AKTU Artificial Intelligence (KDS071) Question Paper 2024-25

Note: Attempt all Sections. In case of any missing data; choose suitably.

Section A

Q1. Attempt all questions in brief · 2 × 10 = 20 marks

1. List examples of convex optimization problems.
2. State the Karush-Kuhn-Tucker (KKT) conditions.
3. State the basic steps of the mirror descent algorithm.
4. Define proximal gradient methods.
5. What are monotone operators?
6. Illustrate the intuition behind Douglas–Rachford splitting.
7. What is Langevin dynamics?
8. State the purpose of averaging methods in stochastic optimization.
9. Differentiate supervised and unsupervised learning.
10. What do you mean by feature extraction in machine learning.

Section B

Q2. Attempt any three of the following · 10 × 3 = 20 marks

1. Illustrate how duality is applied in optimization problems with a simple example.
2. Explain the connection between ODE interpretations and optimization algorithms.
3. Use the Augmented Lagrangian method to solve a constrained optimization problem with quadratic constraints.
4. How does Polyak–Juditsky averaging smooth the optimization trajectory?
5. Discuss various application domains of machine learning.

Section C

Q3

Attempt any one part of the following · 10 × 1 = 10 marks

1. Apply the KKT conditions to solve a simple quadratic programming problem.
2. Derive the dual problem for a given primal linear programming problem.

Q4

Attempt any one part of the following · 10 × 1 = 10 marks

1. Apply the Frank–Wolfe method to solve a simple linear programming problem.
2. Use gradient descent to minimize the quadratic function f(x)=x +4x+4

Q5

Attempt any one part of the following · 10 × 1 = 10 marks

1. Compare and contrast the Augmented Lagrangian method with the standard Lagrangian approach.
2. Analyze the convergence properties of ADMM for non-smooth problems.

Q6

Attempt any one part of the following · 10 × 1 = 10 marks

1. Apply Polyak–Juditsky averaging to improve the convergence of an iterative algorithm.
2. Implement SVRG to optimize a logistic regression problem.

Q7

Attempt any one part of the following · 10 × 1 = 10 marks

1. Explain use case on Bayesian classifier.
2. Create a real-world optimization scenario to demonstrate the use of PCA.

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