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We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non- independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the pivotal sampling algorithm, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50%. We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak one-sided l∞ independence condition (which includes pivotal sampling) can actively learn d dimensional linear functions with O(d log d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under l∞ independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound on O(d) samples.
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On The Effectiveness of Active Learning by Uncertainty Sampling in Classification of High-Dimensional Gaussian Mixture Data
Active learning aims to reduce the cost of labeling through selective sampling. Despite reported empirical success over passive learning, many popular active learning heuristics such as uncertainty sampling still lack satisfying theoretical guarantees. Towards closing the gap between practical use and theoretical understanding in active learning, we propose to characterize the exact behavior of uncertainty sampling for high-dimensional Gaussian mixture data, in a modern regime of big data where the numbers of samples and features are commensurately large. Through a sharp characterization of the learning results, our analysis sheds light on the important question of when uncertainty sampling works better than passive learning. Our results show that the effectiveness of uncertainty sampling is not always ensured. In fact it depends crucially on the choice of i) an adequate initial classifier used to start the active sampling process and ii) a proper loss function that allows an adaptive treatment of samples queried at various steps.
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- PAR ID:
- 10483554
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-6654-0540-9
- Page Range / eLocation ID:
- 4238 to 4242
- Format(s):
- Medium: X
- Location:
- Singapore, Singapore
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICASSP43922.2022.9747685
