Learn · Mathematical Foundations for Machine Learning
Lecture 5 of 70Week 1 Fields, Vectors and Vector spaces
Combining Vectors and Linear Independence
Prof. Ashok Rao and Prof. Arulalan Rajan · IISc Bangalore
Credits and licence
- From
- Mathematical Foundations for Machine Learning, IISc Bangalore (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Why this course?
- Fields and Their Properties – Algebraic Tools for ML
- Fields, Vector Spaces
- Vector Spaces and Subspaces
- Combining Vectors and Linear Independence
- Basis and Dimension
- Linear Transformation - Intuition
- Subspaces associated with Linear Transformations
- Matrix representation of Linear Transformation
- Examples of Linear Transformation
- Eigenvalues and Eigenvectors
- Multiplicity of Eigen Values
- Diagonalization of Matrix
- Diagonalizability, Invariant subspaces
- Dot Product on Vector Space
- Orthogonality on Vector Space
- Orthonormal Basis
- Orthogonal Projections
- Construction of Orthogonal Basis
- Approximating a vector in any given subspace
- Real Symmetric Matrices
- Least Square Fitting and Pseudo Inverse - 1
- Least Square Fitting and Pseudo Inverse - 2
- Principal Component Analysis (PCA)
- Singular Value Decomposition (SVD)
- Singular Value Decomposition (SVD) Interpretation
- Support Vector Machine (SVM)
- Consolidating Week1 to Week 4
- Introduction to Probability - 1
- Introduction to Probability - 2
- Mutually Exclusive Events, Independent Events and Conditional Probability
- Total Probability Theorem and Bayes' Theorem
- Probability - A Measure Theoretic Insight
- Random Experiment and Random Variables
- Discrete Random Variables and Probability Mass Function (PMF)
- Types of Discrete Random Variables and Their Probability Distributions
- Continuous Random Variables
- Expected Value of Random Variable
- Moments and Variance
- Joint Distributions and Marginals
- Joint Moments of Random Variables
- Independence and Correlation
- Correlation and Covariance
- Joint Moments of Continuous random Variables and Conditioning of Random Variables
- Markov Inequality
- Chebychev Inequality
- Central Limit Theorem
- Sample Geometry
- Covariance Matrix & its properties
- Functions, Derivatives, Infinite Series
- Differentiation Rules
- Multivariate functions
- Gradient and Directional Derivatives
- Rules for Partial Derivatives, Jacobian and Hessian
- Matrix derivatives
- Optimization Overview
- Constrained Optimization, Optimal solutions, Saddle point
- Constrained optimization, Lagrange Multiplier
- Revisiting Least squares, Principal Component Analysis
- Minimizing the Cost Function: Gradent Descent Algorithm
- Variants of the Gradient Descent Algorithm
- Neural Networks , Perceptron
- Multilayer Layer Perceptron
- Back Propogation Algorithm
- Data and Patterns
- Classification and a simple binary classifier
- Classification, Clustering Techniques
- Linear Regression : Line of best fit
- Logistic Regression
- Course Summary, Credits & Acknowledgments