Low-shot Visual Recognition by Shrinking and Hallucinating Features

Low-shot visual learning---the ability to recognize novel object categories from very few examples---is a hallmark of human visual intelligence. Existing machine learning approaches fail to generalize in the same way. To make progress on this foundational problem, we present a low-shot learning benchmark on complex images that mimics challenges faced by recognition systems in the wild. We then propose a) representation regularization techniques, and b) techniques to hallucinate additional training examples for data-starved classes. Together, our methods improve the effectiveness of convolutional networks in low-shot learning, improving the one-shot accuracy on novel classes by 2.3x on the challenging ImageNet dataset.Comment: ICCV 2017 spotligh

Approximate Kernel PCA Using Random Features: Computational vs. Statistical Trade-off

Kernel methods are powerful learning methodologies that provide a simple way to construct nonlinear algorithms from linear ones. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation have been proposed to alleviate the problem. However, the statistical consistency of most of these approximate kernel methods is not well understood except for kernel ridge regression wherein it has been shown that the random feature approximation is not only computationally efficient but also statistically consistent with a minimax optimal rate of convergence. In this paper, we investigate the efficacy of random feature approximation in the context of kernel principal component analysis (KPCA) by studying the trade-off between computational and statistical behaviors of approximate KPCA. We show that the approximate KPCA is both computationally and statistically efficient compared to KPCA in terms of the error associated with reconstructing a kernel function based on its projection onto the corresponding eigenspaces. Depending on the eigenvalue decay behavior of the covariance operator, we show that only $n^{2/3}$ features (polynomial decay) or $\sqrt{n}$ features (exponential decay) are needed to match the statistical performance of KPCA. We also investigate their statistical behaviors in terms of the convergence of corresponding eigenspaces wherein we show that only $\sqrt{n}$ features are required to match the performance of KPCA and if fewer than $\sqrt{n}$ features are used, then approximate KPCA has a worse statistical behavior than that of KPCA.Comment: 46 page