# A Critical Review of the Modelling Tools for the Reactive Transport of Organic Contaminants
## 3 Modelling
### Machine Learning Paradigm  
The machine learning paradigm is not inherently stochastic, but in many application areas, it relies on stochastic methods that deal with well-known and classical statistical problems, such as regression, classification, decision, clustering, etc. The difference is not in the problem itself, but in the approach, i.e., analysing huge amounts of sometimes complex and unstructured data and using a large number of algorithms and computational resources [481; 482; 483]. Recently, the ease of data acquisition and storage forces scientists to face the paradox of data abundance or the curse of dimensionality, i.e., the difficulty of finding a structure when there are too many variables [484; 485]. Machine learning (ML) seems to be the perfect method for all ecological data mining problems, as it is able to find hidden patterns, relationships, and correlations in large amounts of data [486; 487; 488; 489]. Machine learning also focuses on the development of algorithms and models that can learn from data and perform predictive analyses [490; 491; 492; 493]. The primary limitations or failure to meet expectations in machine learning methods may result from poor data quality, e.g., missing values, mislabelling, duplicates, and interpretability of results. The researcher must have basic knowledge to explain the high or low accuracy of the model. The greatest challenge in model-based interpretability arises when models characterised by high predictive accuracy are so simple that they can be easily understood by modelers or reviewers [494; 495]. Machine learning (ML) consists of two primary phases: the induction of the model, which involves processing vast amounts of data in various forms (structured, unstructured, semi-structured, metadata, or time series data), and the efficient representation of the model and inference. Stochasticity can manifest in the first phase during data generation, augmentation, or resampling [496; 497]. The behaviour and performance of numerous machine learning algorithms are characterized as stochastic, as many optimization algorithms operate in stochastic domains, while others rely on randomness or probabilistic decisions. Two processes should be considered in the context of stochastic methods and machine learning: optimization, and generalization. Many optimization algorithms must operate in stochastic domains, while others rely on randomness or probabilistic decisions. Although optimization has a complex computational background, its function is simple and practical:to enhance functionality, and address real-world problems. Furthermore, optimization and machine learning can be examined from two perspectives: first, the contribution of optimization to enhancing the performance of machine learning [498; 499; 500; 501]; and second, the optimization of processes facilitated by the outcomes of machine learning algorithms [502; 503]. Another crucial aspect of machine learning is generalization: during generalization, we assume that the algorithm has identified the pattern and captured the regularity. A common algorithm employed in optimization is stochastic gradient descent (SGD), where the gradient of a loss function is computed repeatedly and randomly for a single training sample or for mini-batches of samples, and the model parameters are updated accordingly [504; 505]. Some other machine learning models, such as Gaussian Naive Bayes, Gaussian Mixture Models, and Bayesian Networks, are probabilistic and utilize stochastic principles to represent data and make predictions. Gaussian Naive Bayes, for instance, is among the best-performing probabilistic classifiers based on Bayes' theorem, and tends to perform very well even under unrealistic assumptions, particularly on small training datasets [506]. In summary, stochastic machine learning models find applications in pattern recognition, data mining, image analysis, and risk analysis [507; 508; 509].