# A Quantum-inspired Algorithm for General Minimum Conical Hull Problems

arXiv: https://arxiv.org/abs/1907.06814 · HTML: https://mlsanity.com/paper/1907.06814/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms](https://mlsanity.com/paper/2304.04932/) (2023)

## Abstract (arXiv)

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexity is polynomial in size. However, big data is pushing these polynomial algorithms to their performance limits. In this paper, we propose a sublinear classical algorithm to tackle general minimum conical hull problems when the input has stored in a sample-based low-overhead data structure. The algorithm's runtime complexity is polynomial in the rank and polylogarithmic in size. The proposed algorithm achieves the exponential speedup over DCA and, therefore, provides advantages for high dimensional problems.