## 3 QSAR Today
### Model Validation: Internal Using the Training Dataset and External Using the Test Sataset  
The goal of modeling is to find the optimal settings of the model parameters to accurately predict the activity of new, previously unseen molecules. This is achieved through validation of the developed model [150]. Validation helps avoid chance correlations from numerous descriptors used during model development and prevents data overfitting. In 2003, the Organization for Economic Co-operation and Development (OECD) defined five principles for QSAR validation for regulatory purposes [78]:  
* The QSAR model should be associated with a defined endpoint. * An unambiguous algorithm. * A defined domain of application. * Appropriate measures for goodness-of-fit, robustness, and predictivity. * Mechanistic interpretation, if possible. Models can be validated through internal and external validation procedures. Internal validation of QSAR models involves using compounds from the training set to test the model's predictability and accuracy. The most common method for internal validation is cross-validation using leave-one-out (LOO) or leave-group-out (LGO), also known as k-fold \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Filter** & **Wrapper** & **Embedded** \\ \hline Description & selection is based on the feature relevance score, which identifies and prioritizes the most impactful features based on their contribution to the dependent variable (\(\Upsilon\)) by evaluating the intrinsic properties of the data Can scale high-dimensional datasets; faster and computationally affordable compared to wrapper methods no interaction with the classifier, do not consider feature dependencies/redundancy in various statistical tests that associate X and Y variables, such as the Chi squared test, correlation coefficient scores, information gain, \(t\)-test & selection of a subset of relevant features involves generating all possible feature/descriptor subsets, training a machine learning model for each subset, and comparing their performance & feature selection is based on constructing a classifier using a specific learning method, training the model on all descriptors, and extracting the importance of each feature \\ Advantages & & & \\  & computationally affordable compared to wrapper methods & & classifier interaction; consider feature dependencies \\ Disadvantages & & & \\  & dependencies/redundancy in various statistical tests that associate X and Y variables, such as the Chi squared test, correlation coefficient scores, information gain, \(t\)-test & overfitting, selection based on classifiers, computationally demanding & classifier dependencies \\ \hline Applications & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A brief description of feature selection methods, along with their advantages, disadvantages, and examples, is presented. cross-validation [151; 152]. In LGO cross-validation, the data are divided into k-number of groups. An iterative process excludes one group at a time, and a model is built using the remaining k-1 groups. The excluded group is then predicted, and the process continues until all groups have been left out once. During model runs, the parameters are kept constant. This process is repeated several times, and the scientist adjusts model parameters between each run until optimal model performance is achieved. In the LOO procedure, the process is similar, except that each compound from the training set is excluded one at a time. While this approach is time-consuming, it can provide an overly optimistic model evaluation, leading to potential errors. Commonly used quality assessments for regression QSAR models include the following:  
* The Square of the Correlation Coefficient (R\({}^{2}\)): R\({}^{2}\) measures the strength of the linear relationship between predicted and experimental activity values (y).