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

A Quantum-inspired Algorithm for General Minimum Conical Hull Problems