Bounding the generalization error of learning algorithms has a long history, that yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the hypotheses, (ii) exploiting the dependence between the algorithm's input and output. Progress on the first point was made with the chaining method, originating from the work of Kolmogorov and used in the VC-dimension bound. More recently, progress on the second point was made with the mutual information method by Russo and Zou '15. Yet, these two methods are currently disjoint. In this paper, we introduce a technique to combine chaining and mutual information methods, to obtain a generalization bound that is both algorithm-dependent and that exploits the dependencies between the hypotheses. We provide an example in which our bound significantly outperforms both the chaining and the mutual information bounds. As a corollary, we tighten Dudley inequality under the knowledge that a learning algorithm chooses its output from a small subset of hypotheses with high probability; an assumption motivated by the performance of SGD discussed in Zhang et al. '17.
These days, we receive most information through digital mediums such as emails and social networking applications. Investigating the characteristics of human-paper interactions can help us design more meaningful interactions and better understand why people use paper documents in the age of digitalization. In this study, the interaction of people with physical documents was studied through a mixed-method of conducting a literature review, gathering expert opinions, interviewing subjects, and analysing Instagram photos. By codifying the gathered information, the human-paper interaction framework was developed. This framework articulates the advantages of physical documents compared to electronic documents and serves researchers and practitioners by providing insightful human factors about human-document interaction. Finally, we propose six design themes as the solutions to the findings of this study. These implications can provide practical foundations for future design and research.
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