Active learning (AL) aims to minimize the annotation cost by only querying a few informative examples for each model training stage. However, training a model on a few queried examples suffers from the small-sample bias. In this paper, we address this small-sample bias issue in low-budget AL by exploring a regularizer called Firth bias reduction, which can provably reduce the bias during the model training process but might hinder learning if its coefficient is not adaptive to the learning progress. Instead of tuning the coefficient for each query round, which is sensitive and time-consuming, we propose the curriculum Firth bias reduction (CHAIN) that can automatically adjust the coefficient to be adaptive to the training process. Under both deep learning and linear model settings, experiments on three benchmark datasets with several widely used query strategies and hyperparameter searching methods show that CHAIN can be used to build more efficient AL and can substantially improve the progress made by each active learning query.

Learning accurate classifiers for novel categories from very few examples, known as few-shot image classification, is a challenging task in statistical machine learning and computer vision. The performance in few-shot classification suffers from the bias in the estimation of classifier parameters; however, an effective underlying bias reduction technique that could alleviate this issue in training few-shot classifiers has been overlooked. In this work, we demonstrate the effectiveness of Firth bias reduction in few-shot classification. Theoretically, Firth bias reduction removes the first order term $O(N^{-1})$ from the small-sample bias of the Maximum Likelihood Estimator. Here we show that the general Firth bias reduction technique simplifies to encouraging uniform class assignment probabilities for multinomial logistic classification, and almost has the same effect in cosine classifiers. We derive the optimization objective for Firth penalized multinomial logistic and cosine classifiers, and empirically evaluate that it is consistently effective across the board for few-shot image classification, regardless of (1) the feature representations from different backbones, (2) the number of samples per class, and (3) the number of classes. Finally, we show the robustness of Firth bias reduction, in the case of imbalanced data distribution. Our implementation is available at https://github.com/ehsansaleh/firth_bias_reduction