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Mathematical Foundations of Machine Learning

By Prof. Prathosh A P   |   IISc Bangalore
Learners enrolled: 4993   |  Exam registration: 109
ABOUT THE COURSE:

This course introduces the mathematical foundations of machine learning, covering risk minimization, density estimation, regularization, and generalization. Students learn classical methods such as linear models, kernel machines, SVMs, decision trees, and ensemble techniques, as well as modern deep learning approaches including MLPs, CNNs, RNNs, and Transformers. Probabilistic models, clustering, PCA, and the EM algorithm are presented to build a solid grounding in unsupervised learning. The course concludes with an introduction to generative models (GANs, VAEs) as a bridge to advanced topics. Emphasis is placed on both theory and practice, with coding assignments connecting math to real-world ML applications.

INTENDED AUDIENCE: Senior Undergraduates and Graduate Students from EECS disciplines

PREREQUISITES: BE/BTech. ME/MTech
Basic course on Probability theory, Linear Algebra.
Should have some background in Python Programming

INDUSTRY SUPPORT: Most IT companies including Google, Microsoft, Amazon, IBM, Flipkart, Oracle, Infosys, Accenture, GE etc.
Summary
Course Status : Upcoming
Course Type : Elective
Language for course content : English
Duration : 12 weeks
Category :
  • Computer Science and Engineering
  • Artificial Intelligence
  • Data Science
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 19 Jan 2026
End Date : 10 Apr 2026
Enrollment Ends : 26 Jan 2026
Exam Registration Ends : 13 Feb 2026
Exam Date : 25 Apr 2026 IST
NCrF Level   : 4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.


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Course layout

Week 1: Introduction to Supervised/Unsupervised/Generative, Learning via Empirical Risk Minimization

Week 2: Bayes Optimality and Density Estimation via Divergence Minimization

Week 3: Maximum Likelihood and MAP Estimates, Non-Parametric Estimates (Nearest Neighbours and Parzen Window)

Week 4: Linear Models: Linear regression, least squares, Fisher discriminant, Logistic regressions

Week 5: Regularization & Generalization: Bias–variance Decomposition, Ridge regression, Lasso, Probabilistic interpretation of regularization

Week 6: Kernel Machines & SVMs: Maximum margin classifiers, Dual form, KKT conditions, Kernel trick & RKHS intuition.

Week 7: Perceptron, Neural Networks, Gradient-based Optimization, Error Back Propagation

Week 8: Convolutional Neural Networks: Convolution, pooling, receptive fields, CNN architectures,Transfer learning.

Week 9: Sequence Models: RNNs, backpropagation through time, Vanishing/exploding gradients, GRU, LSTMs

Week 10: Attention & Transformers: Attention mechanism, Self-attention vs recurrence, Encoder–decoder Transformers.

Week 11: Ensembles and Decision trees: Bagging & Random Forests, Boosting (AdaBoost, XGBoost).

Week 12: 
  • Unsupervised Learning & EM: Clustering: k-Means, Gaussian mixtures, EM algorithm, dimensionality reduction and PCA.
  • A preview of Generative Models: GANs and VAEs, Diffusion models (high-level only).

Books and references

1.Bishop, Christopher M., and Nasser M. Nasrabadi. Pattern recognition and machine learning. Vol. 4. No. 4. New York: springer, 2006.
2.Murphy, Kevin P. Probabilistic machine learning: an introduction. MIT press, 2022.
3.Murphy, Kevin P. Probabilistic machine learning: Advanced topics. MIT press, 2023.
4.Duda, Richard O., and Peter E. Hart. Pattern classification. John Wiley & Sons, 2006.
5.Goodfellow I, Bengio Y, Courville A, Bengio Y. Deep learning. Cambridge: MIT press; 2016 Nov 18.
6.Shalev-Shwartz, Shai, and Shai Ben-David. Understanding machine learning: From theory to algorithms. Cambridge university press, 2014.

Instructor bio

Prof. Prathosh A P

IISc Bangalore
Prathosh A.P. received his Ph.D. from the Indian Institute of Science (IISc), Bangalore in 2015 in the area of temporal data analysis, completing his dissertation just three years after his B.Tech in 2011, with several top-tier publications. He subsequently worked in corporate research labs such as Xerox Research India, Philips Research, and a California-based start-up, focusing on healthcare analytics, where he generated 15 U.S. patents, many of which are commercialized. In 2017, he joined IIT Delhi as an Assistant Professor in Electrical Engineering, teaching and researching machine learning and deep learning. He is currently a faculty member in the Department of Electrical Communication Engineering at IISc Bangalore. His research interests include deep representational learning, cross-domain generalization, and signal processing with applications in vision and speech. He is also co-founder of Cogniable.Tech, a healthcare AI start-up (winner of the Government of India AI Start-up Challenge), and actively collaborates with industry and medical institutions such as AIIMS. Beyond his technical work, he is deeply engaged with Sanskrit and Indian philosophical sciences, and often explores the intersections between AI and philosophy

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: April 25, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc Bangalore .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team
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