MS/PhD
The School of Data Science and AI at IIT Madras offers MS/PhD programmes in a variety of areas. We welcome applicants from diverse departments with an applied interest in AI/ML, as well as students from EE/CS/AI departments who are interested in fundamental research areas in AI/ML.
Written Test Syllabus
The written test will have two parts: Theory (objective questions: MCQ, Fill in the blanks, True/False) and Python Coding (problems requiring you to write code in Basic Python).
Probability and Statistics
- Counting (permutation and combinations)
- Independent events, mutually exclusive events
- Marginal, conditional and joint probability
- Bayes Theorem
- Conditional expectation and variance
- Mean, median, mode and standard deviation
- Correlation, and covariance
- Random variables, discrete random variables and probability mass functions
- Uniform, Bernoulli, binomial distribution
- Continuous random variables and probability
- Distribution function, cumulative distribution function, Conditional PDF
- Uniform, exponential, Poisson, normal, standard normal, t-distribution
- Chi-squared distributions
- Central limit theorem
- Confidence interval
- Z-test, t-test, chi-squared test
Linear Algebra
- Vector space, subspaces
- Linear dependence and independence of vectors
- Matrices, projection matrix, orthogonal matrix, idempotent matrix, partition matrix
- Quadratic forms
- Systems of linear equations and solutions
- Gaussian elimination
- Eigenvalues and eigenvectors
- Determinant, rank, nullity
- Projections
- LU decomposition, singular value decomposition
Calculus and Optimization
- Functions of a single variable
- Limit, continuity and differentiability
- Taylor series
- Maxima and minima
- Optimization involving a single variable
Python Coding
You will be given coding tasks that you need to complete and execute by writing Python scripts. You will need to know the following:
- Basic Python syntax – comments, variables, basic data types
- Operators and Control Flow – If/else, for, while, range, break, continue, pass
- Functions – How to define and use them
- Lists/Arrays, Tuples, and associated methods
Interview Topics
For those who qualify after the written test for the online interview, questions from the following additional topics may be asked:
Machine Learning
- Supervised Learning regression and classification problems
- Simple linear regression
- Multiple linear regression
- Ridge regression
- Logistic regression
- K-nearest neighbour
- Naive Bayes classifier
- Linear discriminant analysis
- Support vector machine
- Decision trees
- Bias-variance trade-off
- Cross-validation methods such as leave-one-out (LOO) cross-validation, k-folds cross-validation, multi-layer perceptron, feed-forward neural network
- Unsupervised Learning: clustering algorithms
Artificial Intelligence
- Search: informed, uninformed, adversarial
- Logic: Propositional Logic, Predicate Logic
- Reasoning under Uncertainty Topics
- Conditional Independence Representation
- Exact Inference through Variable Elimination
- Approximate Inference through Sampling
Sample Question Papers
Download sample question papers to prepare for the written test. The GATE DA (Data Science and AI) model question paper is also a good reference, as our test is structured in a similar fashion.