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

## TL;DR

This paper introduces a quantum-inspired classical algorithm that significantly speeds up solving general minimum conical hull problems, especially in high-dimensional data scenarios, by achieving exponential speedup over existing methods.

## Contribution

The paper presents a novel sublinear classical algorithm for minimum conical hull problems with exponential speedup over traditional polynomial-time algorithms.

## Key findings

- Achieves exponential speedup over DCA
- Runtime is polynomial in rank and polylogarithmic in size
- Effective for high-dimensional machine learning tasks

## Abstract

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.