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This paper addresses theory and applications of $\ell_p$-based Laplacian regularization in semi-supervised learning. The graph $p$-Laplacian for $p>2$ has been proposed recently as a replacement for the standard ($p=2$) graph Laplacian in semi-supervised learning problems with very few labels, where Laplacian learning is degenerate. In the first part of the paper we prove new discrete to continuum convergence results for $p$-Laplace problems on $k$-nearest neighbor ($k$-NN) graphs, which are more commonly used in practice than random geometric graphs. Our analysis shows that, on $k$-NN graphs, the $p$-Laplacian retains information about the data distribution as $p\to \infty$ and Lipschitz learning ($p=\infty$) is sensitive to the data distribution. This situation can be contrasted with random geometric graphs, where the $p$-Laplacian forgets the data distribution as $p\to \infty$. We also present a general framework for proving discrete to continuum convergence results in graph-based learning that only requires pointwise consistency and monotonicity. In the second part of the paper, we develop fast algorithms for solving the variational and game-theoretic $p$-Laplace equations on weighted graphs for $p>2$. We present several efficient and scalable algorithms for both formulations, and present numerical results on synthetic data indicating their convergence properties. Finally, we conduct extensive numerical experiments on the MNIST, FashionMNIST and EMNIST datasets that illustrate the effectiveness of the $p$-Laplacian formulation for semi-supervised learning with few labels. In particular, we find that Lipschitz learning ($p=\infty$) performs well with very few labels on $k$-NN graphs, which experimentally validates our theoretical findings that Lipschitz learning retains information about the data distribution (the unlabeled data) on $k$-NN graphs.

Learning from imprecise labels such as "animal" or "bird", but making precise predictions like "snow bunting" at inference time is an important capability for any classifier when expertly labeled training data is scarce. Contributions by volunteers or results of web crawling lack precision in this manner, but are still valuable. And crucially, these weakly labeled examples are available in larger quantities for lower cost than high-quality bespoke training data. CHILLAX, a recently proposed method to tackle this task, leverages a hierarchical classifier to learn from imprecise labels. However, it has two major limitations. First, it does not learn from examples labeled as the root of the hierarchy, e.g., "object". Second, an extrapolation of annotations to precise labels is only performed at test time, where confident extrapolations could be already used as training data. In this work, we extend CHILLAX with a self-supervised scheme using constrained semantic extrapolation to generate pseudo-labels. This addresses the second concern, which in turn solves the first problem, enabling an even weaker supervision requirement than CHILLAX. We evaluate our approach empirically, showing that our method allows for a consistent accuracy improvement of 0.84 to 1.19 percent points over CHILLAX and is suitable as a drop-in replacement without any negative consequences such as longer training times.

Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that {\em bound} the gen-error, we provide an {\em exact} expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen-error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy-to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.

A fundamental limitation of applying semi-supervised learning in real-world settings is the assumption that unlabeled test data contains only classes previously encountered in the labeled training data. However, this assumption rarely holds for data in-the-wild, where instances belonging to novel classes may appear at testing time. Here, we introduce a novel open-world semi-supervised learning setting that formalizes the notion that novel classes may appear in the unlabeled test data. In this novel setting, the goal is to solve the class distribution mismatch between labeled and unlabeled data, where at the test time every input instance either needs to be classified into one of the existing classes or a new unseen class needs to be initialized. To tackle this challenging problem, we propose ORCA, an end-to-end deep learning approach that introduces uncertainty adaptive margin mechanism to circumvent the bias towards seen classes caused by learning discriminative features for seen classes faster than for the novel classes. In this way, ORCA reduces the gap between intra-class variance of seen with respect to novel classes. Experiments on image classification datasets and a single-cell annotation dataset demonstrate that ORCA consistently outperforms alternative baselines, achieving 25% improvement on seen and 96% improvement on novel classes of the ImageNet dataset.

The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance). In this work, we first probe the previously unknown topology-imbalance issue, including its characteristics, causes, and threats to semi-supervised node classification learning. We then provide a unified view to jointly analyzing the quantity- and topology- imbalance issues by considering the node influence shift phenomenon with the Label Propagation algorithm. In light of our analysis, we devise an influence conflict detection -- based metric Totoro to measure the degree of graph topology imbalance and propose a model-agnostic method ReNode to address the topology-imbalance issue by re-weighting the influence of labeled nodes adaptively based on their relative positions to class boundaries. Systematic experiments demonstrate the effectiveness and generalizability of our method in relieving topology-imbalance issue and promoting semi-supervised node classification. The further analysis unveils varied sensitivity of different graph neural networks (GNNs) to topology imbalance, which may serve as a new perspective in evaluating GNN architectures.

We evaluate the effectiveness of semi-supervised learning (SSL) on a realistic benchmark where data exhibits considerable class imbalance and contains images from novel classes. Our benchmark consists of two fine-grained classification datasets obtained by sampling classes from the Aves and Fungi taxonomy. We find that recently proposed SSL methods provide significant benefits, and can effectively use out-of-class data to improve performance when deep networks are trained from scratch. Yet their performance pales in comparison to a transfer learning baseline, an alternative approach for learning from a few examples. Furthermore, in the transfer setting, while existing SSL methods provide improvements, the presence of out-of-class is often detrimental. In this setting, standard fine-tuning followed by distillation-based self-training is the most robust. Our work suggests that semi-supervised learning with experts on realistic datasets may require different strategies than those currently prevalent in the literature.

One paradigm for learning from few labeled examples while making best use of a large amount of unlabeled data is unsupervised pretraining followed by supervised fine-tuning. Although this paradigm uses unlabeled data in a task-agnostic way, in contrast to common approaches to semi-supervised learning for computer vision, we show that it is surprisingly effective for semi-supervised learning on ImageNet. A key ingredient of our approach is the use of big (deep and wide) networks during pretraining and fine-tuning. We find that, the fewer the labels, the more this approach (task-agnostic use of unlabeled data) benefits from a bigger network. After fine-tuning, the big network can be further improved and distilled into a much smaller one with little loss in classification accuracy by using the unlabeled examples for a second time, but in a task-specific way. The proposed semi-supervised learning algorithm can be summarized in three steps: unsupervised pretraining of a big ResNet model using SimCLRv2, supervised fine-tuning on a few labeled examples, and distillation with unlabeled examples for refining and transferring the task-specific knowledge. This procedure achieves 73.9% ImageNet top-1 accuracy with just 1% of the labels ($\le$13 labeled images per class) using ResNet-50, a $10\times$ improvement in label efficiency over the previous state-of-the-art. With 10% of labels, ResNet-50 trained with our method achieves 77.5% top-1 accuracy, outperforming standard supervised training with all of the labels.

In this paper, we aim to improve the performance of semantic image segmentation in a semi-supervised setting in which training is effectuated with a reduced set of annotated images and additional non-annotated images. We present a method based on an ensemble of deep segmentation models. Each model is trained on a subset of the annotated data, and uses the non-annotated images to exchange information with the other models, similar to co-training. Even if each model learns on the same non-annotated images, diversity is preserved with the use of adversarial samples. Our results show that this ability to simultaneously train models, which exchange knowledge while preserving diversity, leads to state-of-the-art results on two challenging medical image datasets.

Predicting properties of nodes in a graph is an important problem with applications in a variety of domains. Graph-based Semi-Supervised Learning (SSL) methods aim to address this problem by labeling a small subset of the nodes as seeds and then utilizing the graph structure to predict label scores for the rest of the nodes in the graph. Recently, Graph Convolutional Networks (GCNs) have achieved impressive performance on the graph-based SSL task. In addition to label scores, it is also desirable to have confidence scores associated with them. Unfortunately, confidence estimation in the context of GCN has not been previously explored. We fill this important gap in this paper and propose ConfGCN, which estimates labels scores along with their confidences jointly in GCN-based setting. ConfGCN uses these estimated confidences to determine the influence of one node on another during neighborhood aggregation, thereby acquiring anisotropic capabilities. Through extensive analysis and experiments on standard benchmarks, we find that ConfGCN is able to outperform state-of-the-art baselines. We have made ConfGCN's source code available to encourage reproducible research.

Smart services are an important element of the smart cities and the Internet of Things (IoT) ecosystems where the intelligence behind the services is obtained and improved through the sensory data. Providing a large amount of training data is not always feasible; therefore, we need to consider alternative ways that incorporate unlabeled data as well. In recent years, Deep reinforcement learning (DRL) has gained great success in several application domains. It is an applicable method for IoT and smart city scenarios where auto-generated data can be partially labeled by users' feedback for training purposes. In this paper, we propose a semi-supervised deep reinforcement learning model that fits smart city applications as it consumes both labeled and unlabeled data to improve the performance and accuracy of the learning agent. The model utilizes Variational Autoencoders (VAE) as the inference engine for generalizing optimal policies. To the best of our knowledge, the proposed model is the first investigation that extends deep reinforcement learning to the semi-supervised paradigm. As a case study of smart city applications, we focus on smart buildings and apply the proposed model to the problem of indoor localization based on BLE signal strength. Indoor localization is the main component of smart city services since people spend significant time in indoor environments. Our model learns the best action policies that lead to a close estimation of the target locations with an improvement of 23% in terms of distance to the target and at least 67% more received rewards compared to the supervised DRL model.