Course11110713760 lectures
Essential Mathematics for Machine Learning
Prof. S. K. Gupta and Prof. Sanjeev Kumar · IIT Roorkee
About
Machine learning (ML) is one of the most popular topics of nowadays research. This particular topic is having applications in all the areas of engineering and sciences. Various tools of machine learning are having a rich mathematical theory. Therefore, in order to develop new algorithms of machine/deep learning, it is necessary to have knowledge of all such mathematical concepts. In this course, we will introduce these basic mathematical concepts related to the machine/deep learning. In particular, we will focus on topics from matrix algebra, calculus, optimization, and probability theory those are having strong linkage with machine learning. Applications of these topics will be introduced in ML with help of some real-life examples.
INTENDED AUDIENCE : UNDERGRADUATE AND POSTGRAUATE STUDENTS OF COMPUTER SCIENCE/MATHEMATICS/DATA SCIENCE…
Lectures
Week 1
- Vectors in Machine Learning
- Basics of Matrix Algebra
- Vector Space: Definition and Examples
- Vector Subspace: Examples and Properties
- Basis and Dimension
Week 2
- Linear Transformation
- Norms and Spaces
- Orthogonal Complement and Projection Mapping
- Eigenvalues and Eigenvectors
- Special matrices and Properties
Week 3
- Spectral Decomposition
- Singular Value Decomposition
- SVD: Properties and Applications
- Low Rank Approximations
- Python Implementation of SVD and Low-rank Approximation
Week 4
- Principal Component Analysis-I
- PCA : Derivation and Examples
- Python Implementation of PCA
- Linear Discriminant Analysis
- Python Implementation of LDA
Week 5
- Least Square Approximation and Minimum Normed Solution
- Linear and Multiple Regression-I
- Linear and Multiple Regression-II
- Logistic Regression-I
- Logistic Regression-II
Week 6
- Classification Metrics
- Gram Schmidt process
- Polar Decomposition
- Minimal Polynomial and Jordan Canonical Form-I
- Minimal Polynomial and Jordan Canonical Form-II
Week 7
- Basic Concepts of Calculus-I
- Basic Concepts of Calculus-II
- Basic Concepts of Calculus-III
- Basic Concepts of Calculus-IV
- Basic Concepts of Calculus-V
Week 8
- Calculus in Python
- Convex Sets and Functions
- Properties of Convex functions-I
- Properties of convex functions-II
- Introduction to Optimization
Week 9
- Unconstrained Optimization
- Constrained optimization-I
- Constrained optimization-II
- Steepest Descent Method
- Newton’s and Penalty function method
Week 10
- Optimization using Python
- Operations on Sets
- Review of Probability
- Bayes theorem and random variable
- Expectation and variance
Week 11
- Discrete probability distributions
- Continuous Probability distributions
- Joint probability and covariance
- Introduction to SVM
- Error minimizing LPP
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Roorkee
- Department
- Mathematics
- Taught by
- Prof. S. K. Gupta, Prof. Sanjeev Kumar
- 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.
- Who can watch
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