Projects - search

Data lakes contain massive amounts of structured tables and unstructured images. Currently, database systems cannot connect them automatically; a table of store products and a folder of product images remain completely isolated. This research bridges that gap using vision-language AI models to map text, data columns, and images into a shared space. Solving this unlocks "dark data," allowing organizations to fully search, analyze, and use all their visual and text data together for the first time.

Tags: 2nd year +, 3rd year +, Linear Algebra, Data Structures, Basic Programming

Understanding this hidden structure could help us visualize data, remove noise, compare examples, and build machine-learning systems that are faster, more reliable, and easier to understand.

In this project, we will try to answer: When can we discover the hidden shape of data accurately and efficiently?

This is a difficult problem. In the most general setting, learning the full shape may require a very large amount of data and computation. Real data are also noisy, so observations may not lie exactly on a clean surface. Even deciding how many underlying dimensions the data have can be challenging.

Tags: Python, Basic Programming, Linear Algebra, Calculus, Statistics, Machine Learning, Optimization, All Years

This project wants to answer: Why does sparse regression often work well in practice, even when the usual theoretical assumptions do not clearly apply?

We will study this question using ideas from geometry, statistics, and optimization. Here, geometry means thinking about variables as directions or points in space. For example, two variables that contain almost the same information can be viewed as pointing in nearly the same direction. This viewpoint may help us understand when sparse regression makes reliable predictions, when it selects meaningful variables, and when its answer is unstable.

Tags: Python, Basic Programming, Linear Algebra, Statistics, Calculus, Optimization, Machine Learning, All Years