Research & Projects

• This project investigates the mathematical foundations of neural network optimization, focusing on gradient descent convergence, Bayesian neural networks, and stochastic gradient methods.

• It bridges theoretical optimization principles with practical training strategies for deep learning models. 

• Applications include uncertainty-aware learning and efficient model training for real-world tasks such as fraud detection. 

Project Supervisor: Dr. Indrajit Jana

Link: M.Sc. Project 

• This project explores the Erdős–Kac Theorem, a landmark result in probabilistic number theory, which states that the number of distinct prime factors of a natural number follows a normal distribution.

•  It presents an accessible proof based on the work of Granville and Soundararajan, supported by essential theorems and background concepts. 

• The study highlights both the theoretical elegance of the result and its practical significance in areas like cryptography.

 Project Supervisor: Dr. Kartick Adhikari

 Link: Summer Internship Project 

• This project on Linear Regression builds a rigorous base in the simple linear model, least-squares estimation, and core properties.

• It then develops inference and diagnostics—confidence/prediction intervals, residual analysis, tests for normality and constant variance, and lack-of-fit F-tests—plus remedies like Box-Cox transformations and LOWESS smoothing.

• Hands-on sections use real datasets (height–weight, Toluca production, PCA-based credit-card features) to compute estimates, intervals, predictions, and visualize fits—linking theory to practice. 

Project Supervisor: Dr. Indrajit Jana

Link: Winter Internship Project