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Preface
Mathematics for Machine Learning
Machine Learning Problems
Classification
Regression
Clustering
Representation Learning
Vector and Function Spaces
Vector Spaces
Polynomial Vector Space
Basis Functions Vector Space
Subspaces
Metric Spaces
Normed Spaces
Inner Product Spaces
Transposition
Calculus and Optimization
Extrema
Gradients
Gradient Descent
Matrix Calculus
Jacobian
Chain Rule
Mean Value Theorem
First Order Condition
Quadratic Optimization
Line Search
Hessian
Taylor’s Theorem
Matrix Analysis
Rank of a Matrix
Determinant
Gaussian Elimination and the PLU Decomposition
Fundamental Equivalences for Square matrices
Trace
Eigenvalues and Eigenvectors
Orthogonal matrices
Symmetric matrices
Rayleigh Quotients
Matrix Norms
Positive (semi-)definite matrices
Principal Components Analysis
Singular value decomposition
Moore-Penrose Pseudoinverse
Orthogonal projections
Fundamental Subspaces
Convexity
Convex sets
Basics of convex functions
Second-Order Optimization
Second Order Condition for Minima
Newton’s Method
Probability
Probability Basics
Random variables
Functions of Random Variables
Expected Value
Variance
Covariance
Random vectors
Functions of Random Vectors
Joint distributions
The Gaussian distribution
Estimation of Parameters
The Exponential Family and Conjugate Priors
Bayesian Inference for the Gaussian
Appendix
Detailed Proofs
Cauchy-Schwarz Inequality
Bolzano-Weierstrass Theorem
Extreme Value Theorem
Rolle's Theorem
Mean Value Theorem
Chain Rule for Scalar-Scalar Functions
Squeeze Theorem
First Fundamental Theorem of Calculus
Second Fundamental Theorem of Calculus
Clairaut's Theorem
Differentiation Rules
Exercise Sheet Solutions
Exercise Sheet 1 Solutions
Exercise Sheet 2 Solutions
Exercise Sheet 3 Solutions
Exercise Sheet 4 Solutions
Repository
Open issue
Index
