Calculus Essentials for Machine Learning
Chapter 1: Introduction: Why Calculus Matters in Machine Learning
Functions and Models in ML
The Concept of Optimization in ML
Measuring Change: The Role of Derivatives
Calculus as a Tool for Understanding Algorithms
Quiz for Chapter 1
Chapter 2: Single-Variable Calculus: Derivatives and Optimization
Understanding Limits: The Foundation
Defining the Derivative
Common Differentiation Rules
Higher-Order Derivatives
Finding Minima and Maxima using Derivatives
Application: Simple Cost Function Optimization
Hands-on Practical: Calculating Derivatives with Python
Quiz for Chapter 2
Chapter 3: Multivariable Calculus: Gradients and Direction
Functions of Multiple Variables
Partial Derivatives
The Gradient Vector
Directional Derivatives
The Hessian Matrix
Multivariable Optimization Concepts
Hands-on Practical: Computing Gradients with NumPy
Quiz for Chapter 3
Chapter 4: Gradient Descent Algorithms
The Intuition Behind Gradient Descent
The Gradient Descent Algorithm Steps
The Learning Rate Parameter
Batch Gradient Descent
Stochastic Gradient Descent (SGD)
Mini-batch Gradient Descent
Challenges: Local Minima and Saddle Points
Hands-on Practical: Implementing Simple Gradient Descent
Quiz for Chapter 4
Chapter 5: The Chain Rule and Backpropagation
Revisiting the Chain Rule for Single Variables
The Chain Rule for Multivariable Functions
Introduction to Neural Networks as Composite Functions
Backpropagation: Applying the Chain Rule
Calculating Gradients for Weights and Biases
Computational Graphs
Hands-on Practical: Manual Backpropagation Example
Quiz for Chapter 5
The Concept of Optimization in ML
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- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Covers fundamental optimization concepts and algorithms used in machine learning, including cost functions and gradient descent, within the context of deep learning.
- Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) DOI: 10.1007/978-0-387-31073-2 - Introduces foundational concepts of pattern recognition and machine learning, detailing the role of error functions and optimization in model parameter estimation.
- An Introduction to Statistical Learning: With Applications in R, Gareth James, Daniela Witten, Trevor Hastie, Rob Tibshirani, 2013 (Springer) DOI: 10.1007/978-1-4614-7138-7 - Provides an accessible introduction to statistical learning methods, explaining optimization through examples like linear regression and the minimization of the residual sum of squares. (1st edition)
- CS229 Lecture Notes: Supervised Learning, Andrew Ng, 2018 (Stanford University) - Specifically covers linear regression, cost functions (e.g., MSE), and the introduction of gradient descent as an optimization method.
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