Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks to unseen tasks from the same task distribution, with a limited amount of labeled data. The underlying requirement for effective few-shot generalization is to learn a good representation of the task manifold. This becomes more difficult when only a limited number of tasks are available for training. In such a few-task few-shot setting, it is beneficial to explicitly preserve the local neighborhoods from the task manifold and exploit this to generate artificial tasks for training. To this end, we introduce the notion of interval bounds from the provably robust training literature to few-shot learning. The interval bounds are used to characterize neighborhoods around the training tasks. These neighborhoods can then be preserved by minimizing the distance between a task and its respective bounds. We then use a novel strategy to artificially form new tasks for training by interpolating between the available tasks and their respective interval bounds. We apply our framework to both model-agnostic meta-learning as well as prototype-based metric-learning paradigms. The efficacy of our proposed approach is evident from the improved performance on several datasets from diverse domains in comparison to recent methods.

Class imbalance is a long-standing problem relevant to a number of real-world applications of deep learning. Oversampling techniques, which are effective for handling class imbalance in classical learning systems, can not be directly applied to end-to-end deep learning systems. We propose a three-player adversarial game between a convex generator, a multi-class classifier network, and a real/fake discriminator to perform oversampling in deep learning systems. The convex generator generates new samples from the minority classes as convex combinations of existing instances, aiming to fool both the discriminator as well as the classifier into misclassifying the generated samples. Consequently, the artificial samples are generated at critical locations near the peripheries of the classes. This, in turn, adjusts the classifier induced boundaries in a way which is more likely to reduce misclassification from the minority classes. Extensive experiments on multiple class imbalanced image datasets establish the efficacy of our proposal.

The fuzzy$k$-nearest neighbor classifier (F$k$NN) improves upon the flexibility of the$k$-nearest neighbor classifier by considering each class as a fuzzy set and estimating the membership of an unlabeled data instance for each of the classes. However, the question of validating the quality of the class memberships estimated by F$k$NN for a regular multiclass classification problem still remains mostly unanswered. In this paper, we attempt to address this issue by first proposing a novel direction of evaluating a fuzzy classifier by highlighting the importance of focusing on the class memberships estimated by F$k$NN instead of its misclassification error. This leads us to finding novel theoretical upper bounds, respectively, on the bias and the mean squared error of the class memberships estimated by F$k$NN. Additionally the proposed upper bounds are shown to converge toward zero with increasing availability of the labeled data points, under some elementary assumptions on the class distribution and membership function. The major advantages of this analysis are its simplicity, capability of a direct extension for multiclass problems, parameter independence, and practical implication in explaining the behavior of F$k$NN in diverse situations (such as in presence of class imbalance). Furthermore, we provide a detailed simulation study on artificial and real data sets to empirically support our claims.

The classification accuracy of a -nearest neighbor ( NN) classifier is largely dependent on the choice of the number of nearest neighbors denoted by . However, given a data set, it is a tedious task to optimize the performance of NN by tuning . Moreover, the performance of NN degrades in the presence of class imbalance, a situation characterized by disparate representation from different classes. We aim to address both the issues in this paper and propose a variant of NN called the Adaptive NN (Ada- NN). The Ada- NN classifier uses the density and distribution of the neighborhood of a test point and learns a suitable point-specific for it with the help of artificial neural networks. We further improve our proposal by replacing the neural network with a heuristic learning method guided by an indicator of the local density of a test point and using information about its neighboring training points. The proposed heuristic learning algorithm preserves the simplicity of NN without incurring serious computational burden. We call this method Ada- NN2. Ada- NN and Ada- NN2 perform very competitive when compared with NN, five of NN's state-of-the-art variants, and other popular classifiers. Furthermore, we propose a class-based global weighting scheme (Global Imbalance Handling Scheme or GIHS) to compensate for the effect of class imbalance. We perform extensive experiments on a wide variety of data sets to establish the improvement shown by Ada- NN and Ada- NN2 using the proposed GIHS, when compared with NN, and its 12 variants specifically tailored for imbalanced classification.