Yuan Yao

Liang Ding, Tianyang Hu, Jiahang Jiang et al.

Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various applications, there has been a lack of systematic study on the regularization ability of random smoothing. In this paper, we aim to bridge this gap by presenting a framework for random smoothing regularization that can adaptively and effectively learn a wide range of ground truth functions belonging to the classical Sobolev spaces. Specifically, we investigate two underlying function spaces: the Sobolev space of low intrinsic dimension, which includes the Sobolev space in $D$-dimensional Euclidean space or low-dimensional sub-manifolds as special cases, and the mixed smooth Sobolev space with a tensor structure. By using random smoothing regularization as novel convolution-based smoothing kernels, we can attain optimal convergence rates in these cases using a kernel gradient descent algorithm, either with early stopping or weight decay. It is noteworthy that our estimator can adapt to the structural assumptions of the underlying data and avoid the curse of dimensionality. This is achieved through various choices of injected noise distributions such as Gaussian, Laplace, or general polynomial noises, allowing for broad adaptation to the aforementioned structural assumptions of the underlying data. The convergence rate depends only on the effective dimension, which may be significantly smaller than the actual data dimension. We conduct numerical experiments on simulated data to validate our theoretical results.

Jinlin Liu, Yuan Yao, Jianqiang Ren

Synthesis of high resolution images using Generative Adversarial Networks (GANs) is challenging, which usually requires numbers of high-end graphic cards with large memory and long time of training. In this paper, we propose a two-stage framework to accelerate the training process of synthesizing high resolution images. High resolution images are first transformed to small codes via the trained encoder and decoder networks. The code in latent space is times smaller than the original high resolution images. Then, we train a code generation network to learn the distribution of the latent codes. In this way, the generator only learns to generate small latent codes instead of large images. Finally, we decode the generated latent codes to image space via the decoder networks so as to output the synthesized high resolution images. Experimental results show that the proposed method accelerates the training process significantly and increases the quality of the generated samples. The proposed acceleration framework makes it possible to generate high resolution images using less training time with limited hardware resource. After using the proposed acceleration method, it takes only 3 days to train a 1024 *1024 image generator on Celeba-HQ dataset using just one NVIDIA P100 graphic card.

Chao Gao, Yuan Yao, Weizhi Zhu

Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like robust estimators using similar techniques that optimize GANs. In this paper, we introduce a general learning via classification framework based on the notion of proper scoring rules. This framework allows us to understand both matrix depth function and various GANs through the lens of variational approximations of $f$-divergences induced by proper scoring rules. We then propose a new class of robust scatter estimators in this framework by carefully constructing discriminators with appropriate neural network structures. These estimators are proved to achieve the minimax rate of scatter estimation under Huber's contamination model. Our numerical results demonstrate its good performance under various settings against competitors in the literature.