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Math for Machine Learning
Introduction
Introduction (2:46)
Linear Regression
Linear Regression (7:32)
The Least Squares Method (11:25)
Linear Algebra Solution to Least Squares Problem (12:50)
Example Linear Regression (4:05)
Summary Linear Regression (0:33)
Problem Set Linear Regression
Solution Set Linear Regression
Linear Discriminant Analysis
Classification (1:15)
Linear Discriminant Analysis (0:44)
The Posterior Probability Functions (3:42)
Modelling the Posterior Probability Functions (7:13)
Linear Discriminant Functions (5:32)
Estimating the Linear Discriminant Functions (6:00)
Classifying Data Points Using Linear Discriminant Functions (3:09)
LDA Example 1 (13:52)
LDA Example 2 (17:38)
Summary Linear Discriminant Analysis (1:34)
Problem Set Linear Discriminant Analysis
Solution Set Linear Discriminant Analysis
Logistic Regression
Logistic Regression (1:15)
Logistic Regression Model of the Posterior Probability Function (3:02)
Estimating the Posterior Probability Function (8:57)
The Multivariate Newton-Raphson Method (9:14)
Maximizing the Log-Likelihood Function (13:51)
Logistic Regression Example (9:55)
Summary Logistic Regression (1:21)
Problem Set Logistic Regression
Solution Set Logistic Regression
Artificial Neural Networks
Artificial Neural Networks (0:36)
Neural Network Model of the Output Functions (12:59)
Forward Propagation (0:51)
Choosing Activation Functions (4:30)
Estimating the Output Functions (2:17)
Error Function for Regression (2:27)
Error Function for Binary Classification (6:15)
Error Function for Multiclass Classification (4:38)
Minimizing the Error Function Using Gradient Descent (6:27)
Backpropagation Equations (4:16)
Summary of Backpropagation (1:27)
Summary Artificial Neural Networks (1:47)
Problem Set Artificial Neural Networks
Solution Set Artificial Neural Networks
Maximal Margin Classifier
Maximal Margin Classifier (2:29)
Definitions of Separating Hyperplane and Margin (5:43)
Proof 1 (6:42)
Maximizing the Margin (3:36)
Definition of Maximal Margin Classifier (1:01)
Reformulating the Optimization Problem (7:37)
Proof 2 (1:13)
Proof 3 (4:52)
Proof 4 (8:41)
Proof 5 (5:10)
Solving the Convex Optimization Problem (1:05)
KKT Conditions (1:24)
Primal and Dual Problems (1:24)
Solving the Dual Problem (3:31)
The Coefficients for the Maximal Margin Hyperplane (0:29)
Classifying Test Points (1:50)
The Support Vectors (0:58)
Maximal Margin Classifier Example 1 (9:50)
Maximal Margin Classifier Example 2 (11:41)
Summary Maximal Margin Classifier (0:31)
Problem Set Maximal Margin Classifier
Solution Set Maximal Margin Classifier
Support Vector Classifier
Support Vector Classifier (3:54)
Slack Variables Points on Correct Side of Hyperplane (3:47)
Slack Variables Points on Wrong Side of Hyperplane (1:37)
Formulating the Optimization Problem (3:52)
Definition of Support Vector Classifier (0:44)
A Convex Optimization Problem (1:46)
Solving the Convex Optimization Problem (Soft Margin) (6:38)
The Coefficients for the Soft Margin Hyperplane (2:09)
The Support Vectors (Soft Margin) (1:37)
Classifying Test Points (Soft Margin) (1:36)
Support Vector Classifier Example 1 (14:53)
Support Vector Classifier Example 2 (9:19)
Summary Support Vector Classifier (0:41)
Problem Set Support Vector Classifier
Solution Set Support Vector Classifier
Support Vector Machine Classifier
Support Vector Machine Classifier (1:19)
Enlarging the Feature Space (5:22)
The Kernel Trick (4:24)
Summary Support Vector Machine Classifier (1:07)
Conclusion
Concluding Letter (Math for Machine Learning)
Solving the Convex Optimization Problem (Soft Margin)
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