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Welcome to our comprehensive guide on fundamental machine learning algorithms! In this blog, we will delve deep into the concepts, mathematics, assumptions, and practical implementations of some of the most widely used algorithms in the field. Whether you’re a beginner looking to build a solid foundation or an experienced practitioner seeking a refresher, this guide will provide you with a clear understanding of linear regression, logistic regression, decision trees, random forests, support vector machines (SVM), and principal component analysis (PCA).
We’ll explore the underlying mathematics, discuss the assumptions made by each algorithm, and provide real-world scenarios for their implementation. Additionally, I have included interview-based questions with answers to help you prepare for machine learning-related interviews. So, let’s dive in and unravel the powerful machine learning techniques!
Linear regression is a supervised learning algorithm used to predict a continuous target variable based on one or more input features. It assumes a linear relationship between the features and the target variable.
Math Formulas
Hypothesis function: hθ(x) = θ₀ + θ₁x₁ + θ₂x₂ + … + θₙxₙ
Cost function: J(θ) = (1/2N) * Σ(hθ(xᵢ) — yᵢ)²
Gradient Descent update rule: θⱼ := θⱼ — α * (1/m) * Σ(hθ(xᵢ) — yᵢ) * xⱼᵢ
Assumptions
- Linearity: The relationship between the features and the target variable is linear.
- Independence: The input features are independent of each other.
- Homoscedasticity: The variance of the residuals is constant across all levels of the target variable.
Interview-based Q&A
Q1. What is the objective of linear regression?
Ans: The objective of linear regression is to find the best-fitting line (or hyperplane in higher dimensions) that minimizes the sum of squared differences between predicted and actual target values.
Q2. What happens if the assumptions of linearity and homoscedasticity are violated in linear regression?
Ans: If the assumptions are violated, the model’s predictions may not be accurate, and the estimates of coefficients may not be reliable.
Q3. How to handle multicollinearity in linear regression?
Ans: Multicollinearity occurs when two or more input features are highly correlated. One approach to handle it is to perform feature selection or dimensionality reduction using techniques like PCA.
Q4. What is the role of the learning rate (α) in gradient descent for linear regression?
Ans: The learning rate determines the step size in each iteration of gradient descent. A larger learning rate may lead to faster convergence but could overshoot the optimal solution, while a smaller rate may result in slow convergence.
Q5. How do you evaluate the performance of a linear regression model?
Ans: The performance of a linear regression model can be evaluated using metrics such as Mean Squared Error (MSE), R-squared (R²), and Mean Absolute Error (MAE).