# Lecture notes on high-dimensional data

arXiv: https://arxiv.org/abs/2101.05841 · HTML: https://mlsanity.com/paper/2101.05841/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2021.

## Built on by (most cited first, 5 of 5)

- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [InfoNCE Induces Gaussian Distribution](https://mlsanity.com/paper/2602.24012/) (2026)
- [TetraDiffusion: Tetrahedral Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2211.13220/) (2022)
- [Towards Compositionality in Concept Learning](https://mlsanity.com/paper/2406.18534/) (2024)
- [SQ Lower Bounds for Learning Bounded Covariance GMMs](https://mlsanity.com/paper/2306.13057/) (2023)

## Abstract (arXiv)

These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random vectors in high dimensions; random projections; separation/disentangling of Gaussian data. A revised version has been published as part of the textbook [Mathematical Introduction to Data Science, Springer, Berlin, Heidelberg, 2024, https://link.springer.com/book/10.1007/978-3-662-69426-8].