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
Connecting Functions and Limits to ML
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- Pattern Recognition and Machine Learning, Christopher Bishop, 2006 (Springer) - Explains the mathematical foundations of machine learning, including linear models, loss functions, and the use of calculus for optimization.
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, Aurélien Géron, 2022 (O'Reilly Media) - Provides practical examples and explanations of linear regression, cost functions, and gradient descent, connecting them to the underlying mathematical functions and optimization principles.
- CS229: Machine Learning Lecture Notes - Main Notes, Andrew Ng, Tengyu Ma, 2023 Stanford University CS229 Course Material (Stanford University) - Covers the mathematical foundations of linear regression, including the model as a function, cost functions, and how gradient descent uses derivatives for optimization.
- Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, 2020 (Cambridge University Press) DOI: 10.1017/9781108679904 - Provides a comprehensive overview of the mathematical concepts essential for machine learning, with dedicated sections on calculus, including functions, limits, and derivatives in the context of optimization.