Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding the Homology of Decision Boundaries with Active Learning   Accurately and efficiently characterizing the decision boundary of
classifiers is important for problems related to model selection and
meta-learning. Inspired by topological data analysis, the characterization of
decision boundaries using their homology has recently emerged as a general and
powerful tool. In this paper, we propose an active learning algorithm to
recover the homology of decision boundaries. Our algorithm sequentially and
adaptively selects which samples it requires the labels of. We theoretically
analyze the proposed framework and show that the query complexity of our active
learning algorithm depends naturally on the intrinsic complexity of the
underlying manifold. We demonstrate the effectiveness of our framework in
selecting best-performing machine learning models for datasets just using their
respective homological summaries. Experiments on several standard datasets show
the sample complexity improvement in recovering the homology and demonstrate
the practical utility of the framework for model selection. Source code for our
algorithms and experimental results is available at
https://github.com/wayne0908/Active-Learning-Homology.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc