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
Recap: Optimization Goal and Gradient Descent
Was this section helpful?
- An Introduction to Statistical Learning: With Applications in R, Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani, 2013 (Springer) DOI: 10.1007/978-1-4614-7138-7 - A widely used textbook that provides a clear explanation of linear regression, cost functions (like MSE), and the fundamental idea of optimizing model parameters to minimize error.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - This authoritative textbook offers a detailed exposition of optimization algorithms, including the mechanics of gradient descent, learning rates, and various cost functions in the context of machine learning.
- Machine Learning Course Notes (CS229) - Linear Regression and Logistic Regression, Andrew Ng, 2008 Stanford University (Stanford University) - These lecture notes from a renowned machine learning course offer a concise and mathematically grounded explanation of gradient descent, cost functions, and their practical application in machine learning.