# Mathematics for Machine Learning

- Institution: IIT Kharagpur
- Department: Mathematics
- Taught by: Prof. Debjani Chakraborty, Prof. Debashree Guha Adhya
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105489)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105489)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 1: Introduction to Machine Learning](https://invisiblenetwork.ai/learn/nptel/111105489/41f7af9a354c) (YouTube)
2. [Lecture 2: Few Instances of Learning](https://invisiblenetwork.ai/learn/nptel/111105489/8ef2b09cf42a) (YouTube)
3. [Lecture 3: Loss Function Optimization](https://invisiblenetwork.ai/learn/nptel/111105489/b2a485d87e67) (YouTube)
4. [Lecture 4: Phases of Machine Learning Systems](https://invisiblenetwork.ai/learn/nptel/111105489/f04407f95e59) (YouTube)
5. [Lecture 5: Single-layer and multi-layer neurons](https://invisiblenetwork.ai/learn/nptel/111105489/11e142236b5b) (YouTube)
6. [Lecture 6: Introduction to Convexity](https://invisiblenetwork.ai/learn/nptel/111105489/4b944a568632) (YouTube)
7. [Lecture 7: Study on Convex Function](https://invisiblenetwork.ai/learn/nptel/111105489/fc0fef1f7bd3) (YouTube)
8. [Lecture 8: Formation of Convex Hull](https://invisiblenetwork.ai/learn/nptel/111105489/1b11c73d3310) (YouTube)
9. [Lecture 9: Optimization of Functions](https://invisiblenetwork.ai/learn/nptel/111105489/00607b113206) (YouTube)
10. [Lecture 10: Convex Optimization Problem](https://invisiblenetwork.ai/learn/nptel/111105489/3df7e12ea700) (YouTube)
11. [Lecture 11: Directional derivative, Gradient, Jacobian, Firest Order Taylor Formula](https://invisiblenetwork.ai/learn/nptel/111105489/440cfd0a7ecb) (YouTube)
12. [Lecture 12: Gradient, Jacobian, First order Taylor formula](https://invisiblenetwork.ai/learn/nptel/111105489/b653b5502149) (YouTube)
13. [Lecture 13: Gradient Descent Optimization Technique](https://invisiblenetwork.ai/learn/nptel/111105489/166d067de835) (YouTube)
14. [Lecture 14: Gradient Descent, Interpretation from Taylor approximation](https://invisiblenetwork.ai/learn/nptel/111105489/65c89b69406e) (YouTube)
15. [Lecture 15: Sub-Gradient Descent Optimization Technique](https://invisiblenetwork.ai/learn/nptel/111105489/5cc7953c3683) (YouTube)
16. [Lecture 16: Introduction to Underfitting & Overfitting](https://invisiblenetwork.ai/learn/nptel/111105489/03a737dce4ab) (YouTube)
17. [Lecture 17: Relation of Bias & Variance to Underfitting & Overfitting](https://invisiblenetwork.ai/learn/nptel/111105489/54aa5d2189cb) (YouTube)
18. [Lecture 18: Bias-Variance Trade-off](https://invisiblenetwork.ai/learn/nptel/111105489/c0bcea22afdc) (YouTube)
19. [Lecture 19: Ridge Regression](https://invisiblenetwork.ai/learn/nptel/111105489/02d27b5b9ce2) (YouTube)
20. [Lecture 20: LASSO Regression](https://invisiblenetwork.ai/learn/nptel/111105489/e3f69ff12fb8) (YouTube)
21. [Lecture 21: Stochastic Gradient descent](https://invisiblenetwork.ai/learn/nptel/111105489/d294e6e9df1b) (YouTube)
22. [Lecture 22: Stochastic Gradient descent (cont.)](https://invisiblenetwork.ai/learn/nptel/111105489/f656d8ffc335) (YouTube)
23. [Lecture 23: Variants of Gradient descent](https://invisiblenetwork.ai/learn/nptel/111105489/9a33b6b1811c) (YouTube)
24. [Lecture 24: Momentum based Gradient descent](https://invisiblenetwork.ai/learn/nptel/111105489/62fad4cc12e4) (YouTube)
25. [Lecture 25: Accelerated Gradient descent](https://invisiblenetwork.ai/learn/nptel/111105489/bf4e158a147a) (YouTube)
26. [Lecture 26: Linear Predictors (Logistic Regression)](https://invisiblenetwork.ai/learn/nptel/111105489/1b0c4554cc62) (YouTube)
27. [Lecture 27: Linear Predictors (Logistic Regression) (Contd..)](https://invisiblenetwork.ai/learn/nptel/111105489/c01a965a466e) (YouTube)
28. [Lecture 28: Linear Predictors (Logistic Regression) (Contd..)](https://invisiblenetwork.ai/learn/nptel/111105489/8148dde01f81) (YouTube)
29. [Lecture 29: Linear Predictors (Logistic Regression) (Contd..)](https://invisiblenetwork.ai/learn/nptel/111105489/5c405fdc7f79) (YouTube)
30. [Lecture 30: Linear Predictors (Support Vector Machines)](https://invisiblenetwork.ai/learn/nptel/111105489/fc739e5c8cc4) (YouTube)
31. [Lecture 31: Introduction to Theory of Estimation](https://invisiblenetwork.ai/learn/nptel/111105489/798b158aa67a) (YouTube)
32. [Lecture 32: Probability Theory](https://invisiblenetwork.ai/learn/nptel/111105489/518864765a08) (YouTube)
33. [Lecture 33: Discrete Probability Distribution](https://invisiblenetwork.ai/learn/nptel/111105489/74158ca40861) (YouTube)
34. [Lecture 34: Continuous Probability Distribution](https://invisiblenetwork.ai/learn/nptel/111105489/c74c450eb67e) (YouTube)
35. [Lecture 35: Maximum likelihood Estimation](https://invisiblenetwork.ai/learn/nptel/111105489/d81c533758cf) (YouTube)
36. [Lecture 36: MLE for Discrete Probability Distribution](https://invisiblenetwork.ai/learn/nptel/111105489/69fbcd66b755) (YouTube)
37. [Lecture 37: MLE for Continuous Probability Distribution](https://invisiblenetwork.ai/learn/nptel/111105489/12f0c44c8a92) (YouTube)
38. [Lecture 38: Properties of Estimators](https://invisiblenetwork.ai/learn/nptel/111105489/0825c491e45f) (YouTube)
39. [Lecture 39: MLE for Linear and Logistic Regression](https://invisiblenetwork.ai/learn/nptel/111105489/34a08c0c2908) (YouTube)
40. [Lecture 40: MLE for Naïve Bayes Model](https://invisiblenetwork.ai/learn/nptel/111105489/0a219921d92e) (YouTube)
41. [Lecture 41: Eigen value & eigen vector, Linearly independent vectors](https://invisiblenetwork.ai/learn/nptel/111105489/b5ea72fb2664) (YouTube)
42. [Lecture 42: Orthogonal Basis, Eigen value decomposition](https://invisiblenetwork.ai/learn/nptel/111105489/803fc3b8e94e) (YouTube)
43. [Lecture 43: Orthogonal Basis, Eigen value decomposition Continued](https://invisiblenetwork.ai/learn/nptel/111105489/6e9b4a2ff3e5) (YouTube)
44. [Lecture 44: Principal Component Analysis](https://invisiblenetwork.ai/learn/nptel/111105489/db20acd77de9) (YouTube)
45. [Lecture 45: Principal Component Analysis Continued](https://invisiblenetwork.ai/learn/nptel/111105489/31eba6c15898) (YouTube)
46. [Lecture 46: Introduction to Dynamical System](https://invisiblenetwork.ai/learn/nptel/111105489/d56f13071b6c) (YouTube)
47. [Lecture 47: Dynamical System and Control](https://invisiblenetwork.ai/learn/nptel/111105489/786db1dbc761) (YouTube)
48. [Lecture 48: Discrete Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105489/ebd4a0e96c3d) (YouTube)
49. [Lecture 49: Inverse Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105489/3546762a60bf) (YouTube)
50. [Lecture 50: Applications: Discrete Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105489/9b36b0fe9d64) (YouTube)
51. [Lecture 51: Introduction to Mixture models](https://invisiblenetwork.ai/learn/nptel/111105489/10da605b6bb0) (YouTube)
52. [Lecture 52: Introduction to Gaussian Mixture Models](https://invisiblenetwork.ai/learn/nptel/111105489/8522865b6874) (YouTube)
53. [Lecture 53: EM Algorithm](https://invisiblenetwork.ai/learn/nptel/111105489/c20a964417c9) (YouTube)
54. [Lecture 54: EM Algorithm (cont.)](https://invisiblenetwork.ai/learn/nptel/111105489/acf7bee1754f) (YouTube)
55. [Lecture 55: A brief application to predict HMM parameters](https://invisiblenetwork.ai/learn/nptel/111105489/1233d7380b9f) (YouTube)
56. [Lecture 56 : Conditional probability, Bayes theorem](https://invisiblenetwork.ai/learn/nptel/111105489/15f4b0299ab4) (YouTube)
57. [Lecture 57 : Bayes Decision Rule](https://invisiblenetwork.ai/learn/nptel/111105489/28e18e32c52a) (YouTube)
58. [Lecture 58 : Bayes Decision Rule](https://invisiblenetwork.ai/learn/nptel/111105489/edecaebf5fb6) (YouTube)
59. [Lecture 59 : Bayes Decision Rule (Bayesian minimum risk classifier)](https://invisiblenetwork.ai/learn/nptel/111105489/2abeba936b8c) (YouTube)
60. [Lecture 60: Bayes Decision Rule (Linear Discriminant Analysis)](https://invisiblenetwork.ai/learn/nptel/111105489/76dd735d6519) (YouTube)