Liangliang Shi

Liangliang Shi, Zhaoqi Shen, Junchi Yan

Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which contracts to the real-world case involving undetermined targets. In this paper, we propose Doubly Bounded Optimal Transport (DB-OT), which assumes that the target distribution is restricted within two boundaries instead of a fixed one, thus giving more freedom for the transport to find solutions. Based on the entropic regularization of DB-OT, three scaling-based algorithms are devised for calculating the optimal solution. We also show that our DB-OT is helpful for barycenter-based clustering, which can avoid the excessive concentration of samples in a single cluster. Then we further develop DB-OT techniques for long-tailed classification which is an emerging and open problem. We first propose a connection between OT and classification, that is, in the classification task, training involves optimizing the Inverse OT to learn the representations, while testing involves optimizing the OT for predictions. With this OT perspective, we first apply DB-OT to improve the loss, and the Balanced Softmax is shown as a special case. Then we apply DB-OT for inference in the testing process. Even with vanilla Softmax trained features, our extensive experimental results show that our method can achieve good results with our improved inference scheme in the testing stage.

Yang Li, Liangliang Shi, Junchi Yan

Despite its success, generative adversarial networks (GANs) still suffer from mode collapse, i.e., the generator can only map latent variables to a partial set of modes in the target distribution. In this paper, we analyze and seek to regularize this issue with an independent and identically distributed (IID) sampling perspective and emphasize that holding the IID property referring to the target distribution for generation can naturally avoid mode collapse. This is based on the basic IID assumption for real data in machine learning. However, though the source samples {z} obey IID, the generations {G(z)} may not necessarily be IID sampling from the target distribution. Based on this observation, considering a necessary condition of IID generation that the inverse samples from target data should also be IID in the source distribution, we propose a new loss to encourage the closeness between inverse samples of real data and the Gaussian source in latent space to regularize the generation to be IID from the target distribution. Experiments on both synthetic and real-world data show the effectiveness of our model.