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Course11110548960 lectures

Mathematics for Machine Learning

Prof. Debjani Chakraborty and Prof. Debashree Guha Adhya · IIT Kharagpur

Start with lecture 1 At NPTEL

About

This course will discuss the rich mathematical theory needed for developing efficient, accurate and robust machine learning algorithms. This course will focus on selected advanced topics from linear algebra, calculus, optimization, probability theory and statistics with strong linkage with machine learning. Applications of these topics will be introduced in ML with help of some real-life examples.

Intended audience: Under graduate

Prerequisites: Basic Mathematics

Lectures

Week 1

  1. Lecture 1: Introduction to Machine Learning YouTube
  2. Lecture 2: Few Instances of Learning YouTube
  3. Lecture 3: Loss Function Optimization YouTube
  4. Lecture 4: Phases of Machine Learning Systems YouTube
  5. Lecture 5: Single-layer and multi-layer neurons YouTube

Week 2

  1. Lecture 6: Introduction to Convexity YouTube
  2. Lecture 7: Study on Convex Function YouTube
  3. Lecture 8: Formation of Convex Hull YouTube
  4. Lecture 9: Optimization of Functions YouTube
  5. Lecture 10: Convex Optimization Problem YouTube

Week 3

  1. Lecture 11: Directional derivative, Gradient, Jacobian, Firest Order Taylor Formula YouTube
  2. Lecture 12: Gradient, Jacobian, First order Taylor formula YouTube
  3. Lecture 13: Gradient Descent Optimization Technique YouTube
  4. Lecture 14: Gradient Descent, Interpretation from Taylor approximation YouTube
  5. Lecture 15: Sub-Gradient Descent Optimization Technique YouTube

Week 4

  1. Lecture 16: Introduction to Underfitting & Overfitting YouTube
  2. Lecture 17: Relation of Bias & Variance to Underfitting & Overfitting YouTube
  3. Lecture 18: Bias-Variance Trade-off YouTube
  4. Lecture 19: Ridge Regression YouTube
  5. Lecture 20: LASSO Regression YouTube

Week 5

  1. Lecture 21: Stochastic Gradient descent YouTube
  2. Lecture 22: Stochastic Gradient descent (cont.) YouTube
  3. Lecture 23: Variants of Gradient descent YouTube
  4. Lecture 24: Momentum based Gradient descent YouTube
  5. Lecture 25: Accelerated Gradient descent YouTube

Week 6

  1. Lecture 26: Linear Predictors (Logistic Regression) YouTube
  2. Lecture 27: Linear Predictors (Logistic Regression) (Contd..) YouTube
  3. Lecture 28: Linear Predictors (Logistic Regression) (Contd..) YouTube
  4. Lecture 29: Linear Predictors (Logistic Regression) (Contd..) YouTube
  5. Lecture 30: Linear Predictors (Support Vector Machines) YouTube

Week 7

  1. Lecture 31: Introduction to Theory of Estimation YouTube
  2. Lecture 32: Probability Theory YouTube
  3. Lecture 33: Discrete Probability Distribution YouTube
  4. Lecture 34: Continuous Probability Distribution YouTube
  5. Lecture 35: Maximum likelihood Estimation YouTube

Week 8

  1. Lecture 36: MLE for Discrete Probability Distribution YouTube
  2. Lecture 37: MLE for Continuous Probability Distribution YouTube
  3. Lecture 38: Properties of Estimators YouTube
  4. Lecture 39: MLE for Linear and Logistic Regression YouTube
  5. Lecture 40: MLE for Naïve Bayes Model YouTube

Week 9

  1. Lecture 41: Eigen value & eigen vector, Linearly independent vectors YouTube
  2. Lecture 42: Orthogonal Basis, Eigen value decomposition YouTube
  3. Lecture 43: Orthogonal Basis, Eigen value decomposition Continued YouTube
  4. Lecture 44: Principal Component Analysis YouTube
  5. Lecture 45: Principal Component Analysis Continued YouTube

Week 10

  1. Lecture 46: Introduction to Dynamical System YouTube
  2. Lecture 47: Dynamical System and Control YouTube
  3. Lecture 48: Discrete Fourier Transform YouTube
  4. Lecture 49: Inverse Fourier Transform YouTube
  5. Lecture 50: Applications: Discrete Fourier Transform YouTube

Week 11

  1. Lecture 51: Introduction to Mixture models YouTube
  2. Lecture 52: Introduction to Gaussian Mixture Models YouTube
  3. Lecture 53: EM Algorithm YouTube
  4. Lecture 54: EM Algorithm (cont.) YouTube
  5. Lecture 55: A brief application to predict HMM parameters YouTube

Week 12

  1. Lecture 56 : Conditional probability, Bayes theorem YouTube
  2. Lecture 57 : Bayes Decision Rule YouTube
  3. Lecture 58 : Bayes Decision Rule YouTube
  4. Lecture 59 : Bayes Decision Rule (Bayesian minimum risk classifier) YouTube
  5. Lecture 60: Bayes Decision Rule (Linear Discriminant Analysis) YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Taught by
Prof. Debjani Chakraborty, Prof. Debashree Guha Adhya
Level
Undergraduate
Language
English
Subjects
Mathematics
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.
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