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Due to lack of data, overfitting ubiquitously exists in real-world applications of deep neural networks (DNNs). We propose advanced dropout, a model-free methodology, to mitigate overfitting and improve the performance of DNNs. The advanced dropout technique applies a model-free and easily implemented distribution with parametric prior, and adaptively adjusts dropout rate. Specifically, the distribution parameters are optimized by stochastic gradient variational Bayes in order to carry out an end-to-end training. We evaluate the effectiveness of the advanced dropout against nine dropout techniques on seven computer vision datasets (five small-scale datasets and two large-scale datasets) with various base models. The advanced dropout outperforms all the referred techniques on all the datasets. We further compare the effectiveness ratios and find that advanced dropout achieves the highest one on most cases. Next, we conduct a set of analysis of dropout rate characteristics, including convergence of the adaptive dropout rate, the learned distributions of dropout masks, and a comparison with dropout rate generation without an explicit distribution. In addition, the ability of overfitting prevention is evaluated and confirmed. Finally, we extend the application of the advanced dropout to uncertainty inference, network pruning, text classification, and regression. The proposed advanced dropout is also superior to the corresponding referred methods. Codes are available at https://github.com/PRIS-CV/AdvancedDropout.

Many established classifiers fail to identify the minority class when it is much smaller than the majority class. To tackle this problem, researchers often first rebalance the class sizes in the training dataset, through oversampling the minority class or undersampling the majority class, and then use the rebalanced data to train the classifiers. This leads to interesting empirical patterns. In particular, using the rebalanced training data can often improve the area under the receiver operating characteristic curve (AUC) for the original, unbalanced test data. The AUC is a widely-used quantitative measure of classification performance, but the property that it increases with rebalancing has, as yet, no theoretical explanation. In this note, using Gaussian-based linear discriminant analysis (LDA) as the classifier, we demonstrate that, at least for LDA, there is an intrinsic, positive relationship between the rebalancing of class sizes and the improvement of AUC. We show that the largest improvement of AUC is achieved, asymptotically, when the two classes are fully rebalanced to be of equal sizes.