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
Optimization: Why Minimize or Maximize?
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- Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016 (MIT Press) - Introduces optimization algorithms, loss functions, and the role of derivatives/gradients in training machine learning models, especially deep neural networks.
- Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) - Provides a comprehensive foundation for machine learning, with detailed explanations of loss functions, model training, and the mathematical principles of optimization for various algorithms.
- Convex Optimization, Stephen Boyd, Lieven Vandenberghe, 2004 (Cambridge University Press) - A foundational textbook covering the theory and applications of optimization, explaining problem formulation and the mathematical properties of minima and maxima in functions.
- CS229 Lecture Notes: Introduction to Machine Learning, Andrew Ng, Tengyu Ma, 2023 (Stanford University) - Covers the fundamental principles of machine learning, including the definition of cost functions and the application of gradient descent for model optimization.