A Quantum-inspired Algorithm for General Minimum Conical Hull Problems
This addresses scalability issues for high-dimensional data in ML tasks like maximum a posteriori estimation, offering a significant performance improvement.
The paper tackles the computational bottleneck of solving general minimum conical hull problems in machine learning by proposing a sublinear classical algorithm that achieves polynomial runtime in rank and polylogarithmic in size, providing exponential speedup over the previous best method.
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.