Random forest is an ensemble learning algorithm that operates by constructing a multitude of decision trees during training and outputting the class that is the mode of the classes of the individual trees. Random forests correct for decision trees’ tendency to overfit their training set.

The random forest algorithm begins with acquiring a large number of data rows containing information about previous loan applicants and whether they defaulted or repaid their loans. This data is used to train the random forest model. The data would contain features/attributes of the applicants like age, income, existing debt, employment status, credit score etc. as well as the target variable which is whether they defaulted or repaid the loan.

The algorithm randomly samples subsets of this data with replacement, so certain rows may be sampled more than once while some may be left out, to create many different decision trees. For each decision tree, a randomly selected subset of features/attributes are made available for splitting nodes. This introduces randomness into the model and helps reduce overfitting.

Each tree is fully grown with no pruning, and at each node, the best split among the random subset of predictors is used to split the node. The variable and split point that minimize the impurity (like gini index) are chosen.

Impurity measures how often a randomly chosen element from the set would be incorrectly labeled if it was randomly labeled according to the distribution of labels in the subset. Splits with lower impurity are preferred as they divide the data into purer child nodes.

Repeatedly, nodes are split using the randomly selected subset of attributes until the trees are fully grown or until a node cannot be split further. The target variable is predicted for each leaf node and new data points drop down the trees from the root to the leaf nodes according to split rules.

After growing numerous decision trees, which may range from hundreds to thousands of trees, the random forest algorithm aggregates the predictions from all the trees. For classification problems like loan default prediction, it takes the most common class predicted by all the trees as the final class prediction.

For regression problems, it takes the average of the predictions from all the trees as the final prediction. This process of combining predictions from multiple decision trees is called bagging or bootstrapping which reduces variance and helps avoid overfitting. The generalizability of the model increases as more decision trees are added.

The advantage of the random forest algorithm is that it can efficiently perform both classification and regression tasks while being highly tolerant to missing data and outliers. It also gives estimates of what variables are important in the classification or prediction.

Feature/variable importance is calculated by looking at how much worse the model performs without that variable across all the decision trees. Important variables are heavily used for split decisions and removing them degrades prediction accuracy more.

To evaluate the random forest model for loan default prediction, the data is divided into train and test sets, with the model being trained on the train set. It is then applied to the unseen test set to generate predictions. Evaluation metrics like accuracy, precision, recall, F1 score are calculated by comparing the predictions to actual outcomes in the test set.

If these metrics indicate good performance, the random forest model has learned the complex patterns in the data well and can be used confidently for predicting loan defaults of new applicants. Its robustness comes from averaging predictions across many decision trees, preventing overfitting and improving generalization ability.

Some key advantages of using random forest for loan default prediction are its strength in handling large, complex datasets with many attributes; ability to capture non-linear patterns; inherent feature selection process to identify important predictor variables; insensitivity to outliers; and overall better accuracy than single decision trees. With careful hyperparameter tuning and sufficient data, it can build highly effective predictive models for loan companies.