Abstract—Typically, a supervised learning model is trained using passive learning by randomly selecting unlabelled instances to annotate. This approach is effective for learning a model, but can be costly in cases where acquiring labelled instances is expensive. For example, it can be time-consuming to manually identify spam mails (labelled instances) from thousands of emails (unlabelled instances) flooding an inbox during initial data collection. Generally, we answer the above scenario with uncertainty sampling, an active learning method that improves the efficiency of supervised learning by using fewer labelled instances than passive learning. Given an unlabelled data pool, uncertainty sampling queries the labels of instances where the predicted probabilities, p, fall into the uncertainty region, i.e., p≈0.5. The newly acquired labels are then added to the existing labelled data pool to learn a new model. Nonetheless, the performance of uncertainty sampling is susceptible to the Area of Unpredictable Responses (AUR) and the nature of the dataset. It is difficult to determine whether to use passive learning or uncertainty sampling without prior knowledge of a new dataset. To address this issue, we propose bell curve sampling, which employs a bell curve weight function to acquire new labels. With the bell curve centred at p=0.5, bell curve sampling selects instances whose predicted values are in the uncertainty area most of the time without neglecting the rest. Simulation results show that, most of the time bell curve sampling outperforms uncertainty sampling and passive learning in datasets of different natures and with AUR.

Key words—Active learning, uncertainty sampling, random sampling

Zan-Kai Chong is an Independent Researcher in Malaysia. Hiroyuki Ohsaki is with School of Science and Technology, Kwansei Gakuin University, Japan. Bok-Min Goi is with Lee Kong Chian Faculty of Engineering Science, Universiti Tunku Abdul Rahman, Malaysia.

Cite:Zan-Kai Chong, Hiroyuki Ohsaki, Bok-Min Goi, "Improving Uncertainty Sampling with Bell Curve Weight Function," International Journal of Applied Physics and Mathematics vol. 13, no. 4, pp. 44-52, 2023.

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