Mathematical Foundations of Statistical Learning

Jakhmola, Yash (2025) Mathematical Foundations of Statistical Learning. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Yash Jakhmola (20MS028)) 20MS028_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Statistical learning is the process of finding patterns in datasets to make predictions without being explicitly programmed. This is done by using the given data to find a function that generalizes well to unseen data. Techniques range from simple linear regression to complex neural networks, all aiming to extract meaningful information from data. This thesis studies the mathematical background required to understand the algo- rithms and techniques used in practice, as well as the attempts made to understand why certain methods work so well in practice. We start by desining the problem setup and then move onto the major issue of the field - minimizing the error over unseen datasets. We then explore SVMs and their extensions using kernels. Then, we dive into neural networks - one of the best performing algorithms, study their architecture, practical implementation and variants. We also state and prove their approximation capabilities.

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