.
• Missing value imputation (forward-fill then mean) may introduce bias if missingness is not random, affecting baseline comparisons.

Evidence (verbatim from paper)

Model performance was assessed using three standard statistical indicators: Root Mean Square Error (RMSE), Coefficient of Determination ($R^{2}$), and Mean Absolute Error (MAE). These are defined as follows:

| | $\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right|$ | | (19) |

Citation

@misc{pahari2025airquality,
  title={Air Quality Prediction Using LOESS-ARIMA and Multi-Scale CNN-BiLSTM with Residual-Gated Attention},
  author={Pahari et al. (2025)},
  year={2025},
  note={arXiv:2510.22818}
}

• arXiv: 2510.22818