Robustness and Generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work

Semi-Supervised Learning by Augmented Distribution Alignment

In this work, we propose a simple yet effective semi-supervised learning approach called Augmented Distribution Alignment. We reveal that an essential sampling bias exists in semi-supervised learning due to the limited number of labeled samples, which often leads to a considerable empirical distribution mismatch between labeled data and unlabeled data. To this end, we propose to align the empirical distributions of labeled and unlabeled data to alleviate the bias. On one hand, we adopt an adversarial training strategy to minimize the distribution distance between labeled and unlabeled data as inspired by domain adaptation works. On the other hand, to deal with the small sample size issue of labeled data, we also propose a simple interpolation strategy to generate pseudo training samples. Those two strategies can be easily implemented into existing deep neural networks. We demonstrate the effectiveness of our proposed approach on the benchmark SVHN and CIFAR10 datasets. Our code is available at \url{https://github.com/qinenergy/adanet}.Comment: To appear in ICCV 201

A Quasi-Wasserstein Loss for Learning Graph Neural Networks

When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To eliminate such inconsistency, in this study we propose a novel Quasi-Wasserstein (QW) loss with the help of the optimal transport defined on graphs, leading to new learning and prediction paradigms of GNNs. In particular, we design a "Quasi-Wasserstein" distance between the observed multi-dimensional node labels and their estimations, optimizing the label transport defined on graph edges. The estimations are parameterized by a GNN in which the optimal label transport may determine the graph edge weights optionally. By reformulating the strict constraint of the label transport to a Bregman divergence-based regularizer, we obtain the proposed Quasi-Wasserstein loss associated with two efficient solvers learning the GNN together with optimal label transport. When predicting node labels, our model combines the output of the GNN with the residual component provided by the optimal label transport, leading to a new transductive prediction paradigm. Experiments show that the proposed QW loss applies to various GNNs and helps to improve their performance in node-level classification and regression tasks