Linear Regression | The Math of AI

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The Math of AI (Course 1): Foundation Classics

AI Calculus Review

AI Calculus Part 1: Derivatives, Extrema, Chain Rule, and Gradient Operator. (13:54)
AI Calculus Part 2: Jacobian and Hessian (18:41)
AI Calculus Part 3: Test of Extrema via Hessian Determinant. (14:49)
AI Calculus Part 4: Extrema Test Example, Hessian Eigenvalue Decomposition. (23:31)
AI Calculus Part 5: Quadratic Approximation via the Hessian (22:18)
AI Calculus Part 6: Properties of Quadratic Approximation (26:10)

Linear Algebra & Probability: Quick Review

Linear Algebra Review: Basis Vectors, Matrix Multiplication, and Neural Nets as Matrices. (26:46)
The Fundamental Theorem of Linear Algebra: AKA Rank-Nullity Theorem (26:07)
Probability Review. (26:50)

Linear Regression & Logistic Regression

Linear Regression (27:49)
Logistic Regression (Part 2): Loss Function Derivation. (35:01)
Logistic Regression (Part 1): Classification Problem Setup. (32:01)

Constrained Optimization

Lagrange Multipliers (24:34)
Karush Kuhn Tucker (KKT) Conditions (31:43)
Lagrangian Duality (Part 1): The Lagrangian Dual Function. (22:02)
Lagrangian Duality (Part 2): The Dual Problem, Weak Duality, Strong Duality, and the Duality Gap. (26:30)
Support Vector Machines (Part 1): Geometry of the Problem and Constraints. (20:45)
Support Vector Machines (Part 2): Deriving the Constraint Optimization Problem. (16:02)
Support Vector Machines (Part 3): Lagrangian Dual Function (28:46)
Support Vector Machines (Part 4): Quadratic Program, Support Vectors, and Kernel Trick. (29:53)

Fourier Analysis

Fourier Series (Part 1): Fourier Basis, Euler's Formula, Complex Fourier Series (29:24)
Fourier Series (Part 2): Complex Fourier Series, Fourier Transform, Inverse Fourier Transform. (26:33)
Discrete Fourier Transform (DFT) (25:57)
Fast Fourier Transform (Part 1): Radix-2 and the Symmetries of the Complex Plane. (26:45)
Fast Fourier Transform (Part 2): Order of NlogN; Matrix Representation of FFT; Sampling Theorem. (20:27)

Eigenvalue Decomposition, SVD, and PCA

Eigenvalue Decomposition (Part 1): Normal Matrices, Spectral Theorem. (27:05)
Eigenvalue Decomposition (Part 2): Spectral Theorem, An Example. (16:15)
Eigenvalue Decomposition (Part 3): The Hessian Matrix Revisited, Extremum Test. (17:51)
Singular Value Decomposition (Part 1): Geometric & Algebraic View. (27:05)
Singular Value Decomposition (Part 2): Relationship between EVD and SVD (26:26)
Principal Component Analysis (Part 1): The Data Matrix, the PCA Objective, and the Covariant Matrix (25:09)
Principal Component Analysis (Part 2): Eigenvalue Decomposition of Covariant Matrix. (23:06)
Principal Component Analysis (Part 3): Proof that Principal Component is Covariant Matrix' Principal Eigenvector. (24:49)

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