  To reduce the label complexity in Agnostic Active Learning (A^2 algorithm),
volume-splitting splits the hypothesis edges to reduce the Vapnik-Chervonenkis
(VC) dimension in version space. However, the effectiveness of volume-splitting
critically depends on the initial hypothesis and this problem is also known as
target-dependent label complexity gap. This paper attempts to minimize this gap
by introducing a novel notion of number density which provides a more natural
and direct way to describe the hypothesis distribution than volume. By
discovering the connections between hypothesis and input distribution, we map
the volume of version space into the number density and propose a
target-independent distribution-splitting strategy with the following
advantages: 1) provide theoretical guarantees on reducing label complexity and
error rate as volume-splitting; 2) break the curse of initial hypothesis; 3)
provide model guidance for a target-independent AL algorithm in real AL tasks.
With these guarantees, for AL application, we then split the input distribution
into more near-optimal spheres and develop an application algorithm called
Distribution-based A^2 (DA^2). Experiments further verify the effectiveness of
the halving and querying abilities of DA^2. Contributions of this paper are as
follows.
