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Course10610870270 lectures

Mathematical Foundations for Machine Learning

Prof. Ashok Rao and Prof. Arulalan Rajan · IISc Bangalore

Start with lecture 1 At NPTEL

About

This course will provide a holistic approach to the mathematical foundations for Machine Learning. The course is focussed on developing mathematical ideas, necessary for machine learning applications, through intuitions and visualizations.The course primarily focuses on three important mathematical domains, namely

Linear Algebra

Probabilty and Statistics and

Multivariable Calculus,

on which the ML and data science ideas are built.

Intended audience: BE/BTech/ME/MTech//BSc/MSc(Maths)/MCA

Prerequisites: Basic Mathematics at school and undergraduate level

Lectures

Week 1 Fields, Vectors and Vector spaces

  1. Why this course? YouTube
  2. Fields and Their Properties – Algebraic Tools for ML YouTube
  3. Fields, Vector Spaces YouTube
  4. Vector Spaces and Subspaces YouTube
  5. Combining Vectors and Linear Independence YouTube
  6. Basis and Dimension YouTube

Week 2 Linear Transformations and Matrix Representations

  1. Linear Transformation - Intuition YouTube
  2. Subspaces associated with Linear Transformations YouTube
  3. Matrix representation of Linear Transformation YouTube
  4. Examples of Linear Transformation YouTube
  5. Eigenvalues and Eigenvectors YouTube
  6. Multiplicity of Eigen Values YouTube
  7. Diagonalization of Matrix YouTube
  8. Diagonalizability, Invariant subspaces YouTube

Week 3 Orthogonality, Projections and Real Symmetric Matrices

  1. Dot Product on Vector Space YouTube
  2. Orthogonality on Vector Space YouTube
  3. Orthonormal Basis YouTube
  4. Orthogonal Projections YouTube
  5. Construction of Orthogonal Basis YouTube
  6. Approximating a vector in any given subspace YouTube
  7. Real Symmetric Matrices YouTube

Week 4 Least Square Fitting, PCA, SVD and SVM

  1. Least Square Fitting and Pseudo Inverse - 1 YouTube
  2. Least Square Fitting and Pseudo Inverse - 2 YouTube
  3. Principal Component Analysis (PCA) YouTube
  4. Singular Value Decomposition (SVD) YouTube
  5. Singular Value Decomposition (SVD) Interpretation YouTube
  6. Support Vector Machine (SVM) YouTube

Week 5 Fundamentals of Probability

  1. Consolidating Week1 to Week 4 YouTube
  2. Introduction to Probability - 1 YouTube
  3. Introduction to Probability - 2 YouTube
  4. Mutually Exclusive Events, Independent Events and Conditional Probability YouTube
  5. Total Probability Theorem and Bayes' Theorem YouTube
  6. Probability - A Measure Theoretic Insight YouTube

Week 6 Random Variables and Probability Distributions

  1. Random Experiment and Random Variables YouTube
  2. Discrete Random Variables and Probability Mass Function (PMF) YouTube
  3. Types of Discrete Random Variables and Their Probability Distributions YouTube
  4. Continuous Random Variables YouTube
  5. Expected Value of Random Variable YouTube
  6. Moments and Variance YouTube

Week 7 Jointly Distribed Random Variables

  1. Joint Distributions and Marginals YouTube
  2. Joint Moments of Random Variables YouTube
  3. Independence and Correlation YouTube
  4. Correlation and Covariance YouTube
  5. Joint Moments of Continuous random Variables and Conditioning of Random Variables YouTube

Week 8 Inequalities, CLT & Sample Geometry

  1. Markov Inequality YouTube
  2. Chebychev Inequality YouTube
  3. Central Limit Theorem YouTube
  4. Sample Geometry YouTube
  5. Covariance Matrix & its properties YouTube

Week 9 Taylor’s series, Partial Derivatives, Chain rule, Gradient, Jacobian, Hessian

  1. Functions, Derivatives, Infinite Series YouTube
  2. Differentiation Rules YouTube
  3. Multivariate functions YouTube
  4. Gradient and Directional Derivatives YouTube
  5. Rules for Partial Derivatives, Jacobian and Hessian YouTube

Week 10 Matrix Derivatives, Optimization and Gradient Descent Algorithm

  1. Matrix derivatives YouTube
  2. Optimization Overview YouTube
  3. Constrained Optimization, Optimal solutions, Saddle point YouTube
  4. Constrained optimization, Lagrange Multiplier YouTube
  5. Revisiting Least squares, Principal Component Analysis YouTube
  6. Minimizing the Cost Function: Gradent Descent Algorithm YouTube
  7. Variants of the Gradient Descent Algorithm YouTube

Week 11 Neural Networks, Perceptron and Backpropagation Algorithm

  1. Neural Networks , Perceptron YouTube
  2. Multilayer Layer Perceptron YouTube
  3. Back Propogation Algorithm YouTube

Week 12 Classification, Clustering and Regression

  1. Data and Patterns YouTube
  2. Classification and a simple binary classifier YouTube
  3. Classification, Clustering Techniques YouTube
  4. Linear Regression : Line of best fit YouTube
  5. Logistic Regression YouTube
  6. Course Summary, Credits & Acknowledgments YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Computer Science and Engineering
Taught by
Prof. Ashok Rao, Prof. Arulalan Rajan
Level
Undergraduate
Language
English
Subjects
Computer science, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
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