We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number of steps sublinear in the number of data points N, namely O( N). The second algorithm illustrates how the classical mistake bound of O( 1γ2) can be further improved to O( 1 γ) through quantum means, where γ denotes the margin. Such improvements are achieved through the application of quantum amplitude amplification to the version space interpretation of the perceptron model.

Neural Information Processing Systems http://nips.cc/

We present a theoretical analysis of active learning with more realistic interactions with human oracles. Previous empirical studies have shown oracles abstaining on difficult queries until accumulating enough information to make label decisions. We formalize this phenomenon with an "oracle epiphany model" and analyze active learning query complexity under such oracles for both the realizable and the agnostic cases. Our analysis shows that active learning is possible with oracle epiphany, but incurs an additional cost depending on when the epiphany happens. Our results suggest new, principled active learning approaches with realistic oracles.

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Let D be an unknown distribution on a spaceZ, and let H be a set of classifiers. Consider a (randomized) learning algorithmA = (An)n 1 that selects an elementˆh in H, based onn i.i.d.