Randomized Sketching Algorithms for Large-Scale Linear Algebra

This independent study investigates randomized sketching and sampling techniques for efficient computation in large-scale linear algebra and machine learning problems.

The project focuses on algorithms that reduce computational complexity while preserving key matrix properties, enabling scalable solutions for high-dimensional datasets.

Key topics explored include:

• Leverage score sampling for efficient regression and matrix approximation
• CountSketch and subspace embeddings for dimensionality reduction
• Hutch++ and randomized trace estimation methods for fast matrix statistics
• Applications of randomized numerical linear algebra in machine learning and data analysis

The study combines theoretical analysis of probabilistic guarantees with practical implementation and experimentation in Python to evaluate the accuracy–efficiency trade-offs of sketch-based algorithms on large datasets.