kernel design
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Abstract We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type of representation as the previously proposed HDMR-GPR scheme while being faster and simpler to use. We tested the approach on cases where highly accurate machine learning is required from sparse data by fitting potential energy surfaces and kinetic energy densities.

Thanks to the popularity of GPU and the growth of its computational power, more and more deep learning tasks, such as face recognition, image retrieval and word embedding, can take advantage of extreme classification to improve accuracy. However, it remains a big challenge to train a deep model with millions of classes efficiently due to the huge memory and computation consumption in the last layer. By sampling a small set of classes to avoid the total classes calculation, sampling-based approaches have been proved to be an effective solution. But most of them suffer from the following two issues: i) the important classes are ignored or only partly sampled, such as the methods using random sampling scheme or retrieval techniques of low recall (e.g., locality-sensitive hashing), resulting in the degradation of accuracy; ii) inefficient implementation owing to incompatibility with GPU, like selective softmax. It uses hashing forest to help select classes, but the search process is implemented in CPU. To address the above issues, we propose a new sampling-based softmax called ANN Softmax in this paper. Specifically, we employ binary quantization with inverted file system to improve the recall of important classes. With the help of dedicated kernel design, it can be totally parallelized in mainstream training framework. Then, we find the size of important classes that are recalled by each training sample has a great impact on the final accuracy, so we introduce sample grouping optimization to well approximate the full classes training. Experimental evaluations on two tasks (Embedding Learning and Classification) and ten datasets (e.g., MegaFace, ImageNet, SKU datasets) demonstrate our proposed method maintains the same precision as Full Softmax for different loss objectives, including cross entropy loss, ArcFace, CosFace and D-Softmax loss, with only 1/10 sampled classes, which outperforms the state-of-the-art techniques. Moreover, we implement ANN Soft-max in a complete GPU pipeline that can accelerate the training more than 4.3X. Equipped our method with a 256 GPUs cluster, the time of training a classifier of 300 million classes on our SKU-300M dataset can be reduced to ten days.

We demonstrate that projecting data points into hyperplanes is good strategy for general-purpose kernel design. We used three different hyperplanes generation schemes, random, convex hull and α-shape, and evaluated the results on two synthetic and three well known image-based datasets. The results showed considerable improvement in the classification performance in almost all scenarios, corroborating the claim that such an approach can be used as a general-purpose kernel transformation. Also, we discuss some connection with Convolutional Neural Networks and how such an approach could be used to understand such networks better.

Graph kernels are of vital importance in the field of graph comparison and classification. However, how to compare and evaluate graph kernels and how to choose an optimal kernel for a practical classification problem remain open problems. In this paper, a comprehensive evaluation framework of graph kernels is proposed for unattributed graph classification. According to the kernel design methods, the whole graph kernel family can be categorized in five different dimensions, and then several representative graph kernels are chosen from these categories to perform the evaluation. With plenty of real-world and synthetic datasets, kernels are compared by many criteria such as classification accuracy, F1 score, runtime cost, scalability and applicability. Finally, quantitative conclusions are discussed based on the analyses of the extensive experimental results. The main contribution of this paper is that a comprehensive evaluation framework of graph kernels is proposed, which is significant for graph-classification applications and the future kernel research.