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Learning with Optimized Random Features: Exponential Speedup by Quantum Machine Learning without Sparsity and Low-Rank Assumptions
Hayata Yamasaki · Sathyawageeswar Subramanian · Sho Sonoda · Masato Koashi

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1490

Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as to minimize the required number of features for achieving the learning to a desired accuracy. Here, we develop a quantum algorithm for sampling from this optimized distribution over features, in runtime O(D) that is linear in the dimension D of the input data. Our algorithm achieves an exponential speedup in D compared to any known classical algorithm for this sampling task. In contrast to existing quantum machine learning algorithms, our algorithm circumvents sparsity and low-rank assumptions and thus has wide applicability. We also show that the sampled features can be combined with regression by stochastic gradient descent to achieve the learning without canceling out our exponential speedup. Our algorithm based on sampling optimized random features leads to an accelerated framework for machine learning that takes advantage of quantum computers.

Author Information

Hayata Yamasaki (IQOQI Vienna, Austrian Academy of Sciences)
Sathyawageeswar Subramanian (University of Cambridge)
Sho Sonoda (RIKEN AIP)
Masato Koashi (The University of Tokyo)

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