Numerical methods for NLP

Basic information

• Credits: 3
• Format: 2 hours weekly
• 2026-2027 instructors: Benoît Crabbé
• 2026-2027 schedule: Fridays 14:00-16:00, room 153
• Moodle page

Description

This course targets students who need an introduction or a refresher in computational linear algebra and numerical optimization. It starts from basic notions of linear algebra, vector space, euclidean space and illustrates how to program them with numerical libraries on examples taken from information retrieval. We then introduce methods involving eigenvectors and eigenvalues and illustrate how to program them: we focus on PageRank and on dimensionality reduction with Latent Semantic Analysis. Finally we introduce to multivariate optimization methods commonly used in Machine Learning such as gradient descent and newton method and to their implementation.

Prerequisites

Students are assumed to be fluent in Python. This supposes to have succeeded in an introductory class to Python.

Learning outcomes

On successful completion of this course, students should be able to:

• Understand main notions of linear algebra and know how to program them
• Understand key applications of eigenvectors and eigenvalues in computational linguistics
• Be able to implement a simple search engine and be aware of the algorithmic issues involved for scaling it up
• Be able to optimize a multivariate function in the convex case and nonconvex case.