# Topics in Random Matrices and Statistical Machine Learning

arXiv: https://arxiv.org/abs/1807.09419 · HTML: https://mlsanity.com/paper/1807.09419/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [Universal consistency of the k-NN rule in metric spaces and Nagata dimension. II](https://mlsanity.com/paper/2305.17282/) (2023)
- [Universal consistency of the k-NN rule in metric spaces and Nagata dimension. III](https://mlsanity.com/paper/2512.17058/) (2025)
- [k-Nearest Neighbors in Gromov--Wasserstein Space](https://mlsanity.com/paper/2606.10295/) (2026)

## Abstract (arXiv)

This thesis consists of two independent parts: random matrices, which form the first one-third of this thesis, and machine learning, which constitutes the remaining part. The main results of this thesis are as follows: a necessary and sufficient condition for the inverse moments of (m,n,β)-Laguerre matrices and compound Wishart matrices to be finite; the universal weak consistency and the strong consistency of the k-nearest neighbor rule in metrically sigma-finite dimensional spaces and metrically finite dimensional spaces respectively. In Part I, the Chapter 1 introduces the (m,n,β)-Laguerre matrix, Wishart and compound Wishart matrix and their joint eigenvalue distribution. While in Chapter 2, a necessary and sufficient condition to have finite inverse moments has been derived. In Part II, the Chapter 1 introduces the various notions of metric dimension and differentiation property followed by our proof for the necessary part of Preiss' result. Further, Chapter 2 gives an introduction to the mathematical concepts in statistical machine learning and then the k-nearest neighbor rule is presented in Chapter 3 with a proof of Stone's theorem. In chapters 4 and 5, we present our main results and some possible future directions based on it.