1. Why Combine Machine Learning (ML) and Statistical Models?

• Statistical models (e.g., regression, ARIMA, Cox models) offer interpretability, inference, and uncertainty quantification.
• Machine learning models (e.g., random forests, neural nets, gradient boosting) excel at capturing complex nonlinearities and interactions but may lack transparency.

Integrating them lets us balance predictive power with interpretability and robustness.

2. Integration Approaches

Here are some practical strategies:

(a) Hybrid (Model-Based + ML Enhancements)

• Use a statistical model (e.g., linear regression or ARIMA) as the baseline.
• Apply ML to capture residual patterns the statistical model misses. Example: ARIMA + neural networks (ARIMA handles trend/seasonality, NN models nonlinear components). Known as hybrid time-series forecasting.

(b) Feature Engineering via Statistical Models

• Derive statistical features (coefficients, p-values, residuals, likelihood ratios) and feed them into ML models. Example: Use logistic regression coefficients as inputs to a random forest for churn prediction.
• Improves ML interpretability and reduces dimensionality.

(c) ML-Assisted Parameter Estimation

• Use ML to estimate parameters or priors in Bayesian statistical models.
• Example: Neural networks can approximate posterior distributions in Bayesian regression, speeding up inference.

(d) Ensemble & Stacking

• Combine predictions from ML and statistical models via stacking or weighted averaging. Example: Blending survival analysis (Cox model) with gradient boosting in healthcare prognosis.
• Often improves predictive accuracy by leveraging complementary strengths.

(e) Regularization & Interpretability

• Many statistical techniques (LASSO, ridge regression) have inspired ML regularization.
• ML models can adopt statistical penalties to avoid overfitting while retaining interpretability.

3. Applications

• Finance: Hybrid GARCH + ML for volatility forecasting.
• Healthcare: Cox models + random forests for patient survival analysis.
• Marketing: Logistic regression + gradient boosting for churn prediction.
• Climate/Energy: ARIMA + LSTMs for energy demand forecasting.

4. Benefits

• Higher predictive accuracy (nonlinear + linear effects captured).
• Interpretability (statistical component explains key drivers).
• Robustness (ML reduces misspecification bias).
• Better generalization (ensembles smooth over individual weaknesses).

✅ In summary: Machine learning can enhance statistical models by capturing complex nonlinearities, improving parameter estimation, and reducing residual error, while statistical models provide interpretability, inference, and uncertainty estimation. The integration creates hybrid systems that are more accurate, interpretable, and reliable than either approach alone.

You can refer to my paper to build an explainable AI model. It is easy to understand and explain how explainable AI gives an explanation of the importance of the ML model for a particular input. Sangle, S. B., Kachare, P. H., Puri, D. V., Al-Shoubarji, I., Jabbari, A., & Kirner, R. (2025). Explaining electroencephalogram channel and subband sensitivity for alcoholism detection. Computers in Biology and Medicine, 188, 109826.

Developing and integrating Explainable AI (XAI) models is crucial for ensuring transparent, fair, and trustworthy decision-making by moving beyond the "black box" nature of complex algorithms. This process starts with the proactive selection of either inherently interpretable models, such as decision trees or linear regression, for high-stakes applications, or by using post-hoc explanation techniques like LIME and SHAP for more complex models like neural networks. To ensure fairness, it's essential to perform data auditing and bias mitigation from the beginning, checking that the training data is diverse and representative. Integration also requires a human-centered approach, tailoring explanations to the user's technical understanding and using visualizations or counterfactuals to make the rationale clear.