The seeded Watershed algorithm / minimax semi-supervised learning on a graph computes a minimum spanning forest which connects every pixel / unlabeled node to a seed / labeled node. We propose instead to consider all possible spanning forests and calculate, for every node, the probability of sampling a forest connecting a certain seed with that node. Leo Grady (2006) already noted its equivalence to the Random Walker / Harmonic energy minimization. We here give a simpler proof of this equivalence and establish the computational feasibility of the Probabilistic Watershed with Kirchhoff's matrix tree theorem. Furthermore, we show a new connection between the Random Walker probabilities and the triangle inequality of the effective resistance.

In this paper, we aim to understand the generalization properties of generative adversarial networks (GANs) from a new perspective of privacy protection. Theoretically, we prove that a differentially private learning algorithm used for training the GAN does not overfit to a certain degree, i.e., the generalization gap can be bounded. Moreover, some recent works, such as the Bayesian GAN, can be re-interpreted based on our theoretical insight from privacy protection. Quantitatively, to evaluate the information leakage of well-trained GAN models, we perform various membership attacks on these models. The results show that previous Lipschitz regularization techniques are effective in not only reducing the generalization gap but also alleviating the information leakage of the training dataset.

Graph-based algorithms are among the most successful paradigms for solving semi-supervised learning tasks. Recent work on graph convolutional networks and neural graph learning methods has successfully combined the expressiveness of neural networks with graph structures. We propose a technique that, when applied to these methods, achieves state-of-the-art results on semi-supervised learning datasets. Traditional graph-based algorithms, such as label propagation, were designed with the underlying assumption that the label of a node can be imputed from that of the neighboring nodes. However, real-world graphs are either noisy or have edges that do not correspond to label agreement.

Graph based semi-supervised learning is the problem of learning a labeling function for the graph nodes given a few example nodes, often called seeds, usually under the assumption that the graph's edges indicate similarity of labels. This is closely related to the local graph clustering or community detection problem of finding a cluster or community of nodes around a given seed. For this problem, we propose a novel generalization of random walk, diffusion, or smooth function methods in the literature to a convex p-norm cut function. The need for our p-norm methods is that, in our study of existing methods, we find those principled methods based on eigenvector, spectral, random walk, or linear system often have difficulty capturing the correct boundary of a target label or target cluster. In contrast, 1-norm or maxflow-mincut based methods capture the boundary, but cannot grow from small seed set; hybrid procedures that use both have many hard to set parameters.

Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data. Existing SSL typically requires all classes have labels. However, in many real-world applications, there may exist some classes that are difficult to label or newly occurred classes that cannot be labeled in time, resulting in there are unseen classes in unlabeled data. Unseen classes will be misclassified as seen classes, causing poor classification performance. The performance of seen classes is also harmed by the existence of unseen classes.

Graph-based semi-supervised learning is a very powerful tool in classification tasks, while in most existing literature the labelled nodes are assumed to be randomly sampled. When the labelling status depends on the unobserved node response, ignoring the missingness can lead to significant estimation bias and handicap the classifiers. This situation is called non-ignorable non-response. To solve the problem, we propose a Graph-based joint model with Non-ignorable Non-response (GNN), followed by a joint inverse weighting estimation procedure incorporated with sampling imputation approach. Our method is proved to outperform some state-of-art models in both regression and classification problems, by simulations and real analysis on the Cora dataset.

This paper addresses the problem of unsupervised discovery of object landmarks. We take a different path compared to that of existing works, based on 2 novel perspectives: (1) Self-training: starting from generic keypoints, we propose a self-training approach where the goal is to learn a detector that improves itself becoming more and more tuned to object landmarks. Compared to previous works, our approach can learn landmarks that are more flexible in terms of capturing large changes in viewpoint. We show the favourable properties of our method on a variety of difficult datasets including LS3D, BBCPose and Human3.6M.

Contrastive self-supervised learning has emerged as a promising approach to unsupervised visual representation learning. In general, these methods learn global (image-level) representations that are invariant to different views (i.e., compositions of data augmentation) of the same image. However, many visual understanding tasks require dense (pixel-level) representations. In this paper, we propose View-Agnostic Dense Representation (VADeR) for unsupervised learning of dense representations. VADeR learns pixelwise representations by forcing local features to remain constant over different viewing conditions.

Generative adversarial networks (GANs) were originally envisioned as unsupervised generative models that learn to follow a target distribution. In this paper, we approach the supervised GAN problem from a different perspective, one that is motivated by the philosophy of the famous Persian poet Rumi who said, "The art of knowing is knowing what to ignore." In the GAN framework, we not only provide the GAN positive data that it must learn to model, but also present it with so-called negative samples that it must learn to avoid -- we call this "The Rumi Framework." This formulation allows the discriminator to represent the underlying target distribution better by learning to penalize generated samples that are undesirable -- we show that this capability accelerates the learning process of the generator. We present a reformulation of the standard GAN (SGAN) and least-squares GAN (LSGAN) within the Rumi setting.

We demonstrate, theoretically and empirically, that adversarial robustness can significantly benefit from semisupervised learning. Theoretically, we revisit the simple Gaussian model of Schmidt et al. that shows a sample complexity gap between standard and robust classification. We prove that unlabeled data bridges this gap: a simple semisupervised learning procedure (self-training) achieves high robust accuracy using the same number of labels required for achieving high standard accuracy. Empirically, we augment CIFAR-10 with 500K unlabeled images sourced from 80 Million Tiny Images and use robust self-training to outperform state-of-the-art robust accuracies by over 5 points in (i) \ell_\infty robustness against several strong attacks via adversarial training and (ii) certified \ell_2 and \ell_\infty robustness via randomized smoothing. On SVHN, adding the dataset's own extra training set with the labels removed provides gains of 4 to 10 points, within 1 point of the gain from using the extra labels.