Pre Lab

Learning Objectives

• Explain the basic idea of Random Forest for classification.
  
  

• Understand how Random Forest combines many decision trees using bagging and majority vote.
  
  

• Connect the idea of Random Forest to the Variational Quantum Classifier (VQC) as another nonlinear classifier.
  
  

• Compare Random Forest and VQC in terms of accuracy.
  
  
  

1. What is Random Forest? 

Random Forest is a classical ensemble learning method.
Instead of training one model, it trains many decision trees and combines their outputs.

Each input sample is a feature vector
X ∈ ℝᵈ
with a label
y∈{0,1}

Random Forest works in three main steps:

1. Bootstrap sampling
   For each tree, we draw a random sample of the training data with replacement.

2. Random feature selection
   At each split inside the tree, we only look at a random subset of features instead of all features.

3. Majority vote
   After training all trees, each tree makes a prediction for a new input x.
   The final class is chosen by majority vote across all trees.
   
   

This makes Random Forest:

• More robust than a single decision tree

• Able to model complex, nonlinear decision boundaries

• Usually a strong baseline for tabular data

2. How Random Forest Makes Predictions  

Each tree in the forest outputs a class prediction (0 or 1).

We can also interpret the output as a probability: Suppose there are 𝑇 trees in the forest.

If 𝑘 trees predict class 1 for an input 𝑥, then the estimated probability of class 1 is

We then convert this probability into a final class label: 

If the output is greater than or equal to 0.5, predict class 1

Otherwise, predict class 0

3. How Does VQC Compare? 

The Variational Quantum Classifier (VQC) is also a nonlinear classifier, but it uses a parameterized quantum circuit instead of a forest of trees.

For each input x, we encode the features into a quantum state and apply trainable quantum gates with parameters θ. After running the circuit, we measure one or more qubits and obtain a probability of class 1