Give the full description of Random forest algorithm with mathematical formulas
Give the full description of Random forest algorithm with mathematical formulas

Random Forest is a popular machine learning algorithm based on the concept of ensemble learning, which combines multiple weak models to create a strong model. It was developed by Leo Breiman in 2001 as an extension of the Decision Tree algorithm.

The Random Forest algorithm creates a set of decision trees during the training phase, where each tree is trained on a random subset of the training data and a random subset of the features. The final prediction is made by aggregating the predictions of all the decision trees.

Here's a simplified description of the Random Forest algorithm:

1. Data Preparation: The input data is prepared by shuffling the data and splitting it into a training set and a test set.

2. Bootstrap Samples: A bootstrap sample is created by randomly selecting data points from the training set with replacement. This means that some data points may appear multiple times in the bootstrap sample, while others may not appear at all.

3. Decision Trees: For each bootstrap sample, a decision tree is constructed. The decision tree is built using the standard Decision Tree algorithm, where at each node, the best split is chosen based on a criterion such as Gini impurity or entropy. However, to prevent overfitting, only a random subset of the features is considered at each node for the best split.

4. Bagging: The decision trees are
Random forest is an ensemble machine learning algorithm that uses multiple decision trees to make predictions. It works by first creating a set of decision trees and then aggregating the results from these decision trees to make a prediction. Each decision tree is built using a subset of the data and the final prediction is made by taking the majority vote of all the decision trees. The advantage of using random forest is that it is able to reduce overfitting and improve accuracy. The mathematical formulas used in random forest are as follows:

P(y=1|X) = 1/(1+exp(-ΣΣi=1nαi))

αi = Σj=1n(Σj=1m(Xj-Xi)j)i

Σ = ΣΣi=1nΣj=1mΣj=1n(Xj-Xi)j

Xi = Σj=1nΣj=1m(Xj-Xi)j

X = Σj=1nΣj=1m(Xj)j

n = 1m

m = 1n