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
The Learning Rate Parameter
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- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - A comprehensive textbook that covers gradient descent and the learning rate as a core hyperparameter in optimization algorithms. Chapter 8, 'Optimization for Training Deep Models,' is especially useful.
- CS229 Lecture Notes - Supervised Learning, Part I, Andrew Ng, Tengyu Ma, 2022 (Stanford University) - Part of the official lecture notes from Stanford's Machine Learning course, offering a fundamental explanation of gradient descent and the setting of the learning rate within the context of linear regression.
- Adam: A Method for Stochastic Optimization, Diederik P. Kingma and Jimmy Ba, 2014 International Conference on Learning Representations (ICLR 2015) DOI: 10.48550/arXiv.1412.6980 - This seminal paper introduces the Adam optimizer, a widely adopted adaptive learning rate algorithm. It offers insights into how learning rates can be dynamically adjusted, a concept mentioned as an advanced topic.