Calculus Fundamentals for Machine Learning
Chapter 1: Why Calculus for Machine Learning?
The Role of Math in Machine Learning
Introducing Functions: Inputs and Outputs
Visualizing Functions: Graphs
What is a Limit?
Intuition Behind Limits
Connecting Functions and Limits to ML
Quiz for Chapter 1
Chapter 2: Derivatives: Measuring Change
Rate of Change: Average vs Instantaneous
The Derivative: Slope of a Tangent Line
Derivative Notation (Leibniz and Lagrange)
Calculating Derivatives: The Power Rule
Calculating Derivatives: Constants and Sums
Introduction to Higher-Order Derivatives
Practice: Calculating Simple Derivatives
Quiz for Chapter 2
Chapter 3: Optimization with Derivatives
Finding Maximum and Minimum Points
Optimization: Why Minimize or Maximize?
Cost Functions in Machine Learning
Goal: Minimizing the Cost Function
Introduction to Gradient Descent
How Derivatives Guide Gradient Descent
Visualizing Gradient Descent
Quiz for Chapter 3
Chapter 4: Handling Multiple Inputs: Partial Derivatives
Functions of Multiple Variables
Partial Derivatives: The Concept
Calculating Partial Derivatives
Partial Derivative Notation
The Gradient Vector
Geometric Meaning of the Gradient
Practice: Calculating Partial Derivatives and Gradients
Quiz for Chapter 4
Chapter 5: Calculus in Action: Simple Optimization
Recap: Optimization Goal and Gradient Descent
Example: Simple Linear Regression Model
Defining a Cost Function for Linear Regression
Calculating Gradients for the Cost Function
Performing a Gradient Descent Step
The Learning Rate Parameter
Putting It All Together: The Optimization Process
Hands-on Practical: Manual Gradient Calculation
Quiz for Chapter 5
Putting It All Together: The Optimization Process
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- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Provides a comprehensive introduction to optimization algorithms, including gradient descent, its mathematical principles, and practical considerations for machine learning.
- An Introduction to Statistical Learning with Applications in R, Gareth James, Daniela Witten, Trevor Hastie, Rob Tibshirani, 2013 (Springer) - Covers linear regression models and the fundamental optimization techniques used to fit them, providing a statistical learning perspective on the process.
- CS229 Lecture Notes: Supervised Learning, Linear Regression, Andrew Ng, 2018 Stanford University CS229 Lecture Notes - Introduces linear regression and thoroughly explains the gradient descent algorithm, including the cost function, partial derivatives, and parameter updates, as part of a foundational machine learning course.
- Numerical Optimization, Jorge Nocedal and Stephen J. Wright, 2006 (Springer) DOI: 10.1007/978-0-387-40065-5 - Offers a rigorous mathematical treatment of optimization algorithms, including the theoretical underpinnings and practical considerations of gradient descent methods.
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