Mathematics of Artifical Intelligence and Machine Learning
Additional Info
- ECTS credits: 5
- University: Leibniz University Hannover
- Semester: 2
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Topics:
This course is designed to provide an introduction to mathematical foundations, concepts, and constructs for artificial intelligence and machine learning algorithm design. A subset from the below exhaustive list of topics would be covered.
Linear Algebra and Matrix Analysis:
Systems of Linear Equations, Vector Spaces, Linear Independence, Basis & Rank, Orthonormal Basis, Orthogonal Complement, Orthogonal Projections, Rotations, Eigenvalue Decomposition & Diagonalization, Singular Value Decomposition, Matrix Approximation.
Vector Calculus and Continuous Optimization:
Gradients of Vector-Valued Functions, Gradients of Matrices, Automatic Differentiation, Higher-Order Derivatives, Linearization and Multivariate Taylor Series, Unconstrained Optimization, Constrained Optimization & Lagrange Multipliers.
Probability and Distributions:
Probability Space, Discrete and Continuous Probabilities, Sum Rule, Product Rule, & Bayes’ Theorem, Summary Statistics and Independence, Gaussian Distribution, Conjugacy and the Exponential Family, Change of Variables/Inverse Transform.
Models and Data:
Models Learning & Selection, Empirical Risk Minimization, Parameter Estimation, Probabilistic Modeling & Inference, Directed Graphical Models, Bayesian Linear Regression, Dimensionality Reduction with Principal Component Analysis, Density Estimation with Gaussian Mixture Models, Classification with Support Vector Machines.
